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Zotero/001_artiklid/Road Safety Indicators/abdellapenalizedconwaymaxwellpoisson2019.md

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+---
+category: literaturenote
+citekey: abdellapenalizedconwaymaxwellpoisson2019
+title: "Penalized Conway-Maxwell-Poisson regression for modelling dispersed discrete data: The case study of motor vehicle crash frequency"
+authors: "Abdella, Galal M.; Kim, Jinho; Al-Khalifa, Khalifa N.; Hamouda, Abdel Magid"
+year: 2019
+date: 2019-00-00 2019
+doi: 10.1016/j.ssci.2019.06.036
+publication: Safety Science
+url: "https://doi.org/10.1016/j.ssci.2019.06.036"
+zotero_key: DEHVSRAU
+zotero_storage: 8IUMGZV6
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "Abdella, Galal M."
+status: converted
+---
+![](_page_0_Picture_1.jpeg)
+
+### Contents lists available at [ScienceDirect](http://www.sciencedirect.com/science/journal/09257535)
+
+## Safety Science
+
+journal homepage: [www.elsevier.com/locate/safety](https://www.elsevier.com/locate/safety)
+
+![](_page_0_Picture_5.jpeg)
+
+# Penalized Conway-Maxwell-Poisson regression for modelling dispersed discrete data: The case study of motor vehicle crash frequency
+
+![](_page_0_Picture_7.jpeg)
+
+Galal M. Abdella[a,](#page-0-0)[⁎](#page-0-1) , Jinho Kim[b](#page-0-2) , Khalifa N. Al-Khalifa[a](#page-0-0) , Abdel Magid Hamoud[aa](#page-0-0),[c](#page-0-3)
+
+- <span id="page-0-0"></span><sup>a</sup> *Department of Mechanical and Industrial Engineering, Qatar University, Doha, Qatar*
+- <span id="page-0-2"></span><sup>b</sup> *Rutgers Business School, Rutgers University, NJ, USA*
+- <span id="page-0-3"></span><sup>c</sup> *Qatar Transportation and Traffic Safety Center, Qatar University, Doha, Qatar*
+
+#### ARTICLE INFO
+
+#### *Keywords:* COM-Poisson regression Motor vehicle crash rate Poisson regression Generalized linear models
+
+ABSTRACT
+
+Statistical modelling of road crashes has been of extreme interest to researchers over the last decades. Such models are necessary for the investigation of the opportunities for road safety improvement. The motor vehicle crash frequency (MVC-F) is probably the most important count of road crashes. In practice, like many of other discrete variables, this count is often diagnosed with over- or underdispersion, i.e. the variance is greater or less than the mean. The traditional regression models, especially those based on the Poisson distribution, are inefficient in modelling dispersed count data. On the contrary, the Conway-Maxwell-Poisson (COM-Poisson) distribution has been proven powerful in modelling count data with a wide range of dispersion. In crash data modelling, many situations may give rise to collinearity between contributory crash factors. Under this situation, the maximum likelihood estimates of the coefficients of the COM-Poisson GLM become increasingly unreliable as the collinearity among the model predictors increases. This paper addresses this issue and proposes a penalized likelihood scheme to be used with the COM-Poisson GLM regression for improving its prediction performance. For better GLM regression output, we suggest implementing the penalized COM-Poisson GLM regression under a K- fold cross-validation framework. A real-world crash example is provided, showing the performance of the penalized COM-Poisson GLM regression compared to the Poisson and the classical COM-Poisson GLM regressions.
+
+### **1. Introduction**
+
+Statistical models for road crash data have become of extreme importance for all aspects of transport and traffic systems (TTS). These models, in particular, are helpful in establishing an evidence-based framework through which transportation authority can develop innovative road safety strategies and interventions. Over the past years, there has been a growing interest in literature on the development of statistical models for road safety studies ([Lord and Persaud, 2000; Lord](#page-6-0) [et al., 2005; Lord and Mannering, 2010; Kokonendji, 2014; Frank and](#page-6-0) [Samia, 2015; Paraskevi et al., 2015; Abdella et al., 2017; Abdur Rouf](#page-6-0) [et al., 2018](#page-6-0)).
+
+The Poisson distributions are the most popular for road safety management and analysis. The motor vehicle crash frequency (MVC-F) is probably the most common crash count variable ([Nazha et al., 2018](#page-6-1)). Since the MVC-F is usually characterized by over- and underdispersion, the use of the traditional Poisson-based models becomes inappropriate. The over-dispersion phenomenon usually occurs when the variance of the crash count exceeds the expected mean, i.e. *V Y E Y* ( ) ( ) > . On the contrary, the under-dispersion occurs when the variance is less than the expected mean, i.e. *V Y E Y* ( ) ( ) < . The over-dispersion in the MVC-F count usually occurs when the dataset on some road segments or timeintervals exhibits a large number of zero values ([Vangala et al., 2015](#page-6-2))*.* Several significant contributions have been conducted over the last years on the applications of the Conway-Maxwell-Poisson (COM-Poisson) in modeling over- and underdispersion count variables. [Guikema and Coffelt \(2008\)](#page-6-3) developed a COM-Poisson GLM formulation using two different links (dual-link) functions for modeling discrete counts. These two functions are = + <sup>=</sup> *ln µ*( ) *x <sup>i</sup> <sup>i</sup>* <sup>0</sup> *<sup>i</sup>* <sup>1</sup> and = + <sup>=</sup> *ln*( ) *z <sup>j</sup> q <sup>i</sup>* <sup>0</sup> *<sup>i</sup>* <sup>1</sup> , where *p* and *q* are the covariates used in the location and the shape link functions. [Lord et al. \(2008\)](#page-6-4) modified the dual-link formulation by replacing the second link function by the value of the shape parameter . The authors used log( ) <sup>1</sup> to link the response variable with the model predictors and then suggested using the
+
+*E-mail addresses:* [gmg5005@qu.edu.qa](mailto:gmg5005@qu.edu.qa) (G.M. Abdella), [jinho.kim@rutgers.edu](mailto:jinho.kim@rutgers.edu) (J. Kim), [Alkhalifa@qu.edu.qa](mailto:Alkhalifa@qu.edu.qa) (K.N. Al-Khalifa), [Hamouda@qu.edu.qa](mailto:Hamouda@qu.edu.qa) (A.M. Hamouda).
+
+<span id="page-0-1"></span><sup>⁎</sup> Corresponding author.
+
+Bayesian method for estimating the coefficients of the resulted model. The selection of the Bayesian estimation here is mainly attributed to its favourable mathematical and practical properties. The study has shown that the COM-Poisson GLMs perform the same as the NB models. One advantage of the COM-Poisson GLM over the NB model is that it can handle both the over- and underdispersed count data [\(Lord et al.,](#page-6-4) [2008\)](#page-6-4). This feature would, for sure, expands the domain of usage of the COM-Poisson-based models to include a wide range of industrial and service sectors. [Sellers and Shmueli, \(2010\)](#page-6-5) considered the log linear form of the Poisson regression by [McCullagh and Nelder, \(1997\)](#page-6-6) and proposed a COM-Poisson GLM formulation using a ( ( )) ( ) *E Y log* = as a link function. This function is often preferable over others for it would lead to a direct estimation of the coefficients of the GLM regressors. Both of the above studies are mainly based on the assumption of having a fixed value of the shape parameter, i.e. the shape parameter is independent of the covariates of the model. [Sellers and Andrew \(2016\)](#page-6-7) developed another format of the COM-Poisson, named as a zero-inflated COM–Poisson (ZICMP), having the capability of modelling both overand under-dispersion dataset. The ZICMP has revealed a performance relatively close to the zero-inflated negative binomial (ZINB) with respect to the Akaike Information Criterion (AIC).
+
+In the practice of road crash modeling, there are many situations may give rise to multicollinearity –or simply collinearity between contributory crash factors. In statistics, the collinearity refers to the existence of a significant linear relationship between the model factors. The collinearity has a severe impact on the reliability of the GLM estimates as well as the interpretation of the results. Despite the attractive prediction performance of the COM-Poisson-based regression models, we believe that there is still a need for developing COM-Poisson regression models that are capable of not only accommodating the dispersion issue but also being insensitive to the potential collinearity between road crash factors.
+
+This work develops a penalized likelihood formulation to be used in the COM-Poisson GLM regression to stabilizing the estimates of the regression parameters. We develop the penalized likelihood function by adding an *L*<sup>2</sup> norm to the squared norm of the GLM coefficients in the likelihood function by [Sellers and Shmueli \(2010\)](#page-6-5). Considering the effectiveness of the COM-Poisson distribution in modelling dispersed count data, our penalized COM-Poisson GLM regression would provide a practitioner with a powerful tool for simultaneously overcoming both the "dispersion" and "collinearity" problems. In order to achieve a better predictive performance of our model, we implement the penalized COM-Poisson GLM regression under a K *fold*-cross-validation framework.
+
+We organize the rest of this research paper as follows: [Section 2](#page-1-0) introduces the COM-Poisson distribution. [Section 3](#page-1-1) describes the penalized COM-Poisson GLM regression model. [Section 4](#page-2-0) describes the cross-validation approach. [Section 5](#page-3-0) illustrates the implementation of the penalized COM-Poisson GLM for modeling a real-world example. [Section 6](#page-5-0) presents a summary of the findings and outlines extensions for future research work.
+
+#### <span id="page-1-0"></span>**2. The COM-Poisson distribution**
+
+The COM-Poisson is usually considered as a general form of the Poisson distribution. [Conway and Maxwell, \(1962\)](#page-6-8) firstly develop the COM-Poisson for analyzing queuing systems. Later, its statistical properties are studied and reported by [Shmueli et al., \(2005\)](#page-6-9). The probability mass function (pmf) of the COM-Poisson distribution is as follows:
+
+$$Pr(Y_i = y_i \mid \gamma_i, \theta) = f(y_i; \gamma_i, \theta) = \frac{\gamma_i^{y_i}}{Q(\gamma_i, \theta)(y_i!)^{\theta}};$$
+  
+
+$$y_i = 0, 1, \dots : i = 1, 2, \dots n$$
+(1)
+
+where *yi <sup>n</sup>* is the *i* th discrete response value, *<sup>i</sup>* is the mean value of the observations ( >0) *<sup>i</sup>* , and is the shape parameter. When < 1 , the problem is called over-dispersion and under-dispersion when > 1 . The function *Q*( , ) *<sup>i</sup>* is defined as the normalization constant and found as follow [\(Shmueli et al., 2005; Sellers and Shmueli, 2010](#page-6-9))
+
+$$Q(\gamma, \theta) = \sum_{j=0}^{\infty} \frac{\gamma^{j}}{(j!)^{\theta}}$$
+(2)
+
+and,
+
+$$Pr(Y_i = y_i \mid Y_i, \ \theta) = \frac{Y_i^{y_i}}{\sum_{j=0}^{m} \frac{y_j^{j}}{(j)^{\beta}}(y_i!)^{\theta}}; \quad y_i = 0, \ 1, \ \cdots; i = 1, \ 2, \ \cdots n$$
+(3)
+
+The sum of COM-Poisson independent variables may reduce to three different probability distributions. These are (1) Poisson ( = 1) ( , *Q* ) = *e <sup>i</sup> <sup>i</sup>*, (2) Geometric ( *<sup>i</sup>*< = 1, 0) ( , *Q <sup>i</sup>* ) 1 (1 ) = *<sup>i</sup>* , and (3) Bernoulli ( [\(Shmueli et al., 2005; Sellers and Shmueli,](#page-6-9) [2010\)](#page-6-9). The moments of the COM-Poisson distribution are estimated as derivations of *Q*( , ) *<sup>i</sup>* ; these are:
+
+<span id="page-1-2"></span>
+$$E(Y_i) = \frac{\partial logQ(\gamma_i, \vartheta)}{\partial log\gamma_i} \approx \gamma_i^{\frac{1}{9}} - \frac{\vartheta - 1}{2\vartheta}; \tag{4}$$
+
+<span id="page-1-3"></span>
+$$V(Y_i) = \frac{\partial E(Y_i)}{\partial \log \gamma_i} = \frac{\partial \log^2 Q(\gamma_i, \, \theta)}{\partial \log^2 \gamma_i};$$
+ (5)
+
+The approximations in Eqs. [\(4\)](#page-1-2) and [\(5\)](#page-1-3) are accurate when 1 or > 10 *<sup>i</sup>* ([Minka et al., 2003\)](#page-6-10).
+
+## <span id="page-1-1"></span>**3. Methodology: the penalized COM-Poisson GLM**
+
+This section introduces the COM-Poisson GLM reported by [Sellers &](#page-6-5) [Shmueli, \(2010\)](#page-6-5) and shows the steps followed in this work to develop its penalized version. The GLM using ( ( )) ( ) *E Y log* = is denoted as follows:
+
+<span id="page-1-4"></span>
+$$logE(Y_i) = log(\gamma) = X_i \beta = \beta_0 + \beta_1 X_{i1} + \beta_2 X_{i2} + \dots + \beta_p X_{ip},$$
+ (6)
+
+where *Xij <sup>n</sup>* is the *i th* observation of the *j th*model predictor. The values are the coefficients of the model predictor in the GLM. There are two well-known techniques for estimating the coefficients of the GLM shown in Eq. [\(6\).](#page-1-4) These are the weighted least squares and the maximum likelihood. As the COM-Poisson is usually classified as one of the exponential family distributions, the maximum likelihood method is more preferable as a way to achieve an accurate estimation. The loglikelihood function for a set of *n* independent readings with constant is as follows ([Sellers and Shmueli, 2010\)](#page-6-5):
+
+$$\log \mathcal{L}(\gamma_{h} \vartheta | y_{1}, y_{2}, \dots, y_{n}) = \Lambda_{\gamma_{l}} = \sum_{i=1}^{n} y_{i} \mathbf{X}_{i} \boldsymbol{\beta} - \sum_{i=1}^{n} \vartheta log y_{i}! - \sum_{i=1}^{n} log Q(\mathbf{X}_{i} \boldsymbol{\beta}, \vartheta).$$
+
+$$\tag{7}$$
+
+The *L*<sup>2</sup> penalized regression shrinks the coefficient estimates of the COM-Poisson GLM towards zeros, but will never become exactly zeros. The purpose of this shrinkage is mainly to prevent overfitting arising due to the collinearity between the model predictors. The penalized scheme of the maximum likelihood is shown in Eq. [\(8\)](#page-1-5) and reformatted in Eq. [\(9\):](#page-1-6)
+
+<span id="page-1-5"></span>
+$$\lambda_{\lambda}^{Ridge} = \sum_{i=1}^{n} y_{i} \mathbf{X}_{i} \dot{\boldsymbol{\beta}} - \sum_{i=1}^{n} \theta \log y_{i}! - \sum_{i=1}^{n} \log Q(\mathbf{X}_{i} \dot{\boldsymbol{\beta}}, \theta) - \lambda \sum_{j=1}^{p} \beta_{j}^{2}.$$
+(8)
+
+<span id="page-1-6"></span>Or;
+
+$$\Lambda_{\lambda}^{Ridge} = \sum_{i=1}^{n} y_{i} X_{i} \beta - \sum_{i=1}^{n} \theta \log y_{i}! - \sum_{i=1}^{n} \log Q(X_{i} \beta, \theta) - \lambda ||\beta||_{2}^{2}.$$
+(9)
+
+Here, 0 is a pre-chosen penalization (shrinkage) parameter that can be chosen to achieve certain penalty strength and . <sup>2</sup> <sup>2</sup> is the squared Euclidean norm. Note that, larger means more shrinkage – and vice versa. The *L*<sup>2</sup> penalization performs particularly well when the
+
+true values of are small or even zero. Let ' and ' be the solution of the penalized log-maximum likelihood in Eq. [\(9\),](#page-1-6) then the following two properties are true:
+
+- Property 1: As <sup>0</sup>, ' , where is the solution of the COM-Poisson GLM model by [Sellers and Shmueli \(2010\).](#page-6-5)
+- Property 2: As , <sup>0</sup> '
+
+Our regression model and the classical COM-Poisson GLM regression by [Sellers & Shmueli \(2010\)](#page-6-5) are similar in that both use the same link function, but they are dissimilar in that they use different maximum likelihood formulations. The classical COM-Poisson GLM regression using a constant dispersion parameter is a special case of our regression model when no shrinkage on the coefficients of the GLM estimates is applied, i.e. =0. In the next section, we refer to our model as the penalized COM-Poisson GLM.
+
+## <span id="page-2-0"></span>**4. Penalized likelihood estimation based on the cross-validation**
+
+The *L*<sup>2</sup> penalization may cause some bias. The proper selection of the penalization parameter ( ) reduces the negative effect of large bias and results in a better mean squared error. [Hoerl and Kennard, \(1970\)](#page-6-11) firstly proposed this parameter when the ridge regression is introduced as a solution for the collinearity problem. Since then, several methods have been developed to find the most efficient estimate of this parameter ([Kibria, 2003; Khalaf and Shukur, 2005; Alkhamisi et al., 2006;](#page-6-12) [Alkhamisi and Shukur, 2008; Muniz and Kibria 2009\)](#page-6-12).
+
+The ridge trace plotted by [Hoerl and Kennard, \(1970\)](#page-6-11) is a graphical method to determine an appropriate value of . This method suggests visualizing the changes in the GLM coefficients over a wide range of values and to select the value of when the changes in these coefficients are insignificant. This method is a kind of trade-off between the variance and the bias of the coefficient estimates. To maintain a small bias, the minimum value of the corresponding range of would be an appropriate choice. This method is applied in this paper to specify the practical range of . Later, K values of are selected from this range, including extremes, and arbitrarily assigned to the K cross-validation cycles. The proposed approach for solving the penalized likelihood estimation under the cross-validation is described below:
+
+- **Step 1**: Split the original dataset into K equally sized sub-datasets.
+- **Step 2**: Define *w n* = K as the sub-dataset size, where *n* is the size of the original dataset.
+- **Step 3:** Let // the subset containing indices of K sub-datasets.
+- **Step 4**: Let *j* // the order index of a sub-dataset, where *j* = 1, 2, , K
+- **Step 5:** Let be a subset of size K containing all possible values of . That is, = { <sup>1</sup>, 2, , *<sup>K</sup>*}.
+- **Step 6**: For *j* = 1 to K
+  - (i) Name the *j* th sub-dataset in as a "training" sub-dataset and the (K 1) remaining sub-datasets as the "validating" sub-datasets.
+  - (ii) Solve Equation [\(9\)](#page-1-6) and find ' *<sup>j</sup>* and ' . Note that, is the tuning parameter applied when the *j th* sub-dataset is selected as the "training" sub-dataset.
+  - (iii) Calculate the Mean Absolute Error (MAE), which is one of the methods available in the literature to measure the prediction accuracy. The Mean Absolute Error for any sub-dataset in is calculated as follows:
+
+$$MAE_j = \frac{1}{w} \sum_{i=1}^{w} |y_i - \hat{y}_i| = \frac{1}{w} \sum_{i=1}^{w} |e_i|,$$
+ (10)
+
+where the fitted value *yi* can be calculated by applying Eq. [\(4\)](#page-1-2) after
+
+setting 
+$$\hat{y}_i = exp\left(x_i^T \hat{\beta}_{\lambda_j}\right)$$
+. The error,  $e_i = y_i - \hat{y}_i$ , is calculated as follows:  
+ $e_i = y_i - \hat{\beta}_0 - \hat{\beta}_1 X_{i1} - \hat{\beta}_2 X_{i2} - \cdots - \hat{\beta}_p X_{ip}$  (11)
+
+(iv) Compare the Median Absolute Deviation (MAD) for each cycle as follows:
+
+$$MAD_j = \text{median } |MAE_t - \text{median}(\mathbf{M}_j)|, t = 1, 2, \dots, (K - 1),$$
+(12)
+
+where **M***<sup>j</sup>* is a list of MAE values defined as
+
+$$\mathbf{M}_{j} = [\mathrm{MAE}_{1}, \, \mathrm{MAE}_{2}, \cdots, \mathrm{MAE}_{j}] \tag{13}$$
+
+- **Step 7**: End of the "For" loop
+- **Step 8**: Let **D** the matrix contains the MAD*<sup>j</sup>* values of all validation cycles.
+- **Step 9**: Find MADmin to specify the optimal penalization parameter as follows:
+
+$$MAD_{min} = argmin\{\mathbf{D}\} = arg \min_{j=1,...,K} \{MAD_j\}$$
+(14)
+
+- **Step 10**: Let *opt* be the value of used in the cross-validation cycle having the minimum MAD. This cycle is already defined in **Step 9**.
+- **Step 11**: By using *opt* , fit the penalized COM-Poisson GLM model to the whole dataset and find *opt* and *opt* .
+- **Step 12**: Let and *opt* be the optimal solution of the penalized maximum likelihood (PML) problem
+
+Eq. [\(9\)](#page-1-6) could be directly solved by using the constrained nonlinear optimization tool (nlminb) available in R software. In this paper, the R Software available at [https://cran.r-project.org/web/packages/](https://cran.r-project.org/web/packages/COMPoissonReg) [COMPoissonReg](https://cran.r-project.org/web/packages/COMPoissonReg) was modified to capture the structure of our penalized likelihood estimation. Further methods for solving such problem are available in [Sellers and Shmueli, \(2010\).](#page-6-5) Another way to find y*<sup>i</sup>* is by obtaining the inverse-CDF of y*<sup>i</sup>* and [\(Sellers and Shmueli, 2010\)](#page-6-5).
+
+In order to specify the optimal penalization parameters, we calculate the MAD for each cycle using the MAE values, which are used to measure the prediction accuracy, and select the parameters for the minimum value of MAD, that is, MADmin, as the optimal penalization parameters. This mechanism for the optimal parameters is described in the steps 6, 9 and 10.
+
+The penalized likelihood estimation is widely used to reduce overfitting in estimating the regression parameters, including linear, logistic, semi-parametric and proportional hazards regression [\(Verweij](#page-6-13) [and Van Houwelingen, 1994; Ciuperca et al., 2003; Rondeau et al.,](#page-6-13) [2003; Goeman, 2010; Göbl et al., 2015\)](#page-6-13). The overfitting problem may arise due to the collinearity among predictors or in the condition of the high dimensionality. [Goeman \(2010\)](#page-6-14) provided several GLMs in R software, named as "*penalized*" package, with *L*<sup>1</sup> – LASSO and/or *L*<sup>2</sup> – ridge penalty terms, using likelihood-cross validations. The regression models supported by the "*penalized*" package are the linear, logistic, Poisson regression, and the Cox Proportional Hazards model.
+
+In this paper, we are specifically interested in tackling the over- and under-dispersion issues arising during the crash count regression for
+
+<span id="page-2-1"></span>**Table 1** Summary statistics for the *K* sub-datasets.
+
+| Statistic | Sub-dataset |       |       |       |  |  |  |  |  |
+|-----------|-------------|-------|-------|-------|--|--|--|--|--|
+|           | 1           | 2     | 3     | 4     |  |  |  |  |  |
+| Min       | 0           | 0     | 0     | 0     |  |  |  |  |  |
+| Max       | 54          | 51    | 53    | 48    |  |  |  |  |  |
+| Mean      | 13.76       | 11.25 | 10.95 | 10.25 |  |  |  |  |  |
+| Median    | 11          | 7     | 7     | 8     |  |  |  |  |  |
+| AIC       | 1401        | 1335  | 1503  | 1332  |  |  |  |  |  |
+| R2        | 0.30        | 0.21  | 0.20  | 0.17  |  |  |  |  |  |
+
+<span id="page-3-1"></span>**Table 2** The VIF and Tolerance values of X1 and X2 for the 4-tested sub-datasets.
+
+|                      | Regressors   |              |              |              |              |              |              |              |  |  |  |  |
+|----------------------|--------------|--------------|--------------|--------------|--------------|--------------|--------------|--------------|--|--|--|--|
+|                      | X1           |              |              |              | X2           |              |              |              |  |  |  |  |
+|                      | Sample 1     | Sample 2     | Sample 3     | Sample 4     | Sample 1     | Sample 2     | Sample 3     | Sample 4     |  |  |  |  |
+| VIF<br>Tolerance (T) | 1.15<br>0.86 | 1.14<br>0.88 | 1.11<br>0.90 | 1.08<br>0.92 | 1.15<br>0.86 | 1.14<br>0.88 | 1.11<br>0.90 | 1.08<br>0.92 |  |  |  |  |
+
+<span id="page-3-2"></span>**Table 3** Comparison of estimated coefficients in the first cycle.
+
+| Parameter | Regression Model |                 |                           |  |  |  |  |  |  |  |
+|-----------|------------------|-----------------|---------------------------|--|--|--|--|--|--|--|
+|           | Poisson          | COM-Poisson GLM | Penalized COM-Poisson GLM |  |  |  |  |  |  |  |
+|           | –                | 0.39360         | 0.37940                   |  |  |  |  |  |  |  |
+| 0         | −9.9467          | −10.988         | −10.761                   |  |  |  |  |  |  |  |
+| 1         | 0.5515           | 0.5819          | 0.5561                    |  |  |  |  |  |  |  |
+| 2         | 0.7361           | 0.8051          | 0.8086                    |  |  |  |  |  |  |  |
+
+which we use the ridge COM-Poisson GLM. Note that the ridge Poisson GLM is a special case of our ridge COM-Poisson GLM when *Q*( , ) = *e <sup>i</sup> <sup>i</sup>*. Even under this special case of similarity, the estimated regression parameters resulted by using the ridge COM-Poisson GLM are expected to be different from [Goeman, \(2010\),](#page-6-14) because the outcomes of the cross-validation vary according to the run-up settings and the criteria of a decision.
+
+### <span id="page-3-0"></span>**5. An illustrative example: the MVC-F in Toronto, Ontario**
+
+In this section, we compare the prediction accuracy of the penalized COM-Poisson GLM with both the Poisson and the classical COM-Poisson GLM. For a fair comparison, this paper uses the overdispersed crash dataset collected in 1995 at 868 signalized intersections located in Toronto, Ontario. Several researchers have used this dataset [\(Lord,](#page-6-15) [2000; Miaou and Lord, 2003; Miranda-Moreno and Fu 2007; Lord et al.,](#page-6-15) [2008; Sellers and Shmueli, 2010](#page-6-15)). For a further detailed description of this dataset, see [Lord et al. \(2008\)](#page-6-4).
+
+There are 868 observations in the dataset which consist of the MVC-F, as a response variable ( Y ), and two log-transformed traffic flow, as predictors ( X1 and X2). In this example, the original dataset is divided into four sub-datasets for applying the systematic K -fold CV approach. Each of them contains 217 observations. According to this division, the parameters K and *w* are set at 4 and 217, respectively. [Table 1](#page-2-1) summarizes the statistics of the sub-datasets of one cycle solution.
+
+Many diagnostics have been proposed in the previous literature to assess the degree of collinearity[\(Abdella et al. 2019\)](#page-5-1). The Pearson correlation coefficient ( ) **R**<sup>2</sup> is the typical among them. The **R**<sup>2</sup> takes a value between −1 and +1, where a negative value indicates a negative correlation, 0 means no correlation between the two variables and a positive value means positive correlation. The **R**<sup>2</sup> in the Toronto crash dataset is 0.31. For each sub-dataset, the **R**<sup>2</sup> of the two traffic flow regressors is calculated and reported in [Table 1](#page-2-1). The collinearity, can also be indicated by using the Variance Inflation Factor (VIF) of regression coefficients, *<sup>i</sup>* . The VIF shows the degree of influence of the multicollinearity on the variance of regression estimates, which is defined as
+
+$$VIF_{i} = \frac{1}{(1 - r_{i}^{2})}; \qquad i = 1, 2, \dots, p,$$
+(15)
+
+where *p* is the number of model variables and *ri* <sup>2</sup> is the **R**<sup>2</sup> value when the regressor X*<sup>i</sup>* is regressed on the other factors. An equivalent indicator to the VIF is the Tolerance (T = VIF−1), which measures the amount of information whether the regressor X*<sup>i</sup>* can deliver under a particular level of collinearity. The Tolerance takes a maximum value of 1. If the regressor X*<sup>i</sup>* has no correlation (*ri* <sup>2</sup> = 0) with the other ( *p* 1 regressors, then the T is equal to 1. The VIF and T values of all subdatasets for the classical Poisson regression are calculated in [Table 2](#page-3-1).
+
+When VIF >10 , the model predictors are considered to be highly correlated with each other. The multicollinearity level in the Toronto crash dataset is relatively low; see [Table 2.](#page-3-1) The effective range of λ of the Toronto crash dataset is found to be from 0.1 to 0.4. Four values of , including extremes, are selected. These are = { <sup>1</sup>, 2 3 4 , , } = { 0.1, 0.2, 0.3, 0.4 }. [Table 3](#page-3-2) displays the results of fitting the penalized COM-Poisson GLM to the first sample of the crash data. Two more regression models are applied in this cycle and compared with the proposed model. These are the Poisson model and the classical COM-Poisson GLM by [Sellers and Shmueli, \(2010\)](#page-6-5).
+
+Note that, the dispersion parameters ( of both the penalized and classical COM-Poisson GLM regression models are assumed constant and unknown across observations. [Table 3](#page-3-2) indicates that the first "training" sub-dataset is characterized with over-dispersion ( = < 0. 3794 1) . This finding is used here to justify the usage of the COM-Poisson instead of the ordinary Poisson model. In order to create a scale consistency of the estimated coefficients of the three compared models, we follow [Sellers](#page-6-5) [and Shmueli, \(2010\)](#page-6-5) and report the estimated coefficients of the penalized and classical COM-Poisson models in terms of . The comparison in [Table 3](#page-3-2) is only to show the extent to which the compared models are close to each other. When developing prediction models, it is essential to test how well the data-set meets the assumptions of the model. To check the assumption that the residuals are uncorrelated with each other, we
+
+<span id="page-3-3"></span>![](_page_3_Figure_15.jpeg)
+
+![](_page_3_Figure_16.jpeg)
+
+![](_page_3_Figure_17.jpeg)
+
+**Fig. 1.** Plotting the deviance residuals produced by the fitted penalized COM-Poisson GLM at *j*=1 versus the observations order.
+
+<span id="page-4-0"></span>![](_page_4_Figure_0.jpeg)
+
+![](_page_4_Figure_1.jpeg)
+
+**Fig. 2.** The Histogram plot for the deviance residuals of the three "validating" sub-datasets of the first cycle.
+
+<span id="page-4-1"></span>![](_page_4_Figure_3.jpeg)
+
+**Fig. 3.** Plotting the Mean Absolute Error (MAE) under different levels of shrinkage in the coefficients of the penalized COM-Poisson GLM regression.
+
+<span id="page-4-2"></span>**Table 4** Calculating the MAD of the first cycle of validation.
+
+| Sample | MAE  | M )1<br>Median( | MAE<br>median(M )  1 | MAD1   |
+|--------|------|-----------------|----------------------|--------|
+| 2      | 3.96 | 3.96            | 0.0000               | 0.1887 |
+| 3      | 4.74 |                 | 0.7843               |        |
+| 4      | 3.77 |                 | 0.1887               |        |
+
+<span id="page-4-3"></span>**Table 5** Summary of the last three cycles of cross-validation.
+
+| Cycle,<br>j | j   |        | Penalized COM-Poisson GLM Coefficients | MADj   |        |        |
+|-------------|-----|--------|----------------------------------------|--------|--------|--------|
+|             |     |        | 0                                      | 1      | 2      |        |
+| 2           | 0.2 | 0.3590 | −12.502                                | 0.7269 | 0.7970 | 0.1866 |
+| 3           | 0.3 | 0.2614 | −11.902                                | 0.6501 | 0.8099 | 0.2136 |
+| 4           | 0.4 | 0.3825 | −10.313                                | 0.5886 | 0.7146 | 0.0289 |
+
+<span id="page-4-4"></span>**Table 6** Estimated GLM coefficients of the Toronto, Ontario crash dataset.
+
+| Parameter | Regression Model |                 |                           |  |  |  |  |
+|-----------|------------------|-----------------|---------------------------|--|--|--|--|
+|           | Poisson          | COM-Poisson GLM | Penalized COM-Poisson GLM |  |  |  |  |
+|           | –                | 0.34917         | 0.33714                   |  |  |  |  |
+| 0         | −10.234          | −11.702         | −11.507                   |  |  |  |  |
+| 1         | 0.6029           | 0.6558          | 0.6333                    |  |  |  |  |
+| 2         | 0.7037           | 0.7911          | 0.7945                    |  |  |  |  |
+| MSE       | 23.60            | 32.57           | 32.54                     |  |  |  |  |
+
+calculated the residual values of the three "validating" sub-datasets and plotted these values versus the order of the observations ([Fig. 1](#page-3-3)). The residual plots are supposed to show random patterns. Non-random patterns may violate the assumption that the residuals are independent of each other. Fortunately, here, the independence assumption of residuals
+
+<span id="page-4-5"></span>![](_page_4_Figure_12.jpeg)
+
+**Fig. 4.** The scatter plot of MSE of fitting the penalized COM-Poisson GLM, classical COM-Poisson GLM and Poisson models for the crash dataset of Toronto.
+
+is confirmed as the three "validating" sub-dataset reveal a random behaviour of residuals. Numerous techniques are available to test the normality assumption of residuals, i.e. *e N µ <sup>i</sup>* ( , )2 . The simplest one is the Histogram, which is also an efficient to present whether the residuals are skewed or whether the dataset includes outliers. [Fig. 2](#page-4-0) shows an approximately normal distribution of the residuals produced by the three "validating" sub-datasets. To build the **M**<sup>1</sup> matrix**,** the first cycle solution and 0.1 is used to compute the MAE of each "validating" sub-dataset. The **M**<sup>1</sup> matrix is found to equal [3.96 4.74 3.77] *<sup>T</sup>***.** In our cross-validation approach, a K -number of values are selected and arbitrarily assigned to the cycles of cross-validation. The best results of our approach should be reached when the value MAE from each "validating" sub-datasets at a cycle *j* is as low as possible which can be achieved over the range of . To investigate the convenience of choosing <sup>1</sup> = 0.1 for the first cycle, we plot the MAE values of the three "validating" sub-datasets versus several values of ; see [Fig. 3](#page-4-1).
+
+Graphically, for all "validating" sub-datasets, setting <sup>1</sup>=0.1 is the best choice among others. Note that, the importance of performing the "suitability check" step decreases as the slope of the practical range of decreases – and vice versa. The MAD1 value is calculated as shown in
+
+<span id="page-5-2"></span>**Table 7** Summary statistics for the *K* = {2,6,8} sub-datasets.
+
+| Statistic | K = 2 |      | K = 6 |      |      |      |      |      | K = 8 |      |      |      |     |      |      |      |
+|-----------|-------|------|-------|------|------|------|------|------|-------|------|------|------|-----|------|------|------|
+|           | 1     | 2    | 1     | 2    | 3    | 4    | 5    | 6    | 1     | 2    | 3    | 4    | 5   | 6    | 7    | 8    |
+| Min       | 0     | 0    | 0     | 1    | 0    | 0    | 0    | 0    | 0     | 1    | 0    | 0    | 0   | 0    | 0    | 0    |
+| Max       | 54    | 53   | 51    | 53   | 47   | 46   | 54   | 50   | 51    | 53   | 47   | 46   | 51  | 50   | 54   | 50   |
+| Mean      | 10.6  | 12.4 | 10.4  | 13.9 | 10.4 | 11.3 | 10.9 | 12.0 | 10.5  | 14.7 | 10.6 | 12.1 | 9.4 | 10.9 | 11.8 | 12.7 |
+| Median    | 8     | 18   | 7     | 10.5 | 8    | 7    | 9    | 10   | 7     | 11   | 8    | 8    | 7.5 | 9    | 10   | 9    |
+
+<span id="page-5-3"></span>**Table 8** The coefficients of estimation using K = {2,6,8}
+
+| Parameter |         | Penalized COM-Poisson GLM |         |  |  |  |  |  |
+|-----------|---------|---------------------------|---------|--|--|--|--|--|
+|           | K = 2   | K = 6                     | K = 8   |  |  |  |  |  |
+| 0         | −3.6828 | −4.737                    | −4.9727 |  |  |  |  |  |
+| 1         | 0.2034  | 0.3168                    | 0.3377  |  |  |  |  |  |
+| 2         | 0.2533  | 0.248                     | 0.2429  |  |  |  |  |  |
+| MSE       | 32.95   | 31.57                     | 29.49   |  |  |  |  |  |
+
+[Table 4.](#page-4-2) Having the MAD1 value is calculated, we repeat the above procedures with *j* = 2, 3 and 4. [Table 5](#page-4-3) summarizes the results of the last three cycles of the cross-validation approach.
+
+Comparing the MAD*<sup>j</sup>* values in [Table 5,](#page-4-3) the fourth cycle in which <sup>4</sup>=0.4 has the lower MAD. Hence, we set *opt* = 0.4 as the optimal shrinkage parameter and fit the penalized COM-Poisson GLM model to the whole crash dataset; see [Table 6](#page-4-4).
+
+The estimated GLM coefficients of both COM-Poisson GLM model are very close ([Table 6\)](#page-4-4). The results of fitting the classical COM-Poisson GLM are identical to those reported by [Sellers and Shmueli \(2010\)](#page-6-5). How well the fitted model predicts the response variable is necessary to assess the model adequacy. In this example, we use the mean squared error (MSE) as a measure of adequacy. Since the well-fitted model leads to the minimum MSE value, the penalized GLM COM-Poisson is the best to fit the Toronto crash dataset (MSE = 32.54) shown in [Table 6](#page-4-4). The last column in [Table 6](#page-4-4) represents the optimal solution of Eq. [\(9\).](#page-1-6) For further understanding of the performance of the penalized COM-Poisson GLM regression model, one can compare its performance with the Negative Binomial (NB) and the restricted generalized Poisson regression (RGPR) models available in [Sellers and Shmueli \(2010\).](#page-6-5)
+
+To draw inference about the sensitivity of the penalized COM-Poisson GLM to changes in , we proposed different levels of *λ* and computed the MSE at each level; see [Fig. 4.](#page-4-5) The MSE values of both the Poisson and the classical COM-Poisson GLM models were plotted for the purpose of comparison. Since the last two models are not penalizationbased models, their MSE values over the proposed range of *λ* are set fixed at their magnitudes reported in [Table 6.](#page-4-4) These are 32.60 and 32.57, respectively.
+
+[Fig. 4](#page-4-5) shows that the penalized COM-Poisson GLM provides the lowest MSE value when it is compared with other models. The one exception here is the case when *λ* = 1.2. In this case, the classical COM Poisson GLM outperforms our model. Moreover, as the range of *λ*, in this example, is set from 0.1 to 0.4, the penalized COM Poisson GLM would deliver the lowest MSE regardless of how the values are assigned to the cycles of the cross-validation.
+
+## <span id="page-5-0"></span>**6. Optimizing the K-parameter**
+
+The selection of K is critical to the quality of the cross-validation. In [Section 5](#page-3-0), we used K = 4. The results have shown the advantage of the penalized-COM Poisson over its counterparts the classical COM-Poisson and the Poisson regression. In this section, we conduct an analytical study to investigate the performance of the Penalized-COM-Poisson under several values of K.
+
+Three different values of K = {2,6,8} were suggested. [Table 7](#page-5-2) shows the descriptive analysis of the sub-dataset under each value of K. [Table 8](#page-5-3) reports the fitting results using the three values of K. The comparison between the MSE values of the three models shows a significant advantage of the third model using K = 8. The case of K = 2 has the worst MSE values comparing with all K values considered in this study. The three proposed models, similar to the case of K = 4, have a negative intercept.
+
+## **7. Conclusion**
+
+This paper integrates the penalized likelihood estimation, more specifically the ridge penalty function, with the COM-Poisson GLM regression to enhance its prediction accuracy under the condition of the collinearity. Using the penalized likelihood estimation makes the COM-Poisson GLM regression more rigorous to inflation in the standard errors of GLM estimates. The real-world example illustrated the excellent performance of the penalized COM-Poisson GLM regression in simultaneously accommodating both the dispersion and collinearity problems.
+
+To specify the value of the penalization parameter , we applied the the penalized likelihood estimation under the K-*fold* cross-validation. A limitation associated with this approach is the case of a small dataset in which the estimate of the penalization parameter *opt* is unreliable. To handle this situation, we recommend to select K = 1 or K n = . The second option ( K n = ) is known in literatures as leave-one-out (LOO) cross-validation.
+
+The preference of the penalized COM-Poisson GLM should significantly arise in high-dimensional count data regression in which the collinearity is more likely to occur. Comparing the COM-Poisson GLM with those in the "*penalized*" package, in modeling high-dimensional crash data, could be one of our future works. Under the high-dimensional road safety, collecting large-scale observations is an expensive task in terms of time and effort.
+
+According to [Sellers and Shmueli, \(2010\),](#page-6-5) the COM-Poisson has the flexibility to reduce to a logistics regression and to produce similar estimates. Motivated by the importance of the logistic regression in several real-world disciplines, this finding would also be interesting for future investigations.
+
+#### **Acknowledgment**
+
+Authors are grateful to Dominique Lord (Texas A&M University) and Srinivas Geedipally (Texas A&M Transportation Institute) for providing us the dataset of the real-example of Toronto, Ontario.
+
+#### **References**
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+- <span id="page-6-5"></span>[Sellers, K.F., Shmueli, G., 2010. A flexible regression model for count data. Ann. Appl.](http://refhub.elsevier.com/S0925-7535(18)31395-X/h0145) [Stat. 4, 943–961.](http://refhub.elsevier.com/S0925-7535(18)31395-X/h0145)
+- <span id="page-6-9"></span>[Shmueli, G., Minka, T.P., Kadane, J.B., Borle, S., Boatwright, P., 2005. A useful dis](http://refhub.elsevier.com/S0925-7535(18)31395-X/h0150)[tribution for fitting discrete data: revival of the Conway-Maxwell-Poisson distribu](http://refhub.elsevier.com/S0925-7535(18)31395-X/h0150)[tion. J. Roy. Stat. Soc.: Ser. C \(Appl. Stat.\) 54, 127–142](http://refhub.elsevier.com/S0925-7535(18)31395-X/h0150).
+- <span id="page-6-2"></span>[Vangala, P., Lord, D., Geedipally, S.R., 2015. Exploring the application of the Negative](http://refhub.elsevier.com/S0925-7535(18)31395-X/h0155) [Binomial – Generalized Exponential model for analyzing traffic crash data with ex](http://refhub.elsevier.com/S0925-7535(18)31395-X/h0155)[cess zeros. Anal. Meth. Accid. Res. 7, 29–36](http://refhub.elsevier.com/S0925-7535(18)31395-X/h0155).
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Zotero/001_artiklid/Road Safety Indicators/abuzwidahcrashriskanalysisdifferent2018.md

@@ -0,0 +1,373 @@
+---
+category: literaturenote
+citekey: abuzwidahcrashriskanalysisdifferent2018
+title: Crash risk analysis of different designs of toll plazas
+authors: "Abuzwidah, Muamer; Abdel-Aty, Mohamed"
+year: 2018
+date: 2018-00-00 2018
+doi: 10.1016/j.ssci.2018.02.024
+publication: Safety Science
+url: "https://doi.org/10.1016/j.ssci.2018.02.024"
+zotero_key: U6P6IF8Z
+zotero_storage: 39EXXHR4
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "Abuzwidah, Muamer"
+status: converted
+---
+![](_page_0_Picture_1.jpeg)
+
+#### Contents lists available at [ScienceDirect](http://www.sciencedirect.com/science/journal/09257535)
+
+## Safety Science
+
+journal homepage: [www.elsevier.com/locate/safety](https://www.elsevier.com/locate/safety)
+
+![](_page_0_Picture_5.jpeg)
+
+# Crash risk analysis of different designs of toll plazas
+
+Muamer Abuzwidah[a,](#page-0-0)[⁎](#page-0-1) , Mohamed Abdel-Aty[b](#page-0-2)
+
+- <span id="page-0-0"></span><sup>a</sup>Department of Civil and Environmental Engineering, University of Sharjah, Sharjah, United Arab Emirates
+- <span id="page-0-2"></span><sup>b</sup>Department of Civil, Environmental and Construction Engineering, University of Central Florida, Orlando, FL 32816-2450, United States
+
+![](_page_0_Picture_10.jpeg)
+
+ARTICLE INFO
+
+Keywords: Traditional toll plaza Hybrid toll plaza All-electronic toll collection And toll by plate Cashless toll Open road tolling Log linear
+
+#### ABSTRACT
+
+The Expressways (toll roads) offer a high level of service, and the Global Electronic Toll Collection market has exceeded the expectation. However, finding optimal designs for toll plazas is an issue with world-wide relevance, and this study makes a significant contribution towards this end. The main goal of this study is to examine for the first time the traffic safety impact of using different designs of the Hybrid Toll Plaza (HTP). In addition to that, this study helps understand the relationship between the crash frequency and several important crash-related factors and circumstances of these facilities. Crash data from a seven-year period was investigated, and a hundred mainline toll plazas in Florida were evaluated. The results of this study proved that there is a significant difference between the different designs of the HTP. And there is an indication that the majority of crashes occurred at diverge-and-merge areas before and after the plaza. Moreover, the results indicated significant relationships between the crash frequency and toll plaza types, annual average daily traffic, and driver-age. This study has also proved that the HTP and the All-Electronic Toll Collection (AETC) were associated with less number of crashes than the Traditional Toll Plazas by 44.7 and 72.6 percent, respectively. Also, one of the findings with interesting safety implications is the interaction between design type and percentage of prepaid transponder vs. manual payment users regarding crash rate. Overall, for those agencies who cannot adopt the AETC system, improving traffic safety at toll plazas should take a priority.
+
+#### 1. Introduction
+
+The use of toll roads has risen dramatically in many countries around the world; and The Global Electronic Toll Collection market is valued at 5.42 billion U.S Dollar in 2014 and it is expected to reach 10.57 to 15.62 billion by 2022 growing at a CAGR of 9.16 to 12.71percent, ([WISE GUY, 2017; MRR, 2017](#page-7-0)). In fact, the factors such as reduction in traffic congestion, low travel time, cashless travel facility and free flow of traffic are driving the Electronic Toll Collection (ETC) market growth ([AB Newswire, 2017](#page-7-1)).
+
+In the United States, there are many tolled road facilities; these facilities vary in type, size, ownership, and tolling systems deployed. Some of these facilities are private along with those owned and operated by various public agencies around the States ([Yang et al., 2014](#page-7-2)). And even though toll roads offer high mobility benefits, traditional toll facilities may pose high traffic safety risk. Moreover, only a limited number of studies have explored the factors that affect safety at toll plazas.
+
+The Transport Department of the Hong Kong SAR government conducted a trial traffic guidance scheme at the toll plaza of a busy road tunnel to improve traffic flow and traffic safety at this facility. A study by [Wong et al. \(2006\)](#page-7-3) conducted an observational before-and-after study to assess the effects of the scheme. The results indicate that the trial scheme provided good guidance to drivers. Traffic safety was improved, and the travel time of auto-toll traffic improved in certain periods. Another study by [Prasetijo et al. \(2016\)](#page-7-4) investigated the accidents at the toll plaza gates due to impacts of the vehicles with concrete crash barriers with results in damage and fatalities. The study conducted a simulation test for crash barrier Tensile Wire Fracture toughness system. The results show that the material for a new alternative crash barrier is likely to reduce the rate of death due to accident and damage with regards to road furniture and vehicles.
+
+[Valdés et al. \(2017\)](#page-7-5) evaluated the effectiveness of different electronic toll collection lane types, and how signage and queues affect safety and driver behavior and operations in toll plazas using driving simulator. The results showed that overhead signage configuration associated with the corresponding speed limits per lane was found to be significant in reducing the acceleration noise, thus reducing the potential for lane change related crash patterns. Also, female drivers tend to have a faster deceleration rate than male drivers in the toll booth approach zone. Moreover, no significant difference between genders on average running speed was found in basic tollway segment at the
+
+E-mail addresses: [mabuzwidah@sharjah.ac.ae](mailto:mabuzwidah@sharjah.ac.ae) (M. Abuzwidah), [m.aty@ucf.edu](mailto:m.aty@ucf.edu) (M. Abdel-Aty).
+
+<span id="page-0-1"></span><sup>⁎</sup> Corresponding author.
+
+beginning of the experiment.
+
+[Saad et al. \(2017\)](#page-7-6) explored some of the factors that affect driving behavior and safety at toll plaza. This study assessed driving behavior using a driving simulator. They found that drivers experiencing the open road tolling (ORT) have safer driving behavior than those who use the tollbooth. [Van Dijk et al. \(1999\)](#page-7-7) studied toll plaza in twofold: to configure the types of toll booths with multiple payment functionalities (cash, credit cards, and electronic payment); and to determine the number of toll booths for each type. The model was also used to validate the spacing, safety, and accessibility of the toll plaza. A hybrid approach of simulation and queueing theory were used in this study. The study showed that fewer toll booths were needed when different payment systems were separated, as a combination of different payment systems at one toll booth would substantially enlarge the variability of service times. This variability appeared to dominate the 'inefficiency' of separate toll booths which may seem counterintuitive. Consequently, the initial design had to be completely redesigned. Overall, none of these studies evaluate or simulate the impacts of using different designs of the toll plazas on traffic safety.
+
+The literature also showed that different toll collection systems have been adopted by different toll agencies around the world with no uniform standard ([Mohamed et al., 2000; Schau](#page-7-8)fler, 1997). The most common toll collection systems can be summarized as follows:
+
+Traditional Toll Plaza (TTP); this design requires vehicles to rapidly decelerate, navigate through different fare transaction options, and then accelerate and merge with traffic [\(Miami-Dade Expressway, 2017;](#page-7-9) [McDonald and Stammer, 2001; Abuzwidah and Abdel-Aty, 2015](#page-7-9)). These confusing maneuvers constitute safety challenges and form high risk locations on toll roads.
+
+Hybrid Toll Plaza (HTP); this system retrofits existing tollbooths with express open Electronic Toll Collection (ETC) lanes. This design is allowing more than 81 percent of the vehicles in Florida to travel at full speeds using electronic transponders or license plate recognition technology in an open road environment with fewer diverge and merge maneuvers before and after the toll plaza. The HTP design combines either express Open Road Tolling (ORT) lanes on the mainline and separate traditional toll collection to the side, or traditional toll collection on the mainline and separate ORT lanes to the side [\(FTE, 2017](#page-7-10)). However, the HTP is widely deployed by many toll authorities such as in Florida, Illinois, New Jersey, and many other states.
+
+All-Electronic Toll Gantry or All-Electronic Toll Collection (AETC); this system is completely barrier-free that replaces all tollbooths with regular express ETC lanes to change the toll plaza to be similar to regular segments. The AETC system allows driving straight through an open road without needing to change lanes, stop the vehicle, or even slow down to pay a toll. The payment will be done automatically, instantly and accurately by using the automatic toll collection transponder known as prepaid transponder [\(FTE, 2017\)](#page-7-10).
+
+Past studies and the current data have indicated that certain locations at the TTP and HTP are more likely to experience traffic crashes than the regular segments on the expressway. In April 2006 in Washington, D.C., investigators for the U.S. National Traffic Safety Board (NTSB) revealed that the most dangerous locations on the highways are toll plazas. In the same year, the NTSB reported that 49 percent of all crashes on expressways in Illinois occurred at toll plazas, and three times as many people died in them as in crashes on the rest of the same roadways. Also, 30 percent of all crashes on the Pennsylvania Turnpike happened at toll plazas and 38 percent of all collisions on New Jersey toll highways are toll plaza incidents [\(NTSB, 2017](#page-7-11)). An older study [\(Mohamed et al., 2000\)](#page-7-8) found that about 32 percent of the total crashes that occurred on the Orlando expressway system were located at the Traditional Toll Plazas.
+
+However, there are some obstacles to the use of the AETC systems in many countries around the world, and that because these systems require good arrangements between the tolling agencies and the department of motor vehicles, as well as the law enforcement and the regulations. These regulations and arrangements are needed to identify and bill drivers who do not have the prepaid transponder.
+
+Although the use of the HTP and AETC systems has demonstrated measured improvements in traffic operations and environmental issues, the question is: What if we cannot apply the AETC? What are the alternative solutions? The answer was either adopting the HTP design or improving the current situations of the TTPs and it was proved that some simple and quick treatments could improve safety at TTP ([Sze](#page-7-12) [et al., 2008](#page-7-12)).
+
+For example, [Wong et al. \(2006\)](#page-7-3) evaluated the effects of a traffic guidance scheme for auto-toll lanes on traffic safety at TTP and they found that the overall lane-changing rate decreased significantly by 23 percent and the pooled conflict count decreased sharply by 44 percent, also the crash count decreased sharply by 38 percent. A better option however is to apply the HTP design and that also has some safety issues and there is a lack of research that compares and evaluates the different designs of the HTP, especially nowadays many agencies are adopting the HTP design without a uniform design standard.
+
+Overall, to the best of our knowledge there were no studies evaluated the safety impacts of using different design of Hybrid Toll plazas ([Fig. 1\)](#page-2-0). Therefore, the main goals are the following:
+
+- 1. Cover the urgent need of assessing the traffic safety impacts of using different designs of the HTP. It is worth mention that many agencies want to adopt Design 2 ([Fig. 1\)](#page-2-0) and that because it just requires adding separate ORT lanes to the side without touching the existing main-line toll plazas.
+- 2. Investigate the relationship between crash frequency and the crash related variables such as geometric characteristics, toll plaza types, traffic volumes, and driver-age.
+
+#### 2. Methodology
+
+## 2.1. Safety Performance Functions (SPFs)
+
+Data from the reference group are used to estimate a safety performance function (SPF) that relates crash frequency of the sites to their traffic and geometrical characteristics. Generally, a safety performance function (SPF) is a crash prediction model, which relates the frequency of crashes to traffic (e.g., annual average daily traffic) and the roadway characteristics (e.g., number of lanes, width of lanes, width of shoulder, etc.). There are two main types of SPFs in the literature: (1) full SPFs and (2) simple SPFs. Full SPF is a mathematical relationship that relates both traffic parameters and geometric parameters as explanatory variables, whereas simple SPF includes annual average daily traffic (AADT) as the sole explanatory variable in predicting crash frequency on a roadway entity. It is worth mentioning that the calibrated Crash Modification Factors in the Highway Safety Manual are based only on the simple 'SPF' [\(Abdel-Aty et al., 2014](#page-7-13)). Therefore, a series of SPFs were developed in the first part of this study using Negative Binomial Regression Models.
+
+## 2.2. Negative binomial regression model
+
+Crash data have a gamma-distributed mean for a population of systems, allowing the variance of the crash data to be more than its mean [\(Shen, 2007\)](#page-7-14). Suppose that the count of crashes on a roadway section is Poisson distributed with a mean λ, which itself is a random variable and is gamma distributed, and then the distribution of frequency of crashes in a population of roadway sections follows a negative binomial probability distribution ([Hauer, 1997\)](#page-7-15). Count data is usually modeled using a Poisson distribution; the main characteristic of the Poisson distribution is that its mean is equal to its variance. Several studies found that a negative binomial distribution fits crash frequency data better [\(Brown et al., 2006](#page-7-16)) [\(Abdel-Aty and Radwan, 2000\)](#page-7-17). The Negative Binomial (NB) is similar to a Poisson distribution, though its
+
+<span id="page-2-0"></span>![](_page_2_Figure_1.jpeg)
+
+Fig. 1. Different designs of the Hybrid Toll Plazas (Source: (Google Earth)).
+
+variance is greater than its mean [\(Agresti, 2002\)](#page-7-18). The NB model can be used to estimate crashes at locations, such as toll plaza segments ([Chang, 2005\)](#page-7-19).
+
+Eq. (1) presents the NB probability distribution function.P (yi) ∼ Negbin (λi, k):
+
+$$\frac{\Gamma(1/k+y_i)}{y_i!\Gamma(1/k)} \left(\frac{k\lambda_i}{1+k\lambda_i}\right)^{y_i} \left(\frac{1}{1+k\lambda_i}\right)^{1/k}$$
+(1)
+
+Where,
+
+y = number of crashes on a certain location at a certain period, λ= Expected number of crashes on a certain location at a certain period
+
+k = over-dispersion parameter.
+
+The NB estimation equation is given as follows;
+
+$$Log\lambda_i = log(EV_i) + (\beta_0 + \beta X_i + \varepsilon_i).$$
+(2)
+
+where λ<sup>i</sup> is the estimated number of crashes at location i; β is a vector of explanatory variables, and EV<sup>i</sup> is the exposure variable which is included in models as an offset term to account for unequal exposure to crashes along toll plazas. Count models such as NB need a mechanism to deal with different exposure scenarios. For example the Annual Average Daily Traffic (AADT), or expected number of crashes, can be included as an exposure offset term in NB models ([Chen, 1997](#page-7-20)). By offsetting the exposure, the response variable becomes the log crash frequency at a certain location. ε<sup>i</sup> is the term adjusting for over dispersion. It is an error term due to a combination of variables omitted from the model and pure randomness. Maximum Likelihood Estimation (MLE) is used to estimate the coefficients of the explanatory variables and the over dispersion parameter. The goodness of fit of the NB model is measured by analyzing the over dispersion parameter.
+
+## 2.3. Log-Linear model
+
+Past studies and current data have indicated that certain locations at toll plazas are more likely to be more risky than regular segments on the expressway. However, to the best of our knowledge there were no studies that investigated the association between traffic crashes and toll plaza types, AADT or driving maneuver variables among various age groups.
+
+A log-linear model is a generalized linear model for Poisson-distributed data; it specifies how the size of a cell count depends on the levels of the categorical variables for that cell. The nature of this specification relates to the association and interaction structure among the variables [\(Christensen, 1990; Abdel-Aty et al., 1998\)](#page-7-21). The log-linear model describes the association and interaction patterns among a set of categorical variables [\(Knoke, and Burke, 1980\)](#page-7-22). The estimates of parameters resulting from the model can be converted to estimate the odds ratio between variables. The formulation of a log-linear model with three variables and two-way interactions is as follows:
+
+$$log m_{ijk} = \nu + \lambda_i^x + \lambda_j^y + \lambda_k^z + \lambda_{ij}^{xy} + \lambda_{jk}^{yz} + \lambda_{ik}^{xz}$$
+(3)
+
+Where:
+
+Log mijk = log the expected frequency of cell in which:
+
+x = i, y = j, z = k;
+
+υ overall effect = .
+
+λ = effect due to the i level of x; <sup>i</sup> x th
+
+λ = effect due to the j level of y; <sup>j</sup> y th
+
+λ = effect due to the k level of z; <sup>k</sup> z th
+
+λ = interaction of x at the i level and y at the j level; ij xy th th
+
+λ = interaction of x at the i level and z at the k level; ik xz th th
+
+λ = interaction of y at the j level and z at the k level. jk yz th th
+
+For instance, when the model contains the term λij xy, which is the effect due to the interaction of x being at level j, it also contains λi , the <sup>e</sup>ffect due to the ith level of x, and λj , the effect due to the jth level of y. A reason for including lower-order terms is that the statistical significance and practicable interpretation of a higher order term depends on how the variables are coded. Since this model contains an X–Y twofactor term, it permits association between X and Y, controlling for Z. It also permits an X–Z association, controlling for Y, and a Y–Z association, controlling for X [\(Abdel-Aty et al., 1998](#page-7-23)). By using Eq. (1) for two
+
+cells, the log odds logit can be determined. And it helps understand how the independent variables affect the response variables (especially the toll plaza types); the logit models are constructed according to the response variables as follows:
+
+$$\begin{split} \log(m_{ijk}/m_{i1k}) &= [\nu + \lambda_{i}^{x} + \lambda_{j}^{y} + \lambda_{k}^{z} + \lambda_{ij}^{xy} + \lambda_{jk}^{yz} + \lambda_{ik}^{xz}] \\ &- [\nu + \lambda_{i}^{x} + \lambda_{j}^{y} + \lambda_{k}^{z} + \lambda_{ij}^{xy} + \lambda_{jk}^{yz} + \lambda_{ik}^{xz}] \\ &= [[\lambda_{j}^{y} - \lambda_{i}^{x}] + [\lambda_{ij}^{yy} - \lambda_{ij}^{xy}] + [\lambda_{jk}^{yz} - \lambda_{ik}^{yz}]] \end{split} \tag{4}$$
+
+Thus, for instance, in Eq. (4), we are modeling the log of the odds that y = j instead of y = 1, when x = I and z = k.
+
+#### 3. Data description
+
+Different tolling systems are expanding on the Florida expressways. In the past decade, many toll agencies converted their Traditional Toll Plaza s to either Hybrid Toll plaza or all-electronic toll collection system.
+
+Multiple sets of data maintained by Florida Department of Transportation ([FDOT, 2017](#page-7-24)) were used in this study including: Crash Analysis Reporting (CAR) system, Roadway Characteristics Inventory (RCI) system, TranStat IView aerial mapping system, and Financial Project Search Database. Moreover, Google Earth and the publication reports of Florida Turnpike and Central Florida Expressway Authority ([CFX, 2017\)](#page-7-25) were used to verify the toll plazas' characteristics. A hundred mainline toll plazas located on approximately 750 miles of toll roads in Florida were selected. Crash data from seven-year period (2007–2013) were investigated. Crashes that occurred within the influence areas (1 mile before and 0.5 mile after the centerline of the mainline toll plaza ([MUTCD, 2017](#page-7-26))) were extracted from the crash database and data in the period when toll plazas were being upgraded in addition to six months after were excluded from the analysis.
+
+## 4. Analysis and results
+
+#### 4.1. Part I: Comparison between different designs of the Hybrid toll plaza
+
+Data from 60 Hybrid Toll Plazas (HTP) were used in this approach and crash data from a seven-year period was investigated. [Fig. 1](#page-2-0) shows different designs of the Hybrid Toll Plazas; Design 1 (D1) combines express Open Road Tolling (ORT) lanes on the mainline and separate traditional toll collection to the side; while Design 2 (D2) combines traditional toll collection on the mainline and separate ORT lanes to side.
+
+A series of Safety Performance Functions (SPFs) using Negative Binomial (NB) models were fitted to establish the relationships between traffic and roadway characteristics, and crash frequency at the vicinity of HTPs. Exploratory modeling indicated that the crash frequency is not significantly associated with traffic direction, number of entry and exit ramps, and distance to entry and exit ramps.
+
+[Table 1](#page-3-0) shows the parameter estimates of the final model. Only log Annual Average Daily Traffic (AADT) and the type of design came out to be significant with the expected signs. The coefficient of AADT has a
+
+<span id="page-3-0"></span>Table 1 Estimates of Coefficients for Different designs of the HTP.
+
+| Negative Binomial                                  |  |
+|----------------------------------------------------|--|
+| Analysis of Maximum Likelihood Parameter Estimates |  |
+
+| Crash type | Injury level | Parameter                                           | Estimates                          | Pr > ChiSq                     | AIC     |
+|------------|--------------|-----------------------------------------------------|------------------------------------|--------------------------------|---------|
+| All        | All          | Intercept<br>Log AADT<br>Design type*<br>Dispersion | −16.755<br>1.883<br>0.169<br>0.113 | < 0.0001<br>< 0.0001<br>0.0433 | 168.653 |
+
+Design type\* = (D1-and-D2) dummy variable (i.e. D1 = 0 and D2 = 1).
+
+positive sign, which indicates that as AADT increases, the frequency of HTP-related crashes increases.
+
+This finding could be attributed to the fact that the AADT is considered as the exposure factor; more traffic at the HTP would lead to higher chances of crash occurrence. This is expected, since higher AADT results in higher exposure of vehicles to weaving maneuvers (change lanes) before and after the toll plaza, which in turn would result in higher crash frequencies.
+
+The design type was found to be significant; the effect of design 2 (D2) of the HTP was compared to the design 1 (D1) (the base case). The parameter estimates given in [Table 1](#page-3-0) can be used to estimate the Incident Rate Ratios (IRR) by exponentiation of the regression coefficients Exp[β]. IRR value shows that the risk of crashes at D2 was approximately 19 percent higher than at the D1, given that all other variables are constant.
+
+The increased crash risk at the D2 may be explained by the fact that more than 81 percent of the vehicles in Florida are equipped with prepaid toll transponders [\(FTE, 2017](#page-7-10)). Thus, the use of D2 will cause more than 81 percent of the traffic to diverge and merge before and after the toll plaza and that could be a very confusing to the drivers; while in D1 only 19 percent or less of the traffic (vehicles without transponders) will need to diverge and merge before and after the toll plaza.
+
+The good news is that Florida Turnpike has scheduled all of the HTPs that have D2 to be converted to All-Electronic Toll Collection. However, D2 could be a good temporary design in the places that have low prepaid transponders users. In the other words, it is dependent upon the percentage of the automatic tolling users. So, as this percentage increases, more traffic will need to diverge and merge; thus, this design becomes riskier.
+
+## 4.2. Part II: Comparison between diverge-and-merge areas
+
+Similar to part I, data from 60 Hybrid Toll Plazas was used in this approach. Crash data from a seven-year period was investigated. [Table 2](#page-3-1) shows the parameter estimates of the final model resulting from 120 observations. Sixty Hybrid Toll Plazas, each one has two locations, one before (Diverge) and one after (Merge) the Toll plaza (60 ∗ 2 = 120 observations).
+
+It should be noted that the data used in this part included only the mainline crashes, i.e. crashes that occurred at the toll booths were excluded. [Fig. 2](#page-4-0) shows the diverge-and-merge areas that were investigated in this part of the analysis.
+
+The log Annual Average Daily Traffic (AADT) and the location came out to be significant with the expected signs in the final SPF model. The coefficient of AADT has a positive sign, which indicates that as AADT increases, the frequency of diverge-and-merge related crashes increases. This is expected, since higher AADT results in higher exposure of vehicles to weaving maneuvers (change lanes) before and after the toll plaza, which in turn would result in higher crash frequencies.
+
+The location (diverge-and-merge) dummy variable (i.e. diverge = 1 and merge = 0) was found to be significant. Since the lengths are
+
+<span id="page-3-1"></span>Table 2 Estimates of Coefficients of diverge and merge areas of the HTP.
+
+| Negative binomial<br>Analysis of maximum likelihood parameter estimates |              |                                                  |                                        |                                |         |
+|-------------------------------------------------------------------------|--------------|--------------------------------------------------|----------------------------------------|--------------------------------|---------|
+| Crash type                                                              | Injury level | Parameter                                        | Estimates                              | Pr > ChiSq                     | AIC     |
+| All                                                                     | All          | Intercept<br>Log AADT<br>Location*<br>Dispersion | −20.6811<br>2.2327<br>0.2103<br>2.2667 | < 0.0001<br>< 0.0001<br>0.0317 | 365.607 |
+
+Location\* = (diverge-and-merge) dummy variable (i.e. diverge = 1 and merge = 0).
+
+<span id="page-4-0"></span>![](_page_4_Picture_0.jpeg)
+
+![](_page_4_Figure_1.jpeg)
+
+Fig. 2. Diverge-and-merge areas before and after the HTP (). Source: [MUTCD, 2017](#page-7-26)
+
+different between the (diverge-and-merge) areas, the frequency of crashes were controlled by the segments' lengths. The effect of diverge was compared to the merge (the base case), and the coefficient of the location was positive indicating that diverge section is associated with more crashes than the merge section. The Incident Rate Ratios (IRR) value shows that the risk of crashes at diverge area before the HTP was approximately 23 percent higher than at the merge area after the plaza, given that all other variables are constant.
+
+The increased crash risk at diverge area may be explained by the fact that diverge section of the Hybrid Toll Plaza is associated with potential sudden lane change. Moreover, drivers may be distracted when they prepare to pay, search for cash or cards, and selecting either the cash or coin lane. While in the merge area, drivers just accelerate and focus on merging with traffic, especially if the acceleration lane has a good design and signage.
+
+However, choosing a good toll plaza location and finding ways to increase the percentage of prepaid transponder users are potential means of reducing lane changes at toll plazas. Adequate warning of no sudden lane change and good signage should be given on the approach to the diverge area. Offering toll discounts for prepaid transponder users and educating drivers can incentivize drivers to enroll in this system.
+
+#### 4.3. Part III: Log-Linear models
+
+Data including all types of toll plazas in Florida were used in this approach. A hundred mainline toll plazas, each one has two locations, one before and one after the toll plaza (100 ∗ 2 = 200 segments). Several Log-linear models with different variables in each model were developed, and only the significant variables and best fit model was presented. The effects of AADT and crash related factors were examined, and interactions among them were considered. Crash data from a seven-year period was used, and only crashes that occurred within the influence areas of the toll plazas were investigated. The final model was developed to investigate the association between toll plaza types and both driver-age and the AADT. The three main effects and all three possible two-way interactions were included in this model. [Fig. 3](#page-5-0) shows different types of mainline toll plazas.
+
+It should be noted that in order for the model to fit the data in a proper way, the variables should be categorized. Thus, toll plaza types categorized to three categories, driver-age categorized to two categories, and the AADT categorized to two categories. These categories were as follows:
+
+(1) " X = Toll Plaza Types: They were categorized into three levels and coded as follows:
+
+i = level:
+
+"1" = Hybrid Toll Plaza (HTP)
+
+"2" = All-Electronic Toll Collection (AETC)
+
+"0" = Traditional Toll Plaza (TTP) - (the base case).
+
+(2) Y = driver-age: It was categorized into two levels and coded as follows:
+
+j = level:
+
+"1" = Young (15–30 years old)
+
+"0" = Not young (Older than 30 years old) - (the base case).
+
+The 30 years old was selected as the cutoff point for age based on the literature ([FDOT, 2017](#page-7-24)) [\(Kim et al., 1995\)](#page-7-27), and criteria similar to those used by car insurance companies for when drivers start to drive more carefully due changes in life style and their life cycle ([FDOT,](#page-7-24) [2017\)](#page-7-24).
+
+(3) Z = Annual Average Daily Traffic (AADT): It was categorized into two levels based on the 50th percentile and coded as follows:
+
+k = level:
+
+"1" = Low
+
+"0" = High (the base case).
+
+<span id="page-5-0"></span>![](_page_5_Picture_1.jpeg)
+
+**Traditional Toll Plaza (TTP)** (Source: FTE, 2017)
+
+![](_page_5_Picture_3.jpeg)
+
+**Hybrid Toll Plaza (HTP)** (Source: CFX, 2017)
+
+![](_page_5_Picture_5.jpeg)
+
+**All-Electronic Toll Collection (AETC)** (Source: FTE, 2017)
+
+Fig. 3. Different types of the Mainline Toll Plazas.
+
+This is a three-variable model with variables x = (toll plaza types), y = (driver-age), and z = (AADT).
+
+Normally, the G2 goodness-of-fit statistic and p-value are used to determine the rejection or acceptance of the model. The larger value of G2, the more evidence there is against the null hypothesis (Ho), where Ho = model fits the relationship and Ha = model does not fit the relationship. Hence, the smaller G2 is better, but it depends on the degrees of freedom. The larger p-value (> 0.05) indicates that the estimated model fits the relationship. The model contains all three main effects and all three possible two-way interactions. [Table 3](#page-6-0) shows the parameter estimates and odds ratios.
+
+The results showed that the values of the G2 = 1.27, Pvalue = 0.5311, and the DF = 2 indicated that the model significantly fits the data. So, it can describe the associations between the variables by computing the odds ratios. With the logit model, the parameters provide a measure of the magnitude and direction of effects of the independent variables on the response variable ([Kim et al., 1995\)](#page-7-27). The parameter estimates for individual and interaction terms and their odds ratios are presented in [Table 3.](#page-6-0) Conceding the total number of crashes, the odds ratio is as follows:
+
+The odds ratio of Hybrid Toll Plaza (level 1) is 0.553 (Safety Effectiveness = 100–55.3 = 44.7 percent) from the base case Traditional Toll Plaza (level 0). Also, the odds ratio of the level 2 = allelectronic toll collection is 0.274 (Safety Effectiveness = 100–27.4 = 72.6 percent) from the base case Traditional Toll Plaza, given that all other variables are constant. These results proved that the HTP and the AETC are much safer than the Traditional Toll Plaza, and this is consistent with the previous finding even with different statistical models [\(Abuzwidah et al., 2014; Yang](#page-7-28) [et al., 2014; Abuzwidah, 2011; Zhang et al., 2009](#page-7-28)).
+
+The estimate of driver-age is negative, so it gives odds of less than one. The decrease of the crash risk of this age group for total crashes at all types of toll plazas may be explained by the fact that the proportion of the young drivers is less than the middle age and older (age > 30). This is same for the interaction of (AETC (level 2) ∗ young age).
+
+The odds of (HTP ∗ young age) is 3.2 percent higher than the base cases. This may be explained by the literature that very young and young drivers probably have less driving experience, and with low AADT they tend to speed and commit driving violations [\(Kim et al.,](#page-7-27) [1995\)](#page-7-27); especially with the risk of diverge-and-merge before and after the Hybrid Toll Plaza. This fact was clear for the total crashes at all types of toll plazas, the odds ratio of the interaction (young age ∗ Low AADT) is 9.5 percent more than the base case (older than 30∗ high AADT), so this might explain their involvement in crashes.
+
+<span id="page-6-0"></span>Table 3 The estimate of log-linear model.
+
+| Response          |    | TPT × Driver-age × AADT |            |  |  |
+|-------------------|----|-------------------------|------------|--|--|
+| Source            | DF | Chi-Square              | Pr > ChiSq |  |  |
+| TPT*              | 2  | 6.36                    | 0.0257     |  |  |
+| Driver-age        | 1  | 2.23                    | 0.1124     |  |  |
+| TPT × driver-age  | 2  | 4.69                    | 0.0581     |  |  |
+| AADT              | 1  | 1.22                    | 0.3153     |  |  |
+| TPT × AADT        | 2  | 0.33                    | 0.8368     |  |  |
+| Driver-age × AADT | 1  | 1.77                    | 0.1664     |  |  |
+| Likelihood Ratio  | 2  | 1.27                    | 0.5311     |  |  |
+
+| Parameter         |           | Estimate& (Odds ratio) | Standard Error | Chi-Square | Pr > ChiSq |
+|-------------------|-----------|------------------------|----------------|------------|------------|
+| TPT*              | 1         | −0.5922                | 0.1335         | 5.79       | 0.0192     |
+|                   |           | (0.553)                |                |            |            |
+|                   | 2         | −1.2935                | 0.2112         | 0.22       | 0.5442     |
+|                   |           | (0.274)                |                |            |            |
+| Driver-age        | Young     | −0.07543               | 0.1324         | 2.23       | 0.1245     |
+|                   |           | (0.927)                |                |            |            |
+| TPT × Driver-age  | 1 Young   | 0.0321                 | 0.1415         | 0.06       | 0.6523     |
+|                   |           | (1.032)                |                |            |            |
+|                   | 2 Young   | −0.3822                | 0.2505         | 4.12       | 0.0352     |
+|                   |           | (0.682)                |                |            |            |
+| AADT              | Low       | 0.0223                 | 0.1107         | 1.22       | 0.2532     |
+|                   |           | (1.022)                |                |            |            |
+| TPT × AADT        | 1 Low     | −0.5229                | 0.1532         | 0.00       | 0.8851     |
+|                   |           | (0.593)                |                |            |            |
+|                   | 2 Low     | −0.9795                | 0.1907         | 0.28       | 0.4211     |
+|                   |           | (0.375)                |                |            |            |
+| Driver-age × AADT | Young Low | 0.0915                 | 0.1292         | 1.77       | 0.1237     |
+|                   |           | (1.095)                |                |            |            |
+|                   |           |                        |                |            |            |
+
+TPT\* = Toll Plaza Types (i.e. TTP (0), HTP (1), and AETC (2)).
+
+The low AADT has odds 2.2 percent higher than the high AADT. This is because at low AADT, the speed is usually high. So, drivers are more likely to make a sideswipe, hit the tollbooths and/or lost control.
+
+## 5. Conclusions
+
+Expressways (toll roads) are considered as an important part of any successful transportation system, because they are carrying a significant number of the daily trips and offering a high level of service. however, traditional toll plazas still experience many crashes, many of which are severe and the literature showed a very limited studies that addressed toll plaza safety, and non of them were evaluated the safety impacts of using different design of Hybrid Toll Plazas (HTP). Therefore, this study examines for the first time the traffic safety impact of using different designs of HTP. And to the best of our knowledge, there is an urgent need for this evaluation since many agencies want to adopt Design 2 of the HTP ([Fig. 1\)](#page-2-0) because it just requires adding separate ORT lanes to the side without touching the existing main-line toll plazas. Also, this study helps understand the relationship between the crash frequency and several important crash-related factors and circumstances such as toll plaza types, traffic volume, and driver-age. Crash data from a sevenyear period was investigated, and a hundred mainline toll plazas were evaluated using multiple analytical techniques. The current data has indicated that certain designs and locations at toll plazas are more likely to experience traffic crashes than regular segments of the expressways.
+
+The Incident Rate Ratios (IRR) value shows that the risk of crashes at design 2 (D2) of the Hybrid Toll Plaza was approximately 19 percent higher than at the design 1 (D1), given that all other variables are constant. The increased crash risk at D2 may be explained by the fact that more than 81 percent of the vehicles in Florida are equipped with prepaid toll transponders. Thus, the use of D2 will cause more than 81 percent of the traffic to diverge and merge before and after the toll plaza. While in D1, only 19 percent or less of the traffic (vehicles without transponders) will need to diverge and merge before and after the toll plaza. However, D2 could be a good temporary design in the places that have low prepaid transponder users. In other words, it is dependent upon the percentage of the ETC users; as this percentage increases, more traffic will need to diverge and merge; thus, this design becomes riskier.
+
+Another finding is there is an indication that the majority of crashes occurred at diverge and merge areas before and after the HTP. The IRR value shows that the risk of crashes at diverge areas were approximately 23 percent higher than at the merge areas, given that all other variables are constant. The increased crash risk at diverge areas may be explained by the fact that diverge sections before the Hybrid Toll Plazas are associated with potential sudden lane change. Moreover, drivers may be distracted when they prepare to pay, search for cash or cards, and selecting either the cash or coin lane, while in the merge area they just accelerate and focus on merging with traffic, especially if the acceleration lane has a good design and signage.
+
+The results also indicated significant relationships between the crash frequency and toll plaza types, annual average daily traffic, and driver-age. This means all of these three variables significantly affect the frequency of toll plazas-related crashes. Moreover, it was found that the HTP and the All-Electronic Toll Collection (AETC) were associated with less number of crashes than at the Traditional Toll Plaza by 44.7 and 72.6 percent, respectively. Therefore, HTPs and AETCs are much safer than the Traditional Toll Plazas. For those agencies that cannot adopt the AETC systems, improving traffic safety at HTP and traditional toll plazas should take a priority.
+
+#### Acknowledgements
+
+The authors would like to thank SAFER-SIM for partially funding this research. SAFER-SIM is funded by a University Transportation Center lead by the University of Iowa.
+
+#### References
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Zotero/001_artiklid/Road Safety Indicators/aguerovalverdespatialanalysisfatalinjury2006.md

@@ -0,0 +1,363 @@
+---
+category: literaturenote
+citekey: aguerovalverdespatialanalysisfatalinjury2006
+title: Spatial analysis of fatal and injury crashes in Pennsylvania
+authors: "Aguero-Valverde, Jonathan; Jovanis, Paul P."
+year: 2006
+date: 2006-00-00 2006
+doi: 10.1016/j.aap.2005.12.006
+publication: "Accident Analysis & Prevention"
+url: "https://doi.org/10.1016/j.aap.2005.12.006"
+zotero_key: 2UJNIEQT
+zotero_storage: HXKQNNQZ
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "Aguero-Valverde, Jonathan"
+status: converted
+---
+![](_page_0_Picture_0.jpeg)
+
+Accident Analysis and Prevention 38 (2006) 618–625
+
+![](_page_0_Picture_2.jpeg)
+
+# Spatial analysis of fatal and injury crashes in Pennsylvania
+
+Jonathan Aguero-Valverde, Paul P. Jovanis ∗
+
+*Department of Civil and Environmental Engineering, Pennsylvania Transportation Institute, University Park, PA 16802-1408, USA* Received 15 July 2005; received in revised form 1 December 2005; accepted 12 December 2005
+
+## **Abstract**
+
+Using injury and fatal crash data for Pennsylvania for 1996–2000, full Bayes (FB) hierarchical models (with spatial and temporal effects and space–time interactions) are compared to traditional negative binomial (NB) estimates of annual county-level crash frequency. Covariates include socio-demographics, weather conditions, transportation infrastructure and amount of travel. FB hierarchical models are generally consistent with the NB estimates.
+
+Counties with a higher percentage of the population under poverty level, higher percentage of their population in age groups 0–14, 15–24, and over 64 and those with increased road mileage and road density have significantly increased crash risk. Total precipitation is significant and positive in the NB models, but not significant with FB. Spatial correlation, time trend, and space–time interactions are significant in the FB injury crash models.
+
+County-level FB models reveal the existence of spatial correlation in crash data and provide a mechanism to quantify, and reduce the effect of, this correlation. Addressing spatial correlation is likely to be even more important in road segment and intersection-level crash models, where spatial correlation is likely to be even more pronounced.
+
+© 2006 Elsevier Ltd. All rights reserved.
+
+*Keywords:* Full Bayes hierarchical model; Spatial correlation; Negative binomial model; Crash risk; Weather conditions and crash risk
+
+# **1. Introduction**
+
+Many factors affecting crashes operate at a spatial scale (e.g. land-use policy, demographic characteristics and highway infrastructure functional class). It is therefore reasonable to explore the use of spatial models of crash occurrence to better understand the implications of these policies.
+
+In most roadway accident studies, crashes are grouped in spatial units that range from intersection or road section level to zip code or county level (e.g. [Amoros et al., 2003; Miaou](#page-7-0) [et al., 2003; Noland and Oh, 2004; Noland and Quddus, 2004;](#page-7-0) [MacNab, 2004\).](#page-7-0) One concern with these studies is the effect of spatial correlation (i.e. the spatial dependence among observations), which produces higher variance of the estimates and therefore, underestimated standard errors.
+
+Recent developments in spatial modeling techniques have enabled researchers to investigate important issues related to risk estimation, unmeasured confounding variables, and spatial dependence [\(Richardson, 1992\).](#page-7-0) An important advantage of spatial models is that spatial effects may reflect unmeasured confounding variables. This is particularly useful for unmeasured confounders that vary in space like weather, population, and others. More important yet, "the methods also facilitate spatial smoothing and data pooling when regions under investigation involve small-population areas", [MacNab \(2004\). H](#page-7-0)ere the term 'small-population areas' refers to areas that present very few events, given a rare-event phenomenon, for example roadway crashes.
+
+Previous research has dealt with the spatial component of road crashes in different ways. Crashes have been modeled as point events (e.g. [Levine et al., 1995; Jones et al., 1996\),](#page-7-0) while others have modeled road crashes at different area levels, ranging from road sections to local census tracks or counties (e.g. [Shankar et al., 1995; Amoros et al., 2003; Miaou et al., 2003;](#page-7-0) [Noland and Oh, 2004; MacNab, 2004\).](#page-7-0)
+
+Honolulu census tract data have been used [\(Levine et al.,](#page-7-0) [1995b\) i](#page-7-0)n a continuous model for predicting crashes. Analysis at the "ward" (census track) level has been conducted [\(Noland and](#page-7-0) [Quddus, 2004\)](#page-7-0) for fatalities, serious injuries, and slight injuries using four different categories of predictor variables: land-use indicator variables (employment and population density), road characteristics, demographic characteristics (age cohorts), and
+
+<sup>∗</sup> Corresponding author. Tel. +1 814 865 9431. *E-mail address:* ppj2@engr.psu.edu (P.P. Jovanis).
+
+traffic flow proxies (proximate and total employment). Countrylevel data for Illinois ([Noland and Oh, 2004\)](#page-7-0) were used to estimate the expected number of crashes using infrastructure characteristics and demographic indicators as independent variables in a negative binomial (NB) model. Limitations of these studies are the use of proxy variables for traffic flow estimation and the lack of spatial correlation analysis. An additional paper ([Amoros et al., 2003\)](#page-7-0) developed NB models at county level in France that included interactions between road type and county.
+
+Poisson-based full Bayes (FB) hierarchical models of countylevel fatal (K), incapacitating (A), and non-incapacitating (B) injuries were estimated using both frequency and rate for the state of Texas ([Miaou et al., 2003\).](#page-7-0) Conditional auto-regressive model (CAR) was used to model spatial correlation and Markov Chain Monte Carlo (MCMC) was used to sample the posterior probability distribution. The main limitation of this paper is the use of the surrogate variables: percent of time that the road is wet, sharp horizontal curves, and roadside hazards. These predictor variables were estimated by proportions of crashes. For example, for percent of time that the road is wet, the variable was estimated by dividing the number of crashes that occurred under wet pavement by the total number of crashes. These estimators are clearly biased in the direction of the effect. Given the poor definition of contributing factors in the model, it is likely that the spatial correlation is overestimated. In a recent paper, [Miaou and Song \(2005\)](#page-7-0) used the same approach and data in the ranking of sites for engineering safety improvements.
+
+The adoption of the FB hierarchical approach by Miaou is an important advance in model estimation and is a departure point for this paper. The purpose of this research is to develop spatial models of road crash frequency for the State of Pennsylvania at the county level while controlling for socioeconomic, transportation-related, and environmental factors. The results from FB hierarchical spatial models are compared with the more traditional approach using an NB distribution to model crash frequency. Particular attention is paid to the inclusion of weather as a predictor and the search for spatial correlation among neighboring counties.
+
+#### **2. Methodology**
+
+# *2.1. The Poisson and negative binomial distributions*
+
+When data arise as counts, the Poisson distribution is typically used to model them. Traffic crashes are a clear example of count data, therefore, a Poisson distribution is a useful stating point (see for example [Jovanis and Chang, 1986; Shankar et al., 1995\).](#page-7-0) An important characteristic of the Poisson distribution is that its variance is equal to its mean. Several authors (e.g. [Shankar et](#page-7-0) [al., 1995; Noland and Quddus, 2004\)](#page-7-0) have argued that vehicle crashes are better represented by an NB distribution, which is a count distribution generated by a Poisson process with variance greater that the mean (see for example, [Hamed et al., 1998;](#page-7-0) [Hamed,1999\).](#page-7-0)
+
+Several goodness-of-fit measures have been proposed for this kind of model including the Poisson *R*2, R<sup>2</sup> <sup>P</sup>, and the Freeman–Tukey *R*2, R<sup>2</sup> PFT ([Fristrøm et al., 1995\).](#page-7-0) Another measure of goodness-of-fit uses the overdispersion parameter α of the NB model [\(Miaou, 1996\).](#page-7-0) NB models are estimated using R statistical Software [\(R Development Core Team, 2004\).](#page-7-0)
+
+## *2.2. Spatial modeling using full Bayes hierarchical approach*
+
+Many spatial modeling techniques may be developed within a Bayesian approach because of its flexibility in structuring complicated models, inferential goals, and analysis [\(Miaou et](#page-7-0) [al., 2003\).](#page-7-0) Bayesian inference has been used in the past in disease mapping and ecological analysis and just recently, it has been applied to crash modeling (e.g. [Miaou et al., 2003;](#page-7-0) [MacNab, 2004; Miaou and Song, 2005\).](#page-7-0) For a detail description of Bayesian inference, see [Gelman et al. \(2003\).](#page-7-0)
+
+The problem of group estimation, namely estimating the parameters of a common distribution thought to underlay a collection of outcomes for similar types of units, has motivated much research in Bayesian statistics. One seeks to make conditional estimates of the true outcome rate in each unit of observation (e.g. fatal crashes rate by county), given the parameters of the common density. Such estimation for sets of similar units is known as 'hierarchical modeling' because of its conditioning on higher stage densities ([Congdon, 2003\).](#page-7-0) At the first stage, the observed counts are modeled as a function of area-level summaries such as risk or relative risk. At the second stage, a joint distribution is specified for the collection of these risks as a function of explanatory variables. The second stage distribution depends on unknown parameters and these are assigned a (hyper) prior distribution at the third stage [\(Wakefield et al.,](#page-7-0) [2000\).](#page-7-0)
+
+In the case of this study, the model developed by [Besag et al.](#page-7-0) [\(1991\)](#page-7-0) is the base of the formulation used, as shown in Eqs. (1) and (2):
+
+$$y_i \sim \text{Poisson}(e_i \theta_i)$$
+ (1)
+
+where *yi* is the number of fatal crashes in county *i*, θ*<sup>i</sup>* the risk in county *i*, and *ei* the exposure in county *i*; in this case the exposure is the total daily vehicle-miles traveled (DVMT) by county. DVMT was also included as explanatory variable to account for possible non-linearity between crash frequency and DVMT. This is the first stage in the model. The log risk is modeled as:
+
+$$\log(\theta_i) = \alpha + x_i' \beta + v_i + u_i \tag{2}$$
+
+where *xi* represents a vector of explanatory variables, or covariates, *β* a vector of fixed effect parameters, vi the uncorrelated heterogeneity or unstructured error and *ui* the correlated heterogeneity or spatial correlation. The last two variables are known as random effects, therefore, this kind of model is commonly known as a mixture model where fixed and random effects are combined.
+
+In the third stage, a uniform prior distribution is assigned to α and a highly non-informative normal distribution is assigned to the *β*'s with mean 0 and variance 1000 corresponding to vague prior beliefs, given the scale of the covariates. On the other hand <span id="page-2-0"></span>the prior distribution for the uncorrelated heterogeneity (vi) is N(0, τ<sup>2</sup> <sup>v</sup> ), where τ<sup>2</sup> <sup>v</sup> is the precision (precision = 1/variance) with a prior gamma distribution Ga (0.5,0.0005) as suggested by [Wakefield et al. \(2000\).](#page-7-0) This prior distribution, as in case of the *β*'s, represents a highly non-informative distribution. The definition of the precision corresponds to the fourth stage of the model hierarchy.
+
+#### *2.3. Conditional auto-regressive model*
+
+A pair of areas are considered neighbors if they are adjacent; *ui* is the correlated heterogeneity or spatial correlation term reflecting a shared border. For the spatial correlation term, the CAR proposed by [Besag \(1974\)](#page-7-0) is used:
+
+$$[u_i|u_j, i \neq j, \tau_u^2] \sim N(\bar{u}_i, \tau_i^2)$$
+(3)
+
+where
+
+$$\bar{u}_i = \frac{1}{\sum_j w_{ij}} \sum_i u_j w_{ij} \tag{4}$$
+
+and
+
+$$\tau_i^2 = \frac{\tau_u^2}{\sum_j w_{ij}} \tag{5}$$
+
+*wij* = 1 if *i*, *j* are adjacent or 0 otherwise.
+
+As in the unstructured case, the τ<sup>2</sup> <sup>u</sup> controls the variability of *u* and its prior was selected Ga (0.5, 0.0005) as suggested by [Wakefield et al. \(2000\).](#page-7-0)
+
+#### *2.4. Space–time models*
+
+Several authors (e.g. [Miaou et al., 2003; Knorr-Held](#page-7-0) [and Besag, 1998; Waller et al., 1997; Knorr-Held, 2000;](#page-7-0) [Bernardinelli et al., 1995\)](#page-7-0) have studied the issue of changes in disease risk over time and space; however, only the work from Bernardinelli et al. presents a clear specification of the time–space interaction term. Extending the model of Bernardinelli to include the effect of covariates:
+
+$$y_{ij} \sim \text{Poisson}(e_{ij}\theta_{ij})$$
+ (6)
+
+$$\log(\theta_{ij}) = \alpha + \sum_{k} \beta_k x_{ijk} + v_i + u_i + (\varphi + \delta_i) t_j$$
+ (7)
+
+where *yij* is the observed number of crashes for the *i*th area, *i* = 1, ..., *N*, and the *j*th time interval, *j* = 1, ..., *T*, *α* the constant term, *xijk* the *k*th covariate for the *i*th area, in the *j*th time interval, *β<sup>k</sup>* the regression coefficient, vi the uncorrelated heterogeneity, *ui* the spatial correlation, *ϕ* the mean linear time trend over all areas, *tj* the time interval *j*, and *δ<sup>i</sup>* the interaction between time and area effect.
+
+This model specification allows for spatiotemporal interactions where temporal trend in crash risk may be different for different spatial locations and may even have spatial structure. However, all temporal trends, including the main temporal trend ϕ, are assumed to be linear, which may be seen as a restrictive assumption [\(Lawson et al., 2003\).](#page-7-0)
+
+For comparison of the different Bayesian hierarchical models the deviance information criterion (DIC), proposed by [Spiegelhalter et al. \(2002\)](#page-7-0) is used. It compares the fit and complexity of hierarchical models in which the number of parameters are not clearly defined. DIC is based on the posterior distribution of the deviance statistic and can be seen as a generalization of the Akaike information criterion (AIC).
+
+DIC is defined as an estimate of fit plus twice the effective number of parameters as in Eq. (8):
+
+$$DIC = \mathbf{D}(\bar{\boldsymbol{\theta}}) + 2\mathbf{p_D} = \bar{\mathbf{D}} + \mathbf{p_D}$$
+ (8)
+
+where *D*(¯ *θ*) is the deviance evaluated at ¯ *θ*, the posterior means of the parameters of interest, *p***<sup>D</sup>** the effective number of parameters in the model, and *D*¯ the posterior mean of the deviance statistic *D*(*θ*). As with AIC, models with lower DIC values are preferred.
+
+For each Bayesian hierarchical model two MCMC from different starting points were estimated in order to assure convergence. Depending on the complexity of the models, the first 3000–5000 iterations in each chain were removed as burn-ins. Finally, other 5000 iterations were performed for each chain resulting in a sample distribution of 10,000 for each parameter. Convergence of the models was monitored by visual examination of MCMC chains, autocorrelation plots, and Gelman–Rubin statistic plots. FB hierarchical models are estimated using Win-BUGS software ([Spiegelhalter et al., 2004\).](#page-7-0)
+
+## **3. Data description**
+
+Fatal and injury crash data are obtained from PennDOT ([Bureau of Highway Safety and Traffic Engineering,](#page-7-0) [1997–2001\).](#page-7-0) Two different sets of crash models were estimated: those using fatal crashes only as the dependent variable and those using just injury crashes. The spatial distribution of crashes has a very particular form. [Fig. 1](#page-3-0) shows the number of fatal crashes by county in year 2000 (similar distributions were obtained for other years). It is clear that the highest values are clustered around the cities of Philadelphia in the southeast portion of the state and Pittsburg in the southwest. The fatal crash rate map [\(Fig. 2\)](#page-3-0) presents a very different pattern as high crash rates occur mainly in counties with low to medium number of crashes. This may be due to the fact that fatal crashes are rare events, the counts are very low and therefore, a small increase of say, two or three crashes will significantly increase the rate especially for those counties with low levels of travel (i.e. DVMT).
+
+Risk factors, all measured at the county level and obtained for the years 1996–2000, are divided into three main categories: socioeconomic, transportation infrastructure-related, and environmental factors. [Table 1](#page-4-0) summarizes the definitions of each of the variables used to characterize the factors and contains descriptive statistics. Several different variable definitions were considered in exploring alternative model specifications.
+
+Socioeconomic factors include county-level summaries of age, sex, level of poverty (all from [US Census Bureau, 2004a,](#page-7-0) [2004b, 2004c\) a](#page-7-0)nd level of drunk driving [\(Pennsylvania Uniform](#page-7-0) [Crime Reporting System, 2004\).](#page-7-0) [Shinar \(1978\),](#page-7-0) [Evans \(1991,](#page-7-0)
+
+<span id="page-3-0"></span>![](_page_3_Figure_2.jpeg)
+
+Fig. 1. Number of fatal crashes by county for the year 2000.
+
+[2004\),](#page-7-0) and [Kam \(2003\)](#page-7-0) have suggested factors including age, sex, and personality to explain crash risk. Age is characterized as the percentage of persons younger than 15 (proxy for young pedestrians), between 15 and 24 (proxy for young drivers), and percent of persons over 65 (proxy for senior drivers) with the percentage of population between 25 and 65 used as a baseline. Note, these variables correspond to the total population rather than the population of drivers, but these are the only data publicly available. Area deprivation has been found to be positively related to crash occurrence (e.g. [Chichester et al., 1998; Abdalla](#page-7-0) [et al., 1997; Noland and Quddus, 2004\)](#page-7-0) and the percentage of persons under poverty is used as a surrogate of area deprivation in this paper. In the case of drunk driving, authors like [Evans](#page-7-0) [\(1991\)](#page-7-0) and [Gary et al. \(2003\)](#page-7-0) have found association between alcohol consumption and crash risk. The number of DUI arrests in a county is used to relate alcohol consumption to driving and crash frequency [\(Pennsylvania Uniform Crime Reporting](#page-7-0) [System, 2004\).](#page-7-0)
+
+Transportation-related factors included daily vehicle-miles traveled and amount of infrastructure [\(PennDOT, 2004\).](#page-7-0)
+
+![](_page_3_Figure_7.jpeg)
+
+Fig. 2. Fatal crash rate by county for the year 2000 (crashes by million DVMT).
+
+<span id="page-4-0"></span>Table 1 Summary statistics of variables included in the models.
+
+| Type                                                                                                 | Variables                                     | Minimum                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     | Median | Mean    | Maximum                                                                               | Standard deviation |
+|------------------------------------------------------------------------------------------------------|-----------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|--------|---------|---------------------------------------------------------------------------------------|--------------------|
+|                                                                                                      | Fatal crash frequency                         | 0                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           | 14     | 20.59   | 137                                                                                   | 19.94              |
+|                                                                                                      | Injury crash frequency                        | 33<br>600<br>1328.85<br>12370<br>35<br>615<br>1349.44<br>12489<br>0<br>5.5<br>5.84<br>136.64<br>254.75<br>270.83<br>142.06<br>261.45<br>276.67<br>14.87<br>19.69<br>19.51<br>9.36<br>12.2<br>13.04<br>9.86<br>15.97<br>16.2<br>46.46<br>48.74<br>48.95<br>4.4<br>10.8<br>10.66<br>18<br>314<br>581.29<br>4231<br>0.87<br>3.38<br>3.55<br>0.16<br>2.33<br>4.09<br>42.65<br>81.93<br>79.34<br>0.31<br>1.68<br>1.78<br>13.78<br>21.98<br>22.59<br>0.78<br>2.45<br>2.96<br>32.14<br>42.11<br>44.57<br>20.44<br>27.69<br>29.4<br>2.44<br>35.76<br>40.5<br>2.49<br>36.16<br>41.96 |        | 1951.17 |                                                                                       |                    |
+|                                                                                                      | Fatal and injury crash frequency              |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |        |         |                                                                                       | 1969.85            |
+|                                                                                                      | Fatal crash rate (by million DVMT)            |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |        |         | 16.51                                                                                 | 2.39               |
+|                                                                                                      | Injury crash rate (by million DVMT)           |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |        |         | 813.46                                                                                | 90.74              |
+|                                                                                                      | Fatal and injury crash rate (by million DVMT) |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |        |         | 821.28                                                                                | 90.84              |
+|                                                                                                      | Population under 15 years (%)                 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |        |         | 22.64                                                                                 | 1.62               |
+| Crashes<br>Socioeconomic<br>factors<br>Transportation-related factors<br>Environment-related factors | Population between 15 and 24 (%)              |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |        |         | 30.04                                                                                 | 2.87               |
+|                                                                                                      | Population 65 years and older (%)             |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |        |         | 21.97                                                                                 | 2.29               |
+|                                                                                                      | Males (%)                                     |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |        |         | 55.71                                                                                 | 1.3                |
+|                                                                                                      | Population under poverty (%)                  |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |        |         | 23.8                                                                                  | 3.11               |
+|                                                                                                      | DUI arrests frequency                         |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |        |         |                                                                                       | 750.89             |
+|                                                                                                      | DUI rate (by 1000 population)                 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |        |         | 12.7<br>25.63<br>89.12<br>5.67<br>36.66<br>16.83<br>68.19<br>43.32<br>127.09<br>114.4 | 1.48               |
+|                                                                                                      | DVMT (millions)                               |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |        |         |                                                                                       | 4.46               |
+|                                                                                                      | Federal aid DVMT (%)                          |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |        |         |                                                                                       | 8.37               |
+|                                                                                                      | Miles of road (Thousand)                      |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |        |         |                                                                                       | 0.95               |
+|                                                                                                      | Federal aid miles of road (%)                 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |        |         |                                                                                       | 4.18               |
+|                                                                                                      | Miles of road density (mi/mi2)                |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |        |         |                                                                                       | 2.28               |
+|                                                                                                      | Mean total precipitation (in)                 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |        |         |                                                                                       | 7.64               |
+|                                                                                                      | Mean number of rainy days                     |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |        |         |                                                                                       | 5.07               |
+|                                                                                                      | Mean total snowfall (in)                      |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |        |         |                                                                                       | 24.42              |
+|                                                                                                      | Mean number of days with snow                 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |        |         |                                                                                       | 26.15              |
+
+Vehicle-miles traveled is often used as indication of exposure to crash risk [\(Miaou et al., 2003; Fristrøm et al., 1995;](#page-7-0) [Jovanis and Chang, 1986\)](#page-7-0) along with the number of miles of different functional classes per county ([Noland and Quddus,](#page-7-0) [2004\).](#page-7-0) The number of miles of infrastructure in each county was included in the model to estimate the effect of different levels of transportation infrastructure supply in the expected crash rate. The functional categories were aggregated in two groups: federal aid (i.e. interstate, other freeways or expressways, other principal arterials, minor arterials and major collectors), and non-federal aid roads (i.e. minor collectors and local roads). Even though the amount of travel (DVMT) was included into the model as an offset term, the proportion of travel occurring on federal aid roads was included in the models as a separate variable to account for the possible differences in design and operation levels between federal aid and nonfederal aid roads where the former are expected to have higher levels.
+
+Environmental factors included descriptors for level of rain and snow ([National Climatic Data Center, 2004\).](#page-7-0) Environmental factors have been investigated in the past by [Jovanis and](#page-7-0) [Chang \(1986\),](#page-7-0) [Shankar et al. \(1995\),](#page-7-0) [Fristrøm et al. \(1995\), a](#page-7-0)nd [Edwards \(1996\), a](#page-7-0)mong others. The studies found positive correlation between weather and crash frequency. The amount of precipitation, snowfall, and number of rainy days and days with snow are analyzed in this study. Hundreds of weather stations are used to generate estimated surfaces for each variable and then the variables are summarized at county level for inclusion in the database. Spatial trend and correlation of weather variables with elevation are included into the models to improve their predictive power and fit. For more details on estimation of weather variables see [Aguero-Valverde \(2005\).](#page-7-0)
+
+#### **4. Results**
+
+A series of NB regression models is used in initial data analysis and to provide a comparison set for FB models to follow. In each model, all variables listed in Table 1 are the starting point; variables are removed if they have significance levels above 0.10. Table 2 presents the NB model of fatal crashes. For this model three transportation-related variables are significant: DVMT, infrastructure mileage, and percentage of travel on federal aid roads. The coefficient for DVMT is negative which implies that the fatal crash rate decrease with DVMT or, in
+
+Table 2 Negative binomial model of fatal crashes
+
+| Variable                         | Estimate | Standard error | z value | Pr(> z ) |
+|----------------------------------|----------|----------------|---------|----------|
+| DVMT                             | −0.033   | 0.005          | −6.46   | 1.08E−10 |
+| Infrastructure<br>mileage        | 0.060    | 0.026          | 2.26    | 0.024    |
+| DVMT on federal<br>aid roads (%) | −0.006   | 0.003          | −2.30   | 0.021    |
+| Persons under<br>poverty (%)     | 0.039    | 0.004          | 9.22    | 2.0E−16  |
+| Persons 0–14 (%)                 | 0.051    | 0.009          | 5.52    | 3.4E−08  |
+| Total precipitation              | 0.014    | 0.004          | 3.74    | 0.000    |
+| 1997                             | 0.290    | 0.083          | 3.49    | 0.000    |
+| 1998                             | 0.238    | 0.077          | 3.11    | 0.002    |
+| 1999                             | 0.236    | 0.070          | 3.38    | 0.001    |
+| 2000                             | 0.274    | 0.071          | 3.86    | 0.000    |
+| Dispersion<br>parameter α        | 0.021    | 0.006          | 3.67    | 0.000    |
+
+Residual deviance, 351.71 on 325 d.f.; AIC, 1980.6; 2 × log-likelihood, <sup>−</sup>1958.611; <sup>R</sup><sup>2</sup> <sup>P</sup>, 0.962; <sup>R</sup><sup>2</sup> FT, 0.967; and <sup>R</sup><sup>2</sup> K, 0.968.
+
+other words, the fatal crash frequency increases with DVMT at a decreasing rate. Total mileage is significant and positively correlated with fatal crash frequency while the percentage of travel in federal aid roads is negatively correlated. Higher design standards for federal aid roads may be responsible for this reduction on fatal crash risk.
+
+Several socioeconomic variables are significant in the model. The variable representing area deprivation, percent of population under poverty, as well as persons less than 15 years are highly significant and positive. These findings are consistent with the expectation of increases in crash risk with increases in area deprivation and number of young persons (under 15).
+
+Within the environmental variables the only one that is significant is total precipitation. Several facts may contribute to this: among them that total precipitation and rainy days as well as total snowfall and snowy days are highly correlated (0.93 and 0.88, respectively).
+
+Fixed time effects are also significant and positive, which means that the expected number of fatal crashes increased for years 1997–2000 compared to the base year of 1996. Overall goodness-of-fit for the model is excellent for all utilized fit statistics. The dispersion parameter is positive and highly significant indicating the presence of overdispersion, which is common with models estimating the expected number of crashes.
+
+For the NB injury crash models (Table 3) the original set of independent variables form the starting point. Fatal and injury models differ in the number of significant predictors, six for the fatal crash model and eight for the injury model without including the fixed time effects that are significant in both models.
+
+For the injury model, four transportation-related variables are significant: DVMT, infrastructure mileage, mileage density, and percentage of federal aid roads. As in the fatal crash model, DVMT is negative suggesting an increasing risk of injury crashes
+
+Table 3 Negative binomial model of injury crashes
+
+| Variable                            | Estimate | Standard error | z value | Pr(> z ) |
+|-------------------------------------|----------|----------------|---------|----------|
+| Intercept                           | 2.257    | 0.498          | 4.53    | 5.96E−06 |
+| DVMT                                | −0.031   | 0.007          | −4.36   | 1.29E−05 |
+| Infrastructure<br>mileage           | 0.147    | 0.024          | 6.14    | 8.08E−10 |
+| Mileage density                     | 0.089    | 0.008          | 11.66   | 2.00E−16 |
+| Mileage of federal<br>aid roads (%) | 0.016    | 0.003          | 5.38    | 7.35E−08 |
+| Persons 0–14 (%)                    | 0.060    | 0.013          | 4.61    | 4.02E−06 |
+| Persons 15–24 (%)                   | 0.024    | 0.007          | 3.55    | 0.000    |
+| Persons 65 and<br>over (%)          | 0.030    | 0.009          | 3.40    | 0.001    |
+| Total precipitation                 | 0.010    | 0.003          | 3.80    | 0.000    |
+| 1997                                | 0.204    | 0.060          | 3.41    | 0.001    |
+| 1998                                | 0.136    | 0.055          | 2.46    | 0.014    |
+| 1999                                | 0.107    | 0.053          | 2.00    | 0.046    |
+| 2000                                | 0.111    | 0.054          | 2.05    | 0.040    |
+| Dispersion<br>parameter α           | 0.030    | 0.003          | 11.93   | 0.000    |
+
+Residual deviance, 338.78 on 322 d.f.; AIC, 4191.1; 2 × log-likelihood, <sup>−</sup>4163.099; <sup>R</sup><sup>2</sup> <sup>P</sup>, 0.981; <sup>R</sup><sup>2</sup> FT, 0.983; and <sup>R</sup><sup>2</sup> <sup>K</sup>, 0.974.
+
+at a decreasing rate. The next two variables represent the amount of infrastructure in absolute and relative terms, respectively, and are both positively correlated with injury crashes, as expected. The third variable measures the percentage of roads under federal aid, and the positive coefficient indicates that increases in the variable value increase the injury crash risk. Federal aid roads in our study have generally higher speeds; non-federal aid roads have low operational speeds, which may generally reduce the probability of injury or fatality.
+
+In the case of socioeconomic variables, percentage of persons under 15 is significant and with the same sign as for fatal crashes. In addition, the surrogates for young drivers and pedestrians (persons between 15 and 24) and elderly drivers and pedestrians (persons 65 and over) are significant, while in the fatal crash model those variables are not found to be significant.
+
+The total precipitation effect is also positive in the injury model. The fixed time effects are positive and significant for injury crash models. Their coefficient values, however, decrease from 0.20 in 1997 to 0.11 in 2000.
+
+# *4.1. Full Bayes hierarchical models*
+
+Several FB fatal crash models are tested. The basic FB fatal crash model includes the variables found to be significant in the NB models as well as fixed time effects and uncorrelated heterogeneity. Fixed time effects are found not significant and as a result they are excluded from further models. When a model including unstructured heterogeneity and spatial correlation is estimated, the overdispersion of the model is due to unstructured heterogeneity, and therefore, fatal crashes do not indicate significant spatial correlation (for more see [Aguero-Valverde,](#page-7-0) [2005\).](#page-7-0)
+
+Finally, an FB model with uncorrelated heterogeneity and without fixed time effects is estimated (see Table 4). DVMT, poverty, and persons under 15 are significant and very similar to the coefficients from the NB model. This FB model presents the lowest value of DIC, which means that, among the models estimated in this work, this is the model that best fits the data. Given the fact that there is no evidence of spatial correlation or time dependence in the fatal crash model, no further models accounting for space–time interactions are estimated.
+
+Table 4 Full Bayes model of fatal crashes with uncorrelated heterogeneity (*vi*)
+
+| Variable                      | Estimate |        | Credible set 95% |         |
+|-------------------------------|----------|--------|------------------|---------|
+|                               | Mean     | S.D.   | 2.50%            | 97.50%  |
+| DVMT                          | −0.0397  | 0.0104 | −0.0600          | −0.0197 |
+| Infrastructure mileage        | 0.0466   | 0.0496 | −0.0504          | 0.1439  |
+| DVMT on federal aid roads (%) | 0.0030   | 0.0033 | −0.0034          | 0.0096  |
+| Persons under poverty (%)     | 0.0273   | 0.0076 | 0.0119           | 0.0420  |
+| Persons 0–14 (%)              | 0.0662   | 0.0128 | 0.0414           | 0.0913  |
+| Total precipitation           | −0.0006  | 0.0016 | −0.0037          | 0.0026  |
+| σ2<br>v                       | 0.0337   | 0.0091 | 0.0190           | 0.0545  |
+
+D¯ , 1842.0; D(¯ θ), 1794.0; DIC, 1890.0; and *p*D, 48.32.
+
+Table 5 Full Bayes model of injury crashes with spatial correlation (*ui*), time trend (ϕ), and space × time interactions (δ*i*)
+
+| Variable                            | Estimate |          | Credible set 95%   |          |  |
+|-------------------------------------|----------|----------|--------------------|----------|--|
+|                                     | Mean     | S.D.     | 2.50%              | 97.50%   |  |
+| Intercept                           | 3.110    | 0.764    | 1.593              | 4.582    |  |
+| DVMT                                | −0.092   | 0.013    | −0.118             | −0.067   |  |
+| Infrastructure mileage              | 0.323    | 0.051    | 0.227              | 0.425    |  |
+| Mileage density                     | 0.131    | 0.022    | 0.086              | 0.174    |  |
+| Mileage of federal aid<br>roads (%) | 0.026    | 0.007    | 0.013              | 0.040    |  |
+| Persons 0–14 (%)                    | 0.047    | 0.020    | 0.008              | 0.088    |  |
+| Persons 15–24 (%)                   | 0.015    | 0.012    | −0.008             | 0.039    |  |
+| Persons 65 and over (%)             | 0.013    | 0.016    | −0.018             | 0.044    |  |
+| Total precipitation                 | 5.86E−05 |          | 2.27E−04 −3.85E−04 | 5.01E−04 |  |
+| σ2<br>u                             | 0.176    | 0.038    | 0.115              | 0.263    |  |
+| ϕ                                   | −0.015   | 0.004    | −0.022             | −0.008   |  |
+| σ2<br>δ                             | 6.66E−04 | 2.15E−04 | 3.31E−04           | 0.001164 |  |
+
+D¯ , 3261.0; D(¯ θ), 3159.0; DIC, 3363.0; and *p*D, 102.1.
+
+An FB injury crash model including fixed time effects and uncorrelated heterogeneity or random error was tested next, then a model that replaces the unstructured error term in each country with a CAR error term, or spatial correlation. From these models it was evident that temporal and spatial effects were significant and therefore, the space–time model shown in Eq. [\(7\)](#page-2-0) is estimated (without including the unstructured error term). The model includes a spatially correlated term (*ui*), a time trend effect (ϕ), and an interaction term between time and area effect (δ*i*) as presented in Table 5.
+
+From the estimates of the coefficients in Table 5, there are several important points to highlight. First, all transportationrelated coefficients are significant and fairly close to the values in the NB model. In the case of age cohorts, persons-under-15 is significant, positive, and very similar to the NB estimate. The coefficients of the other two cohorts are not significant. As in the FB fatal model, the precipitation effect is non-statistically significant for the injury model.
+
+The time trend effect is significant and negative for the FB injury crash model. This means that controlling for all the other variables in the model, the number of injury crashes decreases over time. This is consistent with previous FB models for injury crashes (not presented here), but more important yet, if one examines the NB model for injury crashes, it is evident that the coefficients for the fixed time effects generally decrease with time after a positive 'jump' from 1996 (base year) to1997. Note that the coefficient estimate for the time trend may be biased if the underlying time trend for the population is not linear; however, with only 5 years of data this is very difficult to assess.
+
+The Poisson extra-variation due to spatial correlation (*ui*) is significantly greater than the variation due to the space–time interaction. The variance of *u* (σ<sup>2</sup> <sup>u</sup>) is equal to 0.176, while the variance of δ (σ<sup>2</sup> <sup>u</sup>) is equal to 0.00066. However, the fact that the variance of δ is different from zero indicates that the space–time interaction term is significant.
+
+## **5. Conclusions**
+
+There is no evidence of spatial correlation in fatal crashes; however, spatial correlation was found to be significant in injury crashes. The variance of the spatially correlated term (σ<sup>2</sup> <sup>u</sup>) is significant in the FB injury crash model, which implies that some Poisson extra-variation in the data can be explained by spatial correlation.
+
+Results concerning the effects of the covariates on fatal and injury crash risk are mostly consistent in the direction and magnitude for NB and FB models. In general, highly significant variables in the NB models are also significant in the FB models. On the other hand, variables just marginally significant in the NB models are generally non-significant in the FB models. Because the FB models address spatial correlation and take into consideration all sources of uncertainty, the authors believe the FB models more accurately associate covariates with crash risk and are better suited for this type of data.
+
+Fatal crash models have fewer significant variables compared to injury models. The main reason for this is the small number of events for fatal crashes, roughly a fatal crash for every thousand injury crashes. Given this difference of three orders of magnitude, it is expected that the random variation of the fatal crash data to be small compared to the variation explained by the covariates in the injury models. This may also be a sample size issue; with a larger sample size the noise or random variation is likely to be reduced and therefore, a higher portion of the variation can be explained by the covariates.
+
+## **6. Recommendations for future research**
+
+Crash models at the county level have several advantages over other types of crash models; one of the most important ones is the availability of transportation and socioeconomic data at county level. With the increase in quality and quantity of geographic information systems (GIS) data available in the Internet, public organizations may be able to incorporate additional land-use covariates in crash models, exploring land-use transportation interactions and their effects on crash risk.
+
+Now that data on poverty and other socioeconomic variables are available for the years 2001 and 2002 the database can be increased by 40%. This will have two important benefits: first, more data will improve the explanatory power of the models, especially in the fatal crash models; and secondly, two more years of data will help to estimate more precisely the time effect for both fatal and injury models.
+
+Given the existence of spatial correlation, at least for injury models, it is expected that spatial correlation plays a more important role at smaller spatial scales. FB models with spatial correlation may be even more useful at road section level where units are smaller and closer and therefore, the probability of spatial correlation is higher. Using FB models with spatial correlation is a natural next step in research work.
+
+Area deprivation (in the form of poverty percent in the case of this work) is consistently correlated with crash risk. More research on the causes of this correlation and on the causaleffect relationship between these phenomena is needed. The <span id="page-7-0"></span>relationship likely requires some level of spatial aggregation (e.g. county or census track), so analyses at the segment level are unlikely. This limitation implies that more studies at county or census track level are necessary in order to shed some light on the issue.
+
+From the methodological standpoint, FB hierarchical models are more effectively developed by starting with simple specifications, building to more complex models. The output from the simpler models can be used as initial values in the MCMC. Two or more MCMCs with different initial values for all the parameters are recommended in order to assure convergence to a consistent value. This method allows the modeling to verify output from each model and generally be in greater control of the FB model building process.
+
+# **References**
+
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+- Jones, A.P., Langford, I.H., Bentham, G., 1996. The application of K-function analysis to the geographical distribution of road traffic accident outcomes in Norfolk, England. Soc. Sci. Med. 42 (6), 879–885.
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+- Levine, N., Kim, K.E., Nitz, L.H., 1995b. Spatial Analysis of Honolulu motor vehicle crashes. II. Zonal generators. Accid. Anal. Prev. 27 (5), 675–685.
+- MacNab, Y.C., 2004. Bayesian spatial and ecological models for small-area accident and injury analysis. Accid. Anal. Prev. 36 (6), 1028–1091.
+- Miaou, S.P., 1996. Measuring the Goodness-of-Fit of Accident Prediction Models. FHWA-RD-96-040. Federal Highway Administration, Washington, DC.
+- Miaou, S., Song, J.J., Mallick, B.K., 2003. Roadway traffic crash mapping: a space–time modeling approach. J. Transportation Stat. 6 (1), 33–57. Miaou, S., Song, J., 2005. Accid. Anal. Prev. 37 (4), 699–720.
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+- Noland, R.B., Oh, L., 2004. The effect of infrastructure and demographic change on traffic-related fatalities and crashes: a case study of Illinois country-level data. Accid. Anal. Prev. 36, 525–532.
+- Noland, R.B., Quddus, M.A., 2004. A spatially disaggregate analysis of road casualties in England. Accid. Anal. Prev. 36 (6), 973–984.
+- Pennsylvania Department of Transportation, 2004. Highway Statistics. Web page: [http://www.dot.state.pa.us](http://www.dot.state.pa.us/)/, visited 7/13/2004.
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Zotero/001_artiklid/Road Safety Indicators/ayatiinvestigationroletrafficvolume2011.md

@@ -0,0 +1,311 @@
+---
+category: literaturenote
+citekey: ayatiinvestigationroletrafficvolume2011
+title: Investigation on the role of traffic volume in accidents on urban highways
+authors: "Ayati, Esmaeel; Abbasi, Ehsan"
+year: 2011
+date: 2011-00-00 2011
+doi: 10.1016/j.jsr.2011.03.006
+publication: Journal of Safety Research
+url: "https://doi.org/10.1016/j.jsr.2011.03.006"
+zotero_key: VEX26R2A
+zotero_storage: 9Z5XVDJV
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "Ayati, Esmaeel"
+status: converted
+---
+![](_page_0_Picture_1.jpeg)
+
+# Journal of Safety Research
+
+j o u r n a l h om e p a g e : www. e l s ev i e r. c om / l o c a t e / j s r
+
+![](_page_0_Picture_5.jpeg)
+
+# Investigation on the role of traffic volume in accidents on urban highways
+
+Esmaeel Ayati ⁎, Ehsan Abbasi <sup>1</sup>
+
+Department of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
+
+#### article info abstract
+
+Article history: Received 31 March 2010 Received in revised form 4 January 2011 Accepted 1 March 2011 Available online 27 May 2011
+
+Keywords: No injury accidents More severe accidents Urban highways Light non-passenger car vehicles Negative binomial (NB) regression model
+
+Introduction: Roadway safety is a major concern for the general public and public agencies, as roadway crashes claim many lives and cause substantial economic loss each year. In Iran, a large number of vehicles are involved in road accidents each year, which cause many deaths and extensive property damage; such accidents are among the major causes of death and disability in the country. Method: To reduce roadway accidents, the factors that affect the occurrence and severity of accidents should be scrutinized to prevent or reduce their effect. The method that many researchers have adopted to determine the effective parameters surrounding road accidents in recent years is through statistical modeling of accidents. In this article, the role of different kinds of vehicles in traffic flow are investigated separately in terms of the likelihood of crashes on urban highways, and the vehicles are divided into three groups: passenger cars, heavy vehicles, and light nonpassenger car vehicles. Poisson and negative binomial (NB) regression models were applied to model the accidents in this research, which were categorized into two groups: no injury (property damage only) accidents and more severe (injury and fatal) accidents. Results: Ultimately, we conclude that light nonpassenger car vehicles (i.e., taxis and motorcycles) play the largest role in the occurrence of crashes on urban highways for both types of accidents.
+
+© 2011 National Safety Council and Elsevier Ltd. All rights reserved.
+
+#### 1. Introduction
+
+Roadway safety is a major concern for the general public and public agencies. Indeed, roadway crashes claim many lives and cause substantial economic loss each year [\(Ma, Kockelman, & Damien,](#page-5-0) [2008\)](#page-5-0). In Iran, a large number of vehicles are involved in road accidents each year, causing significant death, disability, and property damage. Recent investigations in Iran indicate that 25% of casualties due to unnatural deaths are caused by traffic accidents ([Attaran,](#page-4-0) [1996\)](#page-4-0). Based on the results of research done on the cost of traffic accidents in Iran in 2001, 19,727 and 117,600 people have been killed and injured, respectively, in about 450,000 accidents [\(Legal Medicine](#page-4-0) [Organization of Iran, 2002\)](#page-4-0), which is estimated to have cost more than 3% of the gross national product ([Ayati, 2008](#page-4-0)). Developing sound or reliable statistical models for analyzing motor-vehicle crashes is important in highway safety studies. The models can be used for identifying hazardous sites, predicting motor-vehicle collisions, and developing accident modification factors ([Lord & Park, 2008\)](#page-4-0).
+
+In this paper, the role of vehicle type volume in traffic flow in the occurrence of accidents on urban highways is investigated through modeling no injury and more severe accidents by Poisson and NB regression models. The vehicle types are divided into three groups, including: passenger cars; heavy vehicles including truck trailers, trucks, buses, and minibuses; and light non-passenger car vehicles including taxis, pickups, and motorcycles. The purpose of the study was to scrutinize the role of each group of vehicles in the likelihood of accidents. The role of heavy vehicles in accident occurrence is often discussed, but it must be determined whether heavy vehicles result in more accidents or whether passenger cars or light non-passenger car vehicles, like taxis or motorcycles, play a key role in accident occurrence or frequency.
+
+# 2. Literature review
+
+Numerous studies have been conducted in recent years to investigate the frequency and severity of accidents on different parts of rural and urban freeways and highways, two-lane roads and arterials, or intersections using various methods of modeling accidents [\(Anastasopoulos & Mannering, 2009; Chang, 2005; Delen, Shadra, &](#page-4-0) [Bessonov, 2006; Lord & Park, 2008; Lord, Washington, & Ivan, 2007; Ma](#page-4-0) [et al., 2008; Milton, Shankar, & Mannering, 2008; Wang, Quddus, & Ison,](#page-4-0) [2009](#page-4-0)). Poisson and NB regression models have been used widely for predicting the occurrence of accidents on highways ([Lord, 2006; Lord &](#page-4-0) [Park, 2008; Savolainen & Tarko, 2005\)](#page-4-0). In addition, more advanced regression models such as zero-inflated negative binomials and Conway–Maxwell–Poisson generalized linear models are applied to modeling crashes [\(Lord, 2006; Lord et al., 2007; Lord & Park, 2008](#page-4-0)). In previous studies, the average daily traffic (ADT) or annual average daily traffic (AADT) were used as volume-related independent variables for
+
+<sup>⁎</sup> Corresponding author. Tel.: +98 0915 310 7483; fax: +98 0511 8676769. E-mail addresses: [esmaeel@ayati.co.uk](mailto:esmaeel@ayati.co.uk) (E. Ayati), [ehsan.abbasi395@gmail.com](mailto:ehsan.abbasi395@gmail.com)
+
+<sup>(</sup>E. Abbasi). <sup>1</sup> Tel.: +98 0915 314 7887.
+
+modeling ([Ma et al., 2008; Wang et al., 2009\)](#page-5-0) or, considering the number of lanes on each side, the average daily traffic per lane was applied ([Chang, 2005; Lee & Mannering, 2002; Milton et al., 2008](#page-4-0)). Researchers also applied variables such as the average daily percentage of trucks in the traffic stream or the average daily truck traffic (ADTT) ([Anastasopoulos & Mannering, 2009; Milton et al., 2008](#page-4-0)) to consider the responsibility of heavy vehicles in the frequency and severity of highway accidents.
+
+In their studies on the frequency and severity of highway accidents using a mixed logit model, [Milton et al. \(2008\)](#page-5-0) concluded that the average daily traffic per lane had an increasing role in the likelihood of no injury accidents on highways [\(Milton et al., 2008](#page-5-0)). [Chang \(2005\)](#page-4-0) concluded, in his investigation on the frequency of freeway accidents with a comparison between NB regression and artificial neural network models using variables such as ADT per lane, the percentage of trucks in the traffic flow and peak hour factor (PHF); [Chang \(2005\)](#page-4-0) concluded that, given the traffic volume in the peak hour, volume-related variables that led to conflicts between vehicles and increased exposure to potential risks of accidents correlated with an increasing number of vehicles and trucks.
+
+#### 3. Methodology
+
+In this research, the accidents on urban highways in Mashhad were modeled by Poisson and NB regression models, two models for no injury accidents and two for more severe accidents (injury or fatal). The specific contribution of this research is the separation of the total traffic volume into the passenger car volume, the heavy vehicle volume, including truck trailers, trucks, buses, and minibuses, and the light non-passenger car vehicle volume, including taxis, pickups, and motorcycles. The role of volume in the occurrence of accidents with property damage and injury or fatalities was investigated thoroughly to determine what kind of traffic has a significant role in accident occurrence. Thus, the independent variables of both no injury and more severe accident models are as follows:
+
+- 1. passenger car volume (Veh/hr)
+- 2. heavy vehicle volume (passenger car equivalent)
+- 3. light non-passenger car vehicle volume (passenger car equivalent)
+
+Accident data are usually two-level data; the first and main level is often road segments (i.e., the highway is divided into several parts or segments). The base of segmentation can differ, and this segmentation was based on total traffic volume in this study (i.e., the total traffic volume [passenger car equivalent] is constant for each part of the highway). The second level is the hours of the day, that is, the traffic peak hours are considered as the first sub-level, the day non-peak hours the second, and the night non-peak hours the third. The accident data for Mashhad urban highways were collected by the Transportation and Traffic Organization of Mashhad. After developing the models, the Poisson and NB models for no injury and more severe accidents were compared, and the better model was then validated to prove the efficiency of that model in modeling urban highway accidents.
+
+# 3.1. Poisson regression model
+
+In the Poisson regression model, the i-th observation of the dependent variable yi is modeled as a random Poisson variable with mean λi:
+
+$$P(y_i) = \frac{e^{-\lambda_i} \lambda_i^{y_i}}{y_i 1} \tag{1}$$
+
+The most important property of the Poisson regression model is the equality of the mean and variance of the distribution, which is the main shortcoming of this model and blocks the "overdispersion" of accident data. In the Poisson model, the conditional variance is equal to the conditional mean:
+
+$$V(y_i|\mathbf{x}_i) = E(y_i|\mathbf{x}_i) = \lambda_i = e^{\mathbf{X}_i'\beta}$$
+(2)
+
+The log-likelihood of the Poisson regression model is given by
+
+$$L = \sum_{i=1}^{n} \ln \frac{e^{-\lambda_i} \lambda_i^{y_i}}{y_i 1} = \sum_{i=1}^{n} \left[ -\lambda_i + y_i \ln \lambda_i - \ln y_i \right]$$
+ (3)
+
+To estimate the regression coefficients by the maximum likelihood method, the derivative of the log-likelihood relative to the vector of coefficients, β, is set equal to zero:
+
+$$\frac{\partial L}{\partial \beta} = \sum_{i=1}^{n} \left( y_i - e^{x_i \beta} \right) \mathbf{x}_i = 0 \tag{4}$$
+
+The estimation of the regression coefficients in the Poisson regression model is not obtained with a direct equation, but the Newton-Raphson iteration procedure is used for estimating the unknown parameters of the model. To perform the estimation process, the corresponding iteration algorithm is analyzed by SAS statistical software to obtain the calculated coefficients. The predicted value of ŷ<sup>i</sup> is the conditional mean or average number of accidents given xi, which is also denoted as λi, that is, the mean of the random variable yi, which follows a Poisson distribution. This value is typically not an integer number, whereas the observed value yi is a count ([Anselin,](#page-4-0) [2002\)](#page-4-0).
+
+#### 3.2. Negative binomial regression model
+
+In the negative binomial (NB) model yi, the i-th observation of the dependent variable has the following probability distribution function:
+
+$$p(y_i) = \frac{\Gamma(y_i + r)}{y_i!\Gamma(r)} \left[ \frac{\mu_i}{\mu_i + r} \right]^{y_i} \left[ \frac{r}{\mu_i + r} \right]^r$$
+ (5)
+
+The conditional mean of yi, for the vector of observed independent variables, xi, is given by
+
+$$E(y_i|\mathbf{x}_i) = \mu_i = e^{\mathbf{x}_i^i \beta} \tag{6}$$
+
+The NB distribution does not have the disadvantage of the Poisson distribution because there is no equality of the mean and variance of the distribution. The relationship between the mean and variance of an NB distribution is
+
+$$V(Y) = \mu + \frac{1}{r}\mu^2 \tag{7}$$
+
+The variance of the NB distribution is always greater than the mean. Thus, it fits the data with a variance greater than the mean. α= 1/r is the dispersion parameter. For accident data with low dispersion, the Poisson distribution gives plausible results, but, if overdispersion exists in the data, the variance of data will be greater than the mean. In such cases, the NB distribution is preferred. In the NB regression model, the dispersion parameter should be estimated in addition to regression parameters. r must be positive, so r\*=lnr is estimated instead, which can take on any value. The log-likelihood function of the NB model for the i-th observation is obtained from the following equation:
+
+$$L_{i} = \sum_{i=0}^{y_{i}-1} \ln(e^{r*} + j) = \ln y_{i}! + e^{r*} \ln(e^{r*}) + y_{i} \ln(\mu_{i}) - (e^{r*} + y_{i}) \ln(\mu_{i} + e^{r*})$$
+
+ð8Þ
+
+<span id="page-2-0"></span>To estimate β and r\*, as in the Poisson model, the iteration procedure of Newton-Raphson is applied ([Agresti, 2002\)](#page-4-0). The related iteration algorithm is written in SAS to obtain the unknown parameters. In the NB regression model, the predicted value of ŷ<sup>i</sup> is the conditional mean or average number of accidents given xi. This is also denoted as μi, that is, the mean of the random variable yi, which follows the NB distribution.
+
+#### 4. Data
+
+The accident data for Mashhad urban highways in the years 2006 and 2007 were used for modeling accidents on urban highways. This information was collected by Traffic and Transportation Organization of Mashhad with the help of GIS and police reports. In this study, the accidents were divided into two groups: accidents with property damage only (no injury) and more severe accidents (injury or fatal). Therefore, accident statistics were collected in two groups: no injury and more severe. Accident data are usually two-level data, the first and main level is often the road segment (i.e., the highway is divided into several parts). In this study, highway segmentation was performed based on total traffic volume. The second level is the hour, that is, traffic peak hours are considered the first sub-level, the day non-peak hours the second, and the night non-peak hours the third. To scrutinize the roles of the different vehicle types in crash occurrence or severity, the traffic was separated into passenger cars, heavy vehicles, and light non-passenger car vehicles. The volume data were not readily available separately from the Traffic and Transportation Organization of Mashhad, which was one of the study limitations. The organization conducts a comprehensive survey once every few years in November and obtains the passing volume of different kinds of vehicles through the main urban roads in terms of daily hours. In November, the traffic conditions in Mashhad are normal, and the models made in this research do not consider the seasonal changes of traffic; this could be another limitation of the research because the statistics of traffic volume in different seasons were not available, and the volume data are related to different hours of the day. According to this statistics, one can perceive the traffic combination and percentage of each vehicle type in traffic and can trust this combination in the future; however, the total (equivalent) traffic volume is updated every year.
+
+The Traffic and Transportation Organization of Mashhad gives the total traffic volume on different urban roads, particularly highways in peak hours, for future years. According to this total equivalent volume, the passenger car equivalent factors of vehicle types, the percentage of each type in traffic combinations, and the ratio of the total volume in non-peak hours to that in peak hours, the volumes of each vehicle type in peak hours and 2 hours representing the day and night nonpeak hours were obtained. The volume of passenger cars and equivalent volume of heavy vehicles and light non-passenger car vehicles at peak hours and 2 representative hours of non-peak day and night hours were also obtained. These calculations were performed with Excel. The passenger car equivalent factors of vehicle types are given in Table 1 ([Transportation and Traf](#page-5-0)fic Organization of [Mashhad, 2008](#page-5-0)).
+
+The total volume (passenger car equivalent) can be obtained with the following equation:
+
+$$V_{te} = e_1 N_1 + \dots + e_n N_n (9)$$
+
+Table 1 The passenger car equivalent factors of vehicle types.
+
+| Heavy<br>vehicles | Bicycle and<br>Motorcycle | Intracity<br>bus | Intercity<br>bus | Minibus | Pickup | Taxi | Passenger<br>car |
+|-------------------|---------------------------|------------------|------------------|---------|--------|------|------------------|
+| 2.5               | 0.5                       | 5                | 2.5              | 2       | 1      | 2    | 1                |
+
+where Vte is the total equivalent volume and ei and Ni are the equivalent factor and number of vehicles of type i, respectively. The number of each type of vehicle is given by
+
+$$N_i = \frac{P_i V_{te}}{e_1 P_1 + \dots + e_n P_n} \tag{10}$$
+
+where Pi is the percentage of vehicles of type i.
+
+Because the number of vehicle types is counted hourly, these data are represented in terms of vehicle per hour, Veh/hr. Eq. (10) was used in Excel to calculate the number of each vehicle type according to the total equivalent volume with the percentage of each vehicle type on any road segment at any hour. The summary statistics of crashes and independent variables of the models in the years 2006 and 2007 for 156 sections of Mashhad urban highways in 936 sub-sections are presented in Table 2.
+
+## 5. Statistical modeling
+
+After collecting the data, the models were developed for accidents with property damage only (no injury) and more severe (injury or fatal) accidents to identify the factors influencing the accident occurrence of urban highways. Independent variables applied in the models included xij,1, xij,<sup>2</sup> and xij,3, the volume of passenger cars, heavy vehicles, and light non-passenger car vehicles on the i-th section in the j-th period.
+
+#### 5.1. Poisson regression model
+
+To estimate the unknown parameters of the model, the iteration method of Newton-Raphson is applied. First, a vector of regression parameters is considered as a primary estimate, β̂ 0, and the second parameter estimate is obtained from iteration relation (11) and so on until the difference between two successive estimates becomes less than the tolerance level. The estimate before the last is the desired estimated coefficient. The iteration relation is as follows:
+
+$$\hat{\beta}_{k+1} = \hat{\beta}_k - \hat{H}_k^{-1} \hat{g}_k \tag{11}$$
+
+where ĝ<sup>k</sup> is the gradient evaluated at β̂ <sup>k</sup>, the first partial derivative of the log likelihood in the gradient, and Ĥ<sup>k</sup> is the Hessian evaluated at β̂ <sup>k</sup>, the second partial derivative of log likelihood, as follows:
+
+$$g = \sum_{i=1}^{n} (y_i - \hat{\lambda}_i) x_i, H = -\sum_{i=1}^{n} \hat{\lambda}_i x_i' x_i$$
+ (12)
+
+For evaluating the significance of independent variables, the inverse Hessian obtained at the last iteration will be the asymptotic variance matrix. The variance of the estimates is the diagonal elements and the standard errors their square roots. The t statistic for each parameter is also constructed as the ratio of the parameter estimate over its standard error. If the p-value of a parameter is less than the required level of significance (0.05 or less), the corresponding variable is significant and will stay in the model. Otherwise, it is
+
+Table 2 Summary statistics of accidents and independent variables.
+
+| Variable                                                                                                        | Mean               | S.D.              | Min            | Max                  |
+|-----------------------------------------------------------------------------------------------------------------|--------------------|-------------------|----------------|----------------------|
+| Dependent variables<br>number of accidents with property loss only<br>number of more severe accidents           | 7.07<br>0.97       | 8.86<br>1.43      | 0<br>0         | 80<br>12             |
+| Independent variables<br>Passenger car volume<br>Heavy vehicle volume<br>Light non-passenger car vehicle volume | 1046<br>562<br>551 | 807<br>427<br>419 | 33<br>29<br>42 | 4593<br>2425<br>2225 |
+
+<span id="page-3-0"></span>neglected in the model [\(Anselin, 2002](#page-4-0)). Such calculations were proceeding by SAS, estimating the parameters and evaluating their significance for no injury and more severe accidents, which is presented in Table 3. Thus, the evaluated number of no injury accidents on section i in period j is obtained from the following equation:
+
+$$\lambda_{ij} = exp(x'_{ij}\beta) = exp(0.0003x_{ij,1} + 0.0005x_{ij,3})$$
+ (13)
+
+The evaluated number of more severe accidents on section i in period j is also as follows:
+
+$$\lambda_{ij} = exp(-0.6134 + 0.00084x_{ij,3})$$
+ (14)
+
+Knowing the evaluated value of λij, the Poisson model developed for estimating the likelihood of yij no injury and more severe accidents is obtained as follows:
+
+$$P(y_{ij}) = \frac{e^{-\lambda_{ij}} \lambda_{ij}^{y_{ij}}}{y_{ij}!} \tag{15}$$
+
+# 5.2. Negative binomial regression model
+
+For estimating the regression coefficients and dispersion parameters, the Newton-Raphson iteration procedure is applied as in the Poisson model. Using r\*= 0(r= 1) in the first (Poisson model), the regression parameters β are estimated with the following iteration:
+
+$$\hat{\beta}^{(t+1)} = \hat{\beta}^{(t)} - \left[\hat{H}_{\beta}^{(t)}\right]^{-1} \hat{g}_{\beta}^{(t)} \tag{16}$$
+
+where g<sup>β</sup> = − ∑ i= 1 ∂Li <sup>∂</sup><sup>β</sup> ; <sup>H</sup><sup>β</sup> <sup>=</sup> − ∑ i= 1 ∂<sup>2</sup>Li ∂β∂β′ . Then, r\* is estimated iteratively as
+
+$$\hat{r}^{*(t+1)} = \hat{r}^{*(t)} - \left[\hat{H}_r^{(t)}\right]^{-1} \hat{g}_r^{(t)}$$
+(17)
+
+where gr <sup>=</sup> −∑ <sup>∂</sup>Li <sup>∂</sup><sup>r</sup> ; Hr <sup>=</sup> −∑ <sup>∂</sup><sup>2</sup> Li <sup>∂</sup><sup>r</sup> <sup>2</sup>. Now, r\* and the estimated regressors are applied as the initial estimate θ in the following iteration to estimate the updated values of r\* and β:
+
+$$\hat{\theta}^{(t+1)} = \hat{\theta}^{(t)} - \left[\hat{H}_{\beta r}^{(t)}\right]^{-1} \hat{g}_{\beta r}^{(t)} \tag{18}$$
+
+Table 3 Estimation results for Poisson and negative binomial (NB) regression models.
+
+| Variable                                  | No injury accidents |                | Injury or fatal<br>accidents |                |  |
+|-------------------------------------------|---------------------|----------------|------------------------------|----------------|--|
+|                                           | Parameter           | t<br>statistic | Parameter                    | t<br>statistic |  |
+| Poisson model                             |                     |                |                              |                |  |
+| Constant                                  | −0.1611             | −1.77          | −0.6134⁎                     | −2.56          |  |
+| Passenger car volume                      | 0.0003              | 15.78          | −0.00006                     | −0.95          |  |
+| Heavy vehicle volume                      | 0.00002             | 0.63           | −0.00024                     | −1.92          |  |
+| Light non-passenger car vehicle<br>volume | 0.0005              | 12.80          | 0.00084                      | 7.31           |  |
+| Negative binomial model                   |                     |                |                              |                |  |
+| Constant                                  | −0.8112             | −2.91          | −0.9231                      | −2.77          |  |
+| Passenger car volume                      | 0.00042             | 5.29           | −0.00012                     | −1.33          |  |
+| Heavy vehicle volume                      | −0.00001            | −0.10          | −0.00014                     | −1.17          |  |
+| Light non-passenger car vehicle<br>volume | 0.00061             | 4.73           | 0.00102                      | 6.33           |  |
+| Dispersion parameter                      | 1.0874              | 17.04          | 0.7832                       | 7.39           |  |
+
+<sup>⁎</sup> Highlighted coefficients are significant at 5%.
+
+where
+
+$$\theta = \begin{bmatrix} \beta \\ r^* \end{bmatrix}, g_{\beta r} = \begin{bmatrix} g_{\beta} \\ g_r \end{bmatrix}, H_{\beta r} = \begin{bmatrix} H_{\beta} & -\sum \frac{\partial^2 L_i}{\partial r^* \partial \beta} \\ \left(-\sum \frac{\partial^2 L_i}{\partial r^* \partial \beta}\right)' & H_r \end{bmatrix}$$
+(19)
+
+The estimated values of r\* and β in the iteration before the last, θ̂ are of interest.r= exp(r\*) is the inverse dispersion parameter [\(Agresti,](#page-4-0) [2002\)](#page-4-0). The significance evaluation of the independent variables of the NB regression model is similar to that of the Poisson model. The results of developing the NB model for no injury and more severe accidents are presented in Table 3. Therefore, the evaluated number of no injury accidents on section i in period j is obtained from following equation:
+
+$$\mu_{ij} = exp(x_{ij}\beta) = exp(-0.8112 + 0.00042x_{ij,1} + 0.00061x_{ij,3})$$
+(20)
+
+The evaluated number of more severe accidents on section i in period j is also obtained as
+
+$$\mu_{ij} = exp(-0.9231 + 0.00102x_{ij,3})$$
+ (21)
+
+Knowing the evaluated value of μij, r= 1/α= 0.92 and r= 1.277 for no injury and more severe accidents, respectively, the NB model for estimating the likelihood of yij no injury and more severe accidents is obtained as
+
+$$p(y_{ij}) = \frac{\Gamma(y_{ij} + r)}{y_{ij}\Gamma(r)} \left[ \frac{\mu_{ij}}{\mu_{ij} + r} \right]^{y_{ij}} \left[ \frac{r}{\mu_{ij} + r} \right]^{r}$$
+(22)
+
+# 6. Goodness-of-fit evaluation and comparison of models
+
+After developing the models and identifying the effective factors in accident occurrence, the evaluation and comparison between models is discussed. To evaluate the goodness-of-fit of the models, the Akaike Information Criterion (AIC) was used. The lower the AIC, the better the model fit, and the model with the least AIC is the best one. The goodness-of-fit of the applied models cannot be evaluated independently, but this fit is evaluated by comparing the value of AIC for each model. For comparing models, first the Poisson and NB models are compared together with respect to the data dispersion. To do this, the significance of the dispersion parameter in the NB model and the likelihood ratio (LR) test were used. The statistic of the LR test is obtained as
+
+$$LR = -2\left(LL_p - LL_{NB}\right) \tag{23}$$
+
+where LLp and LLNB are the log-likelihood of the Poisson and NB models, respectively. This statistic has a Chi-squared distribution with k−1 degrees of freedom, in which k is the number of regression coefficients. If this statistic is greater than the value of χ0.05 <sup>2</sup> (k−1), then the second model is better than the first. The consequence of this test for comparing models is usually equivalent to evaluating the significance of the dispersion parameter. The second stage of comparison is the goodnessof-fit evaluation of models and their fit comparison. The AIC is calculated using the following equation [\(Liu & Cela, 2008](#page-4-0)):
+
+$$AIC = -2LL + 2k (24)$$
+
+where LL is log-likelihood and k is the number of parameters. The results of the second stage often approve the conclusion of the first stage. The <span id="page-4-0"></span>results of the goodness-of-fit evaluation of models and their comparison are presented in Table 4.
+
+The results for no injury accidents show that the dispersion parameter is significant in the NB model, and the negative value of two times the log likelihood is much greater for the Poisson model than the NB model. The value of the LR statistic is LR=−2(LLp−LLNB)= 3377.3, which is much greater than χ0.05 <sup>2</sup> (3) equal to 7.81. Therefore, it is concluded that the NB regression model is better than the Poisson model for no injury accidents. The comparison of the AIC value between models demonstrates that the NB model with lower AIC is better than the Poisson model for no injury accidents.
+
+For more severe accidents, the dispersion parameter is also significant, and the LR statistic is equal to LR=−2(LLp−LLNB)= 148.4, which indicates that the NB model is better than the Poisson model. Because the AIC value for the NB model is less than that of the Poisson model, it is evident that this model is better than the Poisson model for modeling injury or fatal accidents on urban highways. Therefore, the NB regression model is an efficient and worthy model for modeling no injury and more severe accidents on urban highways. This claim can be evaluated by examining the validity of this model in predicting crashes on urban highways.
+
+## 7. Validating the NB regression model
+
+To validate the NB regression model for modeling accidents, this model was used to predict the number and likelihood of no injury and more severe accidents on other urban highways to examine the validity of the model by comparing the observed and predicted numbers of accidents on each section of highway over a specified period. The statistics for the accidents and traffic flow on the highway were provided as before. The Pearson residuals test was used for validation, which is described as follows (Agresti, 2002):
+
+$$S = \sum_{i=1}^{n} \sum_{j=1}^{3} s_{ij} = \sum_{i=1}^{n} \sum_{j=1}^{3} \left( \frac{y_{ij} - M(y_{ij})}{\sqrt{V(y_{ij})}} \right)^{2} = \sum_{i=1}^{n} \sum_{j=1}^{3} \frac{(y_{ij} - \mu_{ij})^{2}}{\mu_{ij} + \alpha \mu_{ij}^{2}}$$
+(25)
+
+where yij is the observed and μij the predicted number of accidents on i-th section of the highway in the j-th period of the day, α is the dispersion parameter and n is the number of sections of the highway. S follows a Chi-squared distribution with N-k degrees of freedom, where N is the number of observations and k is the number of regression coefficients. The closer together the observed and predicted numbers of accidents are, the more valid the model is. The critical value of S is equal to χ0.05 <sup>2</sup> (N−k), and a value of S less than it implies the validity of the model. Referring to the development of the NB model, the predicted numbers of no injury and more severe accidents on the i-th section of the highway in the j-th period of the
+
+Table 4 Results of goodness of fit evaluation and comparison between the Poisson and NB models.
+
+|                           | Poisson | Negative binomial |
+|---------------------------|---------|-------------------|
+| No injury accidents       |         |                   |
+| alpha                     |         | 1.0874 (17.04)    |
+| -2LL                      | 9054.8  | 5377.6            |
+| AIC                       | 9062.8  | 5387.6            |
+| Injury or fatal accidents |         |                   |
+| alpha                     |         | 0.7832 (7.39)     |
+| -2LL                      | 2485.3  | 2336.9            |
+| AIC                       | 2493.3  | 2346.9            |
+
+day were obtained from Eqs. [\(20\) and \(21\),](#page-3-0) respectively. The highway was divided into 40 sections and three periods of the day, leading to N= 120. For accidents with property loss only, S was equal to 41.32, which is less than χ0.05 <sup>2</sup> (120−3)= 143.21 and implies that the model is valid. However, for more severe accidents, S was equal to 39.72, which is less than χ0.05 <sup>2</sup> (120−2)= 144.62 and implies the validity of NB regression model for modeling more severe accidents.
+
+### 8. Conclusions
+
+The results of this research indicate that the volume of passenger cars and light non-passenger car vehicles plays a significant role in the likelihood of no injury accidents, but the volume of heavy vehicles does not have much effect on the likelihood of no injury accidents on urban highways. The volume of light non-passenger car vehicles increases the likelihood of more severe accidents, but the volume of passenger cars and heavy vehicles do not have much influence on the likelihood of more severe accidents. Therefore, it is concluded that light non-passenger car vehicles, including taxis and motorcycles, play a considerable part in the occurrence of accidents on urban highways, including both no injury and more severe accidents, but heavy vehicles do not. These conclusions will be helpful for future projects involving the management of traffic on urban highways. In these projects, planning to control the role of taxis and motorcycles in accident occurrence should be adopted. This could include the separation of these vehicles types from normal flow on urban highways. The results also indicate that the negative binomial regression model is a valid and efficient model for modeling and predicting the accidents on urban highways. The study had some limitations, two of which are related to the research data, as mentioned in [Section 4:](#page-2-0) the volume data for each kind of vehicle were not readily available, and the models did not consider the seasonal changes of traffic because the statistics for traffic volume in different seasons were not available. The other limitation of the research is related to the models used for modeling accidents. Poisson and NB regression models have their own limitations.
+
+#### References
+
+Agresti, A. (2002). Categorial Data Analysis: Case Study - Negative Binomial Regression model. Nascar Lead Changes, 1975–1979. Hoboken, NJ: Wiley [www.nascar.com](http://www.nascar.com)
+
+Anastasopoulos, C., & Mannering, F. L. (2009). A note on modeling vehicle accident frequencies with random-parameters count models. Accident Analysis and Prevention, 41, 153–159.
+
+Anselin, L. (2002). Appendix C: Ordinary Least Square and Poisson Regression Models. Champaign-Urbana, IL: University of Illinois.
+
+Attaran, H. (1996). : Iran Journal of Legal Medicine.
+
+Ayati, E. (2008). The cost of traffic accidents in Iran (Publication No. 345). : Ferdowsi University of Mashhad.
+
+Chang, L. -Y. (2005). Analysis of freeway accident frequencies: Negative binomial regression versus artificial neural network. Journal of Safety Science, 43, 541–557.
+
+Delen, D., Shadra, R., & Bessonov, M. (2006). Identifying significant predictors of injury severity in traffic accidents using a series of artificial neural networks. Accident Analysis and Prevention, 38, 434–444.
+
+Lee, J., & Mannering, F. (2002). Impact of roadside features on the frequency and severity of run-off-roadway accidents: an empirical analysis. Accident Analysis and Prevention, 41, 798–808.
+
+Legal Medicine Organization of Iran. (2002).
+
+Liu, W., & Cela, J. (2008). Count Data Models in SAS (Paper 371–2008). SAS Global Forum 2008: Statistics and Data Analysis.
+
+Lord, D. (2006). Modeling motor vehicle crashes using Poisson-gamma models: examining the effects of low sample mean values and small sample size on the estimation of the fixed dispersion parameter. Accident Analysis and Prevention, 38 (4), 751–766.
+
+Lord, D., & Park, Y. -J. (2008). Investigating the effects of the fixed and varying dispersion parameters of Poisson-gamma models on empirical Bayes estimates. Accident Analysis and Prevention, 40(4), 1441–1457.
+
+Lord, D., Washington, S. P., & Ivan, J. N. (2007). Further notes on the application of Zero-inflated models in highway safety. Accident Analysis and Prevention, 39,
+
+- <span id="page-5-0"></span>Ma, J., Kockelman, K. M., & Damien, P. (2008). A multivariate Poisson-lognormal regression model for prediction of crash counts by severity, using Bayesian methods. Accident Analysis and Prevention, 40, 964–975.
+- Milton, J. C., Shankar, V. N., & Mannering, F. L. (2008). Highway accident severities and the mixed logit model: An exploratory empirical analysis. Accident Analysis and Prevention, 40, 260–266.
+- Savolainen, P. T., & Tarko, A. P. (2005). Safety impacts at intersections on curved segments. Transportation Research Record, 1908, 130–140.
+- Transportation and Traffic Organization of Mashhad, Iran (2008). Comprehensive studies of transportation office. Fourth statistical paper of transportation of Mashhad.
+- Wang, C., Quddus, M. A., & Ison, S. G. (2009). Impact of traffic congestion on road accidents: A spatial analysis of the M25 motorway in England. Accident Analysis and Prevention, 41, 798–808.
+
+Ehsan Abbasi is a M.Sc. He received his M.D. in the Road and Transportation Engineering from the Ferdowsi University of Mashhad, Iran. His areas of expertise include safety of traffic and modeling accidents. His recent work has been on modeling accidents on urban highways in terms of traffic flow and road geometry characteristics, using Poisson, NB and ZI regression models.
+
+Dr. Esmaeel Ayati is a Full Professor in the Department of Engineering at Ferdowsi University of Mashhad, Iran. He received his M.D. in Road and Civil Engineering from Tehran University and his Ph.D. in Road and Transportation Engineering from Aston University. His area of expertise is safety of traffic and his researches on evaluating the cost of traffic accidents is unique in Iran and his book titled "The Cost of Traffic Accidents in Iran" is the only valid reference in this area in Iran.

Zotero/001_artiklid/Road Safety Indicators/cenajroadaccidentfatalitiesforecasting2024.md

@@ -0,0 +1,310 @@
+---
+category: literaturenote
+citekey: cenajroadaccidentfatalitiesforecasting2024
+title: "Road Accident Fatalities Forecasting Models using Smeed’s Regression Analysis: A Case Study"
+authors: "Cenaj, Erjola; Dervishi, Raimonda"
+year: 2024
+date: 2024-00-00 2024
+doi: 10.24018/ejeng.2024.9.6.3213
+publication: European Journal of Engineering and Technology Research
+url: "https://doi.org/10.24018/ejeng.2024.9.6.3213"
+zotero_key: 2SGNNE3S
+zotero_storage: VEQ5AUQ2
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "Cenaj, Erjola"
+status: converted
+---
+## RESEARCH ARTICLE
+
+![](_page_0_Picture_2.jpeg)
+
+# Road Accident Fatalities Forecasting Models using Smeed's Regression Analysis: A Case Study
+
+Erjola Cena[j\\*](#page-0-0) and Raimonda Dervishi
+
+#### *ABSTRACT*
+
+**Fatalities and injuries triggered by road traffic accidents are worthwhile traffic safety problems, especially for developing and developed countries. Several academic works have convinced that using data from a given group, a weighty relationship between the number of road traffic fatalities (RTFs) and registered vehicles and population size is designed. This paper uses historical data from over ten years in Albania to identify the relationship between the same factors. The study divulges that such a relationship cannot be impacted with a good degree of exactness by Smeed's Equation (SE). Additionally, road accident prediction models by the structural form of Smeed's regression method enable estimating RTFs tied to population size and number of active vehicles. The modified forms of SE are the key to a satisfactory match in predicting RTFs in Albania.**
+
+**Keywords:** Number of vehicles, regression analysis, Smeed's equation, traffic accident fatalities.
+
+**Submitted:** October 10, 2024
+
+**Published:** November 28, 2024
+
+*[10.24018/ejeng.2024.9.6.3213](http://dx.doi.org/10.24018/ejeng.2024.9.6.3213)*
+
+*Department of Mathematical Engineering, Faculty of Mathematical and Physical Engineering, Polytechnic University of Tirana, Albania.*
+
+<span id="page-0-0"></span>\**Corresponding Author:* e-mail: [erjola\\_cenaj@yahoo.com](mailto:erjola_cenaj@yahoo.com)
+
+# 1. Introduction
+
+Fatalities and injuries due to road traffic accidents are substantial traffic safety problems for both developing and well-constructed countries. According to the statistics of the World Health Organization (WHO), worldwide, 1.3 million people die, and as many as 20–50 million people are also injured annually linked with traffic accidents. The same statistics point out that approximately 90% of fatalities from road traffic accidents transpire in low-andmiddle-income countries, despite the fact they hold a 50% share of motor vehicle ownership in the world [\[1\]](#page-3-0).
+
+On the other hand, road traffic accidents are the leading cause of all injuries and are representative of most deaths, crafting road traffic injuries the 9th leading matter of disability-adjusted life years lost worldwide [\[2\]](#page-3-1). Impetuosity and insanity, in many cases, are the foremost sources, especially in Balkan countries, and lack of proper sense of using traffic signs are some of RTFs sources. However, it is effective, entitizing other components such as population size, the number of vehicles in use, the total length of roads, and the population density, as if these factors can be translocated to reduce the future number of accidents [\[3\]](#page-3-2), [\[4\]](#page-3-3).
+
+Many studies have shown that population size and number of registered vehicles are dominant factors affecting road traffic fatalities worldwide [\[5\]](#page-3-4), [\[6\]](#page-3-5).
+
+Smeed's Equation (SE) is the earliest model used to approximate the number of fatalities in road traffic accidents, comprising the independent variables of population and number of registered vehicles and the dependent variable of the number of fatalities [\[7\]](#page-3-6). It has been found that SE is adequate for utilization in some developed countries [\[8\]](#page-3-7), and according to Ponnaluri [\[9\]](#page-3-8), it is a poorly method in developing countries [\[10\]](#page-3-9)–[\[12\]](#page-3-10).
+
+The process of RTFs evaluation was introduced for the first time in 1949, by Smeed. Smeed started to work based on available data linked to road traffic fatalities (RTFs), official data on active vehicle numbers, and population size referring to 1938 from the group of 20 countries selected (mostly EU). Then, he discovered a nonlinear relationship among RTFs and influencing demographic and motorization rates through the mathematical expression given in [\(1\)](#page-0-1) [\[13\]](#page-3-11):
+
+<span id="page-0-1"></span>
+$$\frac{F}{V} = 0.0003 \left(\frac{V}{P}\right)^{\frac{-2}{3}} \tag{1}$$
+
+where
+
+*F –* number of road traffic fatalities (RTFs)
+
+*V –* number of registered vehicles
+
+*P –* population size
+
+The Smeed equation provides a good match referring to available data from the selected countries for that year. The factors of experiencing possible road traffic accidents are coupled to RTFs, population size, and the number of registered vehicles. This approach is used to carry out important sizes handling identical factors as Smeed. We used the number of RTFs, official vehicle number registered vehicles, and population size, including the time fraction 2014–2023. As in many other countries worldwide, the population size and number of registered vehicles are dominant factors affecting road traffic fatalities in Albania. The study shows that Smeed's Equation is inadequate to be used for definitively predicting RTFs in Albania over the study period. The model is tested using the statistics from INSTAT Albania. It has been shown that these modified forms of SE lead to a satisfactory fit for the tested period.
+
+# 2. Data Source
+
+In this research work, the factors mentioned in the Smeed equation, such as population size, number of registered vehicles, and number of road traffic fatalities for the tested period under consideration, 2014–2023, are provided from the domestic official sources, Albanian Statistical Institute (INSTAT) [\[14\]](#page-3-12).
+
+According to INSTAT, around 16,192 road traffic accidents in Albania have been declared during the last 10 years. Furthermore, around 24,020 people were involved in road accidents, split into 2199 cases of fatalities, and 19,622 were injured between the 2014–2023 period, as depicted in [Table I.](#page-1-0)
+
+#### 3. Methodology
+
+## *3.1. Application of Smeed's Regression Model to Estimate RTFs*
+
+Smeed's model is an empirical rule that binds RTFs to variables, the vehicle registered, and the population size for a given region, or country. As it is expected, increasing the number of vehicles will decrease fatalities per vehicle. This principle was first introduced based on 1938 work, which was employed later to test RTFs in 1960 up to1967 period or even later in many other scientific efforts included in the research work of [\[15\]](#page-4-0).
+
+<span id="page-1-0"></span>TABLE I: Statistical Data for the Tested Period (2014–2023)
+
+| Year | Fatalities | Population | No. of vehicle |
+|------|------------|------------|----------------|
+| 2014 | 264        | 2,895,947  | 415,121        |
+| 2015 | 270        | 2,893,005  | 443,227        |
+| 2016 | 269        | 2,875,592  | 479,217        |
+| 2017 | 222        | 2,876,591  | 460,299        |
+| 2018 | 213        | 2,870,324  | 500,894        |
+| 2019 | 227        | 2,862,427  | 499,779        |
+| 2020 | 181        | 2,845,955  | 539,497        |
+| 2021 | 197        | 2,829,741  | 593,280        |
+| 2022 | 164        | 2,793,592  | 639,379        |
+| 2023 | 192        | 2,761,785  | 699,337        |
+
+Smeed's equation model can be given from [\(2\)](#page-1-1) [\[13\]](#page-3-11):
+
+<span id="page-1-1"></span>
+$$\frac{F}{V} = \alpha \cdot \left\{ \left( \frac{V}{P} \right)^{\beta} \right\} \cdot \varepsilon \tag{2}$$
+
+where
+
+*F –* number of RTFs
+
+*V –* number of registered vehicles
+
+*P –* population size
+
+*E –* error term
+
+*α* and *β –* parameters that are a matter of estimation
+
+<span id="page-1-2"></span>On the other hand, [\(2\)](#page-1-1) can be expressed as following in [\(3\):](#page-1-2)
+
+$$Y = aX^{\beta}\varepsilon\tag{3}$$
+
+where
+
+*X* – the predictor variable is *V/P* (vehicle density)
+
+*Y* the dependent variable, *F/V* (fatality rate per vehicle)
+
+In the process of evaluating RTFs, Smeed was based on the least squares regression (LSR) techniques to assess the parameters linked to [\(3\).](#page-1-2) However, the LSR approach does not allow parameter variability and it is very sensitive to infraction of the normality assumption.
+
+## *3.2. Literature Review on the Application of Modified Smeed's Regression Model*
+
+A lot of efforts are undertaken by many authors in the field of RTFs theory. The research work and contribution of Koren and Borsos have led to a modified form of the original Smeed's equation as can be given in the following mathematical expression given in [\(4\)](#page-1-3) [\[16\]](#page-4-1):
+
+<span id="page-1-3"></span>
+$$\frac{F}{P} = \alpha \left(\frac{V}{P}\right)^{\beta} \varepsilon \tag{4}$$
+
+where *α* and *β* are the parameters necessary to be determined, for the known variables, such as the number of road traffic fatalities (*F*), the number of registered vehicles (*V*), and the population (*P*).
+
+After transforming [\(4\)](#page-1-3) and supposing both side logarithms, to base e, the nonlinear model in [\(4\)](#page-1-3) can be expressed in a linear form as follows in [\(5\):](#page-1-4)
+
+<span id="page-1-4"></span>
+$$Y_i = \alpha_0 + \beta X + e_i \tag{5}$$
+
+where
+
+*Yi* – ln(F/P), Xi = ln(V/P)
+
+*α<sup>0</sup>* – ln*α*
+
+*ei* – ln*ε*
+
+*i –* 1, 2, *...* , n
+
+Moreover, during this transformation, it is required that *ei*, *i* = *1, 2 ... , n* are *iid* distributed *N(0, σ2)*.
+
+Further on, using least squares regression (LSR) method to estimate the mentioned above parameters, should pass through employing expression in [\(6\):](#page-1-5)
+
+$$\hat{\beta} = \frac{\sum_{i=1}^{n} x_i y_i - \frac{1}{n} \sum_{i=1}^{n} x_i \sum_{i=1}^{n} y_i}{\sum_{i=1}^{n} x_i^2 - \frac{1}{n} (\sum_{i=1}^{n} x_i)^2}$$
+(6)
+
+Or *α*ˆ <sup>0</sup> is linked as following in [\(7\):](#page-1-6)
+
+<span id="page-1-6"></span><span id="page-1-5"></span>
+$$\hat{\alpha}_0 = \overline{y} - \hat{\beta}\overline{x} \tag{7}$$
+
+Using the equation *α*<sup>0</sup> = *lnα*, then the least squares estimation of the parameter *α* can be evaluated using [\(8\):](#page-2-0)
+
+$$\hat{\alpha} = e^{\hat{\alpha}_0} \tag{8}$$
+
+Thus, in terms of initial variables, the expression given in [\(9\)](#page-2-1) is carried out:
+
+<span id="page-2-1"></span>
+$$\frac{F}{P} = \hat{\alpha} \left(\frac{V}{P}\right)^{\hat{\beta}} \tag{9}$$
+
+#### *3.3. Test of Regression*
+
+The regression hypothesis that none of the *x*'s predict *y* can be expressed as *H0*: *β* = *0*. The modeling process does not include *β* = 0 as part of our hypothesis, enabling the restriction of *y* to ensure realizing an intercept of zero.
+
+We can test *H0: β* = *0* by [\(10\):](#page-2-2)
+
+<span id="page-2-2"></span>
+$$F = \frac{SSR}{SSE/(n-2)} \tag{10}$$
+
+It is simply distributed as *F* (*1, n*−*2*) when *H0*: *β<sup>1</sup>* = *0* is true. If *F* > *F* (*α; 1, n*−*2*), then it is worth rejecting *H0* from simulations.
+
+#### 4. Discussion and Results
+
+# *4.1. Estimation of RTFs using Smeed's Regression Model in Albania*
+
+The results of our research work are introduced in [Table II.](#page-2-3)
+
+As it can be depicted from the results [\(Table II\)](#page-2-3), the application of Smeed's equation leads to an overestimation of the number of RTFs in Albania.
+
+The result shows that on average, the expected fatalities estimated by Smeed's formula exceed the observed values by 4.8%, which compared to official data's (2.19%) is higher. Given the relatively large deviations between observed and expected values of fatalities as stated in [Table II,](#page-2-3) Smeed's equation is ineffective in predicting RTFs in Albania.
+
+Using [\(2\)](#page-1-1) and performing LSR technique on the data given in [Table I,](#page-1-0) we get the mathematical expression as given in [\(11\):](#page-2-4)
+
+<span id="page-2-4"></span>
+$$\frac{F}{V} = 0.0000232 \left(\frac{V}{P}\right)^{-1.6992} \tag{11}$$
+
+<span id="page-2-3"></span>TABLE II: Simulation Results on Estimated Fatalities based on Smeed's Regression Models
+
+| Year  | Fatalities | F<br>ˆ | Error (%)   | F<br>˜ | Error       |
+|-------|------------|--------|-------------|--------|-------------|
+| 2014  | 264        | 454    | 190 (71.9%) | 261    | 3 (1.2%)    |
+| 2015  | 270        | 464    | 194 (71.8%) | 249    | 21 (7.7%)   |
+| 2016  | 269        | 474    | 205 (76.2%) | 233    | 36 (13.4%)  |
+| 2017  | 222        | 468    | 246 (110%)  | 240    | −18 (8.1%)  |
+| 2018  | 213        | 481    | 268 (125%)  | 226    | −13 (6.1%)  |
+| 2019  | 227        | 479    | 252 (111%)  | 225    | 2 (0.8%)    |
+| 2020  | 181        | 490    | 309 (170%)  | 211    | −30 (16.5%) |
+| 2021  | 197        | 504    | 307 (155%)  | 196    | 1 (0.5%)    |
+| 2022  | 164        | 512    | 348 (212%)  | 182    | −18 (10.9%) |
+| 2023  | 192        | 560    | 368 (191%)  | 167    | 26 (13.5%)  |
+| Total | 2199       | 4886   |             | 2190   |             |
+
+Note: *F* = number of RTFs, *F* (as in the 5th column title) = estimate of F from Smeed's formula.
+
+<span id="page-2-5"></span><span id="page-2-0"></span>TABLE III: ANOVA Test: The Estimated Smeed's Regression Model ANOVA df SS MS F Significance F Regression 1 0.859457 0.859457 76.82324 2.25E-05 Residual 8 0.0895 0.011187 Total 9 0.948956
+
+TABLE IV: ANOVA Test: The Estimated Modified Smeed's
+
+<span id="page-2-7"></span>
+
+| Regression Model |    |          |          |          |                |
+|------------------|----|----------|----------|----------|----------------|
+| ANOVA            | df | SS       | MS       | F        | Significance F |
+| Regression       | 1  | 0.145557 | 0.145557 | 13.01249 | 0.006909       |
+| Residual         | 8  | 0.089488 | 0.011186 |          |                |
+| Total            | 9  | 0.235045 |          |          |                |
+
+Using [\(11\),](#page-2-4) the result of this application, the estimated *F*˜ , which portrays the estimate of *F* from [\(11\)](#page-2-4) is introduced in [Table II.](#page-2-3)
+
+From the simulation results it is shown that the application of Smeed's regression model is adequate for assessing the RTFs in Albania [\(Table II\)](#page-2-3). The result shows that on average, the expected fatalities as estimated by Smeed's formula exceeded the observed by 2.19% but results tightly to the average of real fatalities.
+
+[Table III](#page-2-5) presents the analysis of variance from the estimated Smeed's regression model. From the test of regression, the statistic:
+
+$$F = \frac{regression \, mean \, square}{residual \, mean \, square}$$
+
+where H0 is true for a significance level of 0.05, then it has Fisher distribution with 1 and n-2 degrees of freedom. If the calculated value of *F* is greater than F(0.05; 1, n-2), it necessitates the rejection of H0. Since Fcalculated = 76.82 > 5.32 = F(0.05;1,8), the test is significant at the 5% accuracy level. From the simulation results and analyses, it is concluded that a linear relationship between the expected value of *y* = *ln(F/V)* and *x* = *ln(V/P)* is observed.
+
+## *4.2. Estimation of RTFs using Modified Smeed's Regression Model in Albania*
+
+Using [\(4\)](#page-1-3) and LSR method based on [Table I,](#page-1-0) we get the mathematical expression as follows in [\(12\):](#page-2-6)
+
+<span id="page-2-6"></span>
+$$\frac{F}{P} = 0.0000231 \left(\frac{V}{P}\right)^{-0.6992} \tag{12}$$
+
+TABLE V: Estimated Fatalities from the Modified Smeed's
+
+<span id="page-2-8"></span>
+
+| Regression Model |            |        |             |  |  |
+|------------------|------------|--------|-------------|--|--|
+| Year             | Fatalities | F<br>ˆ | Error       |  |  |
+| 2014             | 264        | 260    | 4 (1.5%)    |  |  |
+| 2015             | 270        | 248    | 22 (8.15)   |  |  |
+| 2016             | 269        | 232    | 36 (13.4%)  |  |  |
+| 2017             | 222        | 239    | −17 (7.6%)  |  |  |
+| 2018             | 213        | 225    | −12 (5.6%)  |  |  |
+| 2019             | 227        | 224    | 3 (1.3%)    |  |  |
+| 2020             | 181        | 210    | −29 (16%)   |  |  |
+| 2021             | 197        | 195    | 2 (1%)      |  |  |
+| 2022             | 164        | 181    | −17 (10.4%) |  |  |
+| 2023             | 192        | 167    | 25 (13%)    |  |  |
+| Total            | 2199       | 2181   |             |  |  |
+
+<span id="page-3-13"></span>
+
+|    | Coefficient    |                            | Standart error |                            | R square       |                            |
+|----|----------------|----------------------------|----------------|----------------------------|----------------|----------------------------|
+|    | Smeed's method | Modified Smeed's<br>method | Smeed's method | Modified Smeed's<br>method | Smeed's method | Modified Smeed's<br>method |
+| αˆ | −10.6722       | −10.6724                   | 0.331394       | 0.331372                   | 0.90           | 0.62                       |
+| βˆ | −1.69923       | −0.69929                   | 0.193868       | 0.193855                   |                |                            |
+
+TABLE VI: Regression Results: Estimated Coefficients (*α*ˆ;*β*ˆ*)*
+
+[Table IV](#page-2-7) presents the analysis of variance from the estimated modified Smeed's regression model. From the regression test, if the calculated value of F is greater than F(0.05; 1, n-2), it is recommended to reject H0. Since Fcalculated = 13.01 > 5.32 = F(0.05;1,8) the test is significant at the 5% level. We conclude that there is a linear relationship between the expected value of *y* = *ln(F/P)* and *x* = *ln(V/P)*.
+
+The estimated *F*ˆ , which represents the estimate of F evaluated from [\(12\),](#page-2-6) is given in [Table V.](#page-2-8) From the simulation results [\(Table V\)](#page-2-8), it is shown that the application of modified Smeed's regression model is adequate for [Table V.](#page-2-8) Estimated fatalities from the modified Smeed's regression model assessing RTFs in Albania case. The result shows that, on average, the expected fatalities, as estimated by Smeed's formula, exceeded the observed by 2.181% but results tightly to the average of real fatalities.
+
+In [Table VI,](#page-3-13) the coefficients estimated from both regression models, the standard errors for the LSM, and the R Square coefficient are given. From the simulation results included in [Table VI,](#page-3-13) the estimated coefficient *α*ˆ, β , and standard error for both coefficients are almost equal. The R<sup>2</sup> coefficients of the determination chosen model results are 0.90 and 0.62, respectively. These values recommend that Smeed's regression model properly fit the data of the Albanian case referring to the 2014–2023 period.
+
+# 5. Conclusions
+
+Smeed's equation is a valuable tool to forecast fatalities linking to independent predictors, population size, and number of registered vehicles based on a non-linear mathematical expression form. Referring to official data within the period 2016–2023, Smeed's Equation cannot be specified as a good approximation due to its low degree of accuracy. Based on the approved index of safety (0.0003) in SE [\[8\]](#page-3-7), and compared to other case studies, it is clearly stated that the number of fatalities in Albania is apparently away from the international average. Furthermore, in this research work, the structural form of Smeed's regression method to assess fatalities was employed for estimating RTFs in Albania. Once again, referring to official data within the period 2016–2023, Smeed's Equation can be specified as a good approximation due to its high degree of accuracy. Performing F tests, a high statistical significance (*p <* 0.001) for both developed models are observed. Moreover, the results carried out in this scientific work are a good starting point for predicting traffic safety conditions in the future.
+
+The prediction of RTFs is a major issue for the safety of human life, which should be addressed more carefully together with the problems identified in studies [\[17\]](#page-4-2)–[\[19\]](#page-4-3) constitute the full dimensions of safety towards a reliable transport sector that meets the general notion of reliability in developing countries in 2030 and beyond.
+
+In conclusion, the developed models led to the conclusion that increasing the number of registered vehicles may decrease fatalities.
+
+## Conflict of Interest
+
+The authors declare that they do not have any conflict of interest.
+
+## References
+
+- <span id="page-3-0"></span>[1] World Health Organization. Global plan for the decade of action for road safety. 2011. Available from: [http://www.who.int/](http://www.who.int/roadsafety/decadeofaction/plan/planenglish.pdf) [roadsafety/decadeofaction/plan/planenglish.pdf.](http://www.who.int/roadsafety/decadeofaction/plan/planenglish.pdf)
+- <span id="page-3-1"></span>[2] Peden M. *World Report on Road Traffic Injury Prevention*. Geneva: World Health Organization; 2004. Available from: https://www. [who.int/publications/i/item/world-report-on-road-traffic-injury-pr](https://www.who.int/publications/i/item/world-report-on-road-traffic-injury-prevention/) evention/.
+- <span id="page-3-2"></span>[3] Mogyorósi P, Szénási S, Laufer E. Fuzzy-based road accident risk assessment. *Mathematics*. 2024;12:1144. doi: [10.3390/math12081144.](https://doi.org/10.3390/math12081144)
+- <span id="page-3-3"></span>[4] Paulozzi LJ, Ryan GW, Espitia-Hardeman VE, Xi Y. Economic development's effect on road transport-related mortality among different types of road users: a cross-sectional international study. *Accid Anal Prev*. 2007;39(3):606–17. doi: [10.1016/j.aap.2006.10.007.](https://doi.org/10.1016/j.aap.2006.10.007)
+- <span id="page-3-4"></span>[5] Sauerzapf VA. An examination of national fatality rates and factors associated with the variation in fatality rates between nations with reference to the World Health Organisation Decade of Action for Road Safety 2011–2020, Road traffic crash fatalities. 2012. Available from: [https://core.ac.uk/download/pdf/19088388.pdf/.](https://core.ac.uk/download/pdf/19088388.pdf/)
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+- <span id="page-3-6"></span>[7] Cansiz OF. Improvements in estimating a fatal accident model formed by an Artificial Neural Network. *Simulation*. 2011;87(6):512–22. doi: [10.1177/0037549710370842.](https://doi.org/10.1177/0037549710370842)
+- <span id="page-3-7"></span>[8] Pitsiava-Latinopoulou M, Tsohos G. The application of Smeed's equation for road accidents in Greece. *Accid Anal Prev*. 1982;14(1):1–6. doi: [10.1016/0001-4575\(82\)90002-1.](https://doi.org/10.1016/0001-4575(82)90002-1)
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+- <span id="page-3-9"></span>[10] Hesse CA, Ofosu JB, Lamptey B. A regression model for predicting road traffic fatalities in Ghana. *Open Sci Repository Math*. (openaccess). 2014;e23050497. doi: [10.7392/openaccess.23050497.](https://doi.org/10.7392/openaccess.23050497)
+- [11] Bener A, Hussain SJ, Al-Malki M, Shotar MM, Al-Said MF, Jadaan KS. Road traffic fatalities in Qatar, Jordan and the UAE: estimates using regression analysis and the relationship with economic growth. *East Mediterr Health J*. 2010;16(3):318–23. doi: [10.26719/2010.16.3.318.](https://doi.org/10.26719/2010.16.3.318)
+- <span id="page-3-10"></span>[12] Beenstock M, Gafni D. Globalization in road safety: explaining the downward trend in road accident rates in a single country (Israel). *Accid Anal Prev*. 2000;32(1):71–84. doi: [10.1016/S0001-4575\(99\)00053-6.](https://doi.org/10.1016/S0001-4575(99)00053-6)
+- <span id="page-3-11"></span>[13] Smeed R. Some statistical aspects of road safety research. *J Royal Stat Soc, Ser–A*. 1949;112(1):1–34. doi: [10.2307/2984177.](https://doi.org/10.2307/2984177)
+- <span id="page-3-12"></span>[14] Transporti STAT. Aksidentet dhe Karakteristikat e Mjetet Rrugore. 2024. (Last Accessed Date 07 November 2024). Available from: [https://www.instat.gov.al/.](https://www.instat.gov.al/)
+
+- <span id="page-4-0"></span>[15] Smeed RJ. Methods available to reduce the number of road casualties. *Traffic Eng Control*. 1964;6:509–12.
+- <span id="page-4-1"></span>[16] Koren C, Borsos A. The advantage of late-comers: analysis of road fatality rates in the EU member states. *Procedia Soc Behav Sci*. 2012;48:2101–10. doi: [10.1016/j.sbspro.2012.06.1183.](https://doi.org/10.1016/j.sbspro.2012.06.1183)
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+- <span id="page-4-3"></span>[19] Malka L, Bidaj F. Opacity evaluation for passenger diesel vehicle cars in Tirana. *J Environ Sci Eng A*. 2015;4(7):352–8. doi: [10.17265/2162-5298/2015.07.003.](https://doi.org/10.17265/2162-5298/2015.07.003)

Zotero/001_artiklid/Road Safety Indicators/chapelonroadsafetyfrancehard2010.md

@@ -0,0 +1,418 @@
+---
+category: literaturenote
+citekey: chapelonroadsafetyfrancehard2010
+title: "Road safety in France: The hard path toward science-based policy"
+authors: "Chapelon, Jean; Lassarre, Sylvain"
+year: 2010
+date: 2010-00-00 2010
+doi: 10.1016/j.ssci.2010.04.015
+publication: Safety Science
+url: "https://doi.org/10.1016/j.ssci.2010.04.015"
+zotero_key: X7GDB7CB
+zotero_storage: XNJZCH6R
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "Chapelon, Jean"
+status: converted
+---
+![](_page_0_Picture_1.jpeg)
+
+### Contents lists available at [ScienceDirect](http://www.sciencedirect.com/science/journal/09257535)
+
+# Safety Science
+
+![](_page_0_Picture_4.jpeg)
+
+![](_page_0_Picture_5.jpeg)
+
+# Road safety in France: The hard path toward science-based policy
+
+Jean Chapelon a,1, Sylvain Lassarre b,\*
+
+- <sup>a</sup> Conseil général de l'Environnement et du Développement durable, Paris la Défense, France
+- <sup>b</sup> Institut National de Recherche dans les Transports et leur Sécurité, Champs sur Marne, France
+
+#### article info
+
+Article history: Received 30 July 2009 Received in revised form 12 March 2010 Accepted 25 April 2010
+
+Keywords: Road safety Policy Management Attributable risk Accident data
+
+#### abstract
+
+Very considerable advances have been made in road safety over the long term and especially in the recent years. This improvement was achieved in part due to the effectiveness of French decision-making system, even if it remained very perfectible. An analysis of the road safety management system is carried out in order to understand the strengths and weaknesses of the organisation of road safety in France.
+
+The organisation of road safety in France is extremely centralised. The basis of road safety policy at the national level rests on an extensive information system (covering accidents, risk exposure, speed, utilisation of mobile phones) and on analyses of road risk (the risks attributable to alcohol, speed and the use of mobile phones).
+
+This statistical information and these risk models are integrated in risk management tools such as monitoring, ranking and policing. Monitoring makes it possible to track the development of road safety, bench-marking to compare the performance of the country's different departments with each other, and policy making to refine the details of a policy.
+
+The development of the governance of road risk is leading managers and decision-makers to perfect data-gathering procedures, standardise and simplify the analytical tools used, and broaden the range of risks covered.
+
+> -2010 Elsevier Ltd. All rights reserved.
+
+# 1. Introduction
+
+Very considerable advances have been made in road safety over the past 30 years. In France, these advances have resulted in a fall in the numbers killed on the roads by about 2% a year, whereas the volume of traffic grew by around 2.5% annually, signifying an improvement of about 4.5% in the effectiveness of road safety policies. This is in line with the long-term model of fatality risk developed on an annual basis, over 50 years, which shows a decreasing trend over time accompanied by sharp falls in risk due to national road safety measures such as speed cameras (a 48% drop between 2002 and 2008) [\(Chapelon, 2006; Lassarre and Hoyau, 2008](#page-8-0)).
+
+This improvement was achieved despite the fact that the French decision-making system remained very perfectible.
+
+This article aims to demonstrate the strengths and weaknesses of the organisation of road safety in France and to show how decision-makers are made aware of the findings of research reports and surveys and the extent to which decisions are taken and followed up on a scientific basis.
+
+E-mail addresses: [Jean.Chapelon@developpement-durable.gouv.fr](mailto:Jean.Chapelon@developpement-durable.gouv.fr) (J. Chapelon), [sylvain.lassarre@inrets.fr](mailto:sylvain.lassarre@inrets.fr) (S. Lassarre).
+
+After outlining in Section [2](#page-1-0) the organisation of road safety in France and the role played by the National Inter-Ministerial Road Safety Observatory (Observatoire National Interministériel de Sécurité Routière), we will start, in Section [3.1](#page-2-0), by discussing the basis of a policy founded on scientific findings, including the role of essential information systems such as accident records, risk exposure data, speed measurements and measurements of other behavioural phenomena, including the use of mobile phones. The evaluation of ''objective" risk through the calculation of attributable risk will be taken in Section [3.2](#page-3-0) as an example for three factors: alcohol, speeding and mobile phones. The risk models adopted are based on epidemiological methods and time series analysis, as recommended by the experts of the [OECD \(2008\).](#page-8-0)
+
+Secondly, the article will show in Section [3.3](#page-5-0) how this information and these models are integrated in three basic risk management tools:
+
+- monitoring, which makes it possible to track the development of road safety,
+- bench-marking, which enables different departments to be compared with each other, and
+- policy making, which makes it possible to refine the details of a policy.
+
+<sup>\*</sup> Corresponding author. Tel.: +33 1 4592 5764.
+
+<sup>1</sup> Tel.: +33 1 4081 2364.
+
+<span id="page-1-0"></span>We will end in Section [4](#page-7-0) by highlighting the inadequacies of the present structure, despite the progress made, and pointing to the avenues for improvement in the future as part of a discussion on the governance of road risk.
+
+### 2. French organisation of road safety and the role played by the Road Safety Observatory
+
+The Inter-Ministerial Road Safety delegate is in charge of road safety in France. He prepares the Inter-Ministerial Road Safety Committee (Comité Interministériel de Sécurité Routière – CISR) which takes decision, and implements these decisions. The interministerial character of the delegation is more paraded than real. Of course, there are five or six advisors detached from different ministries, such as Interior, Justice, Education and Health, but their ties with their ministries of origin are loose and they have very little influence over their ministry's actions in the area of road safety, which remains in the hands of the new Ministry of Sustainable Development, assisted by a Secretariat of Transport.
+
+On the other hand, the strong point in the French organisation is its hierarchical nature, with the important role played by the Prefect of each department (Fig. 1) who, together with the head of road safety projects, one of his close collaborators, coordinates the local actions of the different ministries and encourages the activities of local community groups.
+
+At the same time, the majority of road safety decisions are taken at meetings of officials on the basis of administrative and legal rather than technical and scientific factors. Scientific arguments hardly penetrate the decision-making body (CISR) or the adviser body (National Road Safety Council: Conseil National de Sécurité Routière – CNSR). The cost and effectiveness of measures are only two criteria among others. Comprehensive studies of the costeffectiveness or cost–benefit outcomes are rare, whereas this was a common practice in the 1970s.
+
+As these measures form part of the government's action programme, the way they are presented to the press and the public is extremely important. Since this tends to be determined by the political agenda, the attempt to create an effect of surprise takes precedence over in-depth studies and discussions with all the parties involved.
+
+Our knowledge of the risks and the effectiveness of measures is evolving. The effectiveness of vehicle testing, which was introduced in France in 1985 and is now in use throughout Europe, has been brought into question ([Christensen and Elvik, 2007\)](#page-8-0).
+
+Decision-making is not a regular and linear process and may be subject to comings and goings. The principle of regular medical checks decided in March 2003 was dropped a few years later, when its systematic nature raised questions about its cost and the ensuing debate highlighted the fact that the risk of error (a false negative) represented a major shortcoming of the measure, since it
+
+![](_page_1_Figure_10.jpeg)
+
+Fig. 1. Organisation of road safety in France.
+
+prevented perfectly fit drivers from driving, including some elderly people, with disastrous consequences for their daily lives ([Leproust](#page-8-0) [et al., 2008a,b\)](#page-8-0).
+
+The mission assigned to the National Inter-Ministerial Road Safety Observatory, which is under the authority of the road safety delegate, is to gather scientific information for the benefit of decision-maker in order to improve the quality of decisions, as well as to guide the activities of departmental road safety observatories (Observatoires Départementaux de Sécurité Routière – ODSR).
+
+To do that, it relies in particular on a committee of experts (Fig. 1) composed of a small number of specialists, who are not necessarily the most qualified experts themselves but are able to call on the most competent specialists in every area they have to deal with.
+
+Matters may be referred to this committee of experts by the Chairman of the National Road Safety Council or the minister responsible for road safety, or the committee may act on its own initiative.
+
+Among the most recent reports produced by the committee experts, one can cite two examples:
+
+- An in-depth study on drinking and driving, which required more than 6 months' work and for which the committee heard evidence from a score of outside personalities [\(Chapelon et al.,](#page-8-0) [2007](#page-8-0)). Produced on the committee's own initiative, the report contained some 10 recommendations, a good number of which have since been acted on (see Section 3.2.1.4).
+- A more immediate study on the advisability of introducing a specific regulation limiting young people's access to powerful vehicles, which was carried out at the request of the minister. It gave rise to a recommendation (no prohibition) that was approved by the National Road Safety Council and was adopted by the government.
+
+The last element in the organisation of road safety in France is the National Road Safety Council (Fig. 1), which is a sort of Road Safety Parliament. It enables all the parties involved in road safety (Members of Parliament, highway administrators, insurance companies, motor manufacturers, accident victim defence associations, associations representing particular categories of road user) to meet and debate all road safety issues. As far as our area of interest is concerned, it has the enormous advantage of disseminating the culture of road safety in such a way that all the parties involved have the same level of information.
+
+# 3. What is a science-based policy?
+
+Road safety policy is founded above all on the input of a system of reliable information composed of, on the one hand, quick indicators, accident records, safety performance indicators (SPI: risk exposure data, and measurements of speed and of the use of mobile phones obtained from roadside surveys) and on the other hand, estimates of the risks attributable to major factors, such as alcohol consumption, speeding, and the use of mobile phones. Lastly, it is based on the management of road risk using three preferred instruments: monitoring, bench-marking, and policy making.
+
+The following section presents the information system (Section [3.1](#page-2-0)), the attributable risk (Section [3.2](#page-3-0)), and the risk management (Section [3.3](#page-5-0)). All these analysis and tools are enforced in routine by the ONISR. The results are presented on the web-site of ONISR and CNSR.2
+
+<sup>2</sup> [www.securiteroutiere.gouv.fr/observatoire](http://www.securiteroutiere.gouv.fr/observatoire) and [www.securiteroutiere.gouv.fr/](http://www.securiteroutiere.gouv.fr/cnsr) [cnsr](http://www.securiteroutiere.gouv.fr/cnsr).
+
+#### <span id="page-2-0"></span>3.1. The information system
+
+The rule that there is no management without measures applies to the management of road safety and necessitates very broadbased information gathering [\(OECD, 2008](#page-8-0)), with some national specificities.
+
+# 3.1.1. Quick indicators (accidents, deaths, injuries and hospitalised victims)
+
+Due to the complexity of accident records (which comprise some 70 items) and of our organisation, the data took, until now before the improvement that are made (see end of Section 3.1.2), around 5 months to arrive. That is why we utilised a very simple system of quick indicators that was confined to the monthly numbers of accidents, fatalities, and injured and hospitalised victims. This system enables departmental police forces to return information to the national level within 3 or 4 days of the end of the month, making it possible for the results to be published around the seventh day of the following month.
+
+We were obliged to adjust corrector coefficients because of a number of errors, but the margin of error is less than 2%.
+
+The advantage of this organisation is that the monthly publication of road accident data by means of a press release is a big event that interests the media. As a result, the coverage given in the media is equivalent to roughly three times of the media impact of our public information campaign.
+
+#### 3.1.2. Accident records
+
+Every personal injury traffic accident must be recorded in a BAAC (analytical bulletin of a personal injury road accident), which has to be filled in by the relevant police force and comprises very full information broken down into four main parts: the characteristics and location of the accident, and the vehicles and users involved, knowing that the users are attached to the vehicles that are attached to the location.
+
+The importance of accident records for the study of accidents requires one to be concerned about their quality. That is why a project was launched in 2000 for modernising accident records, which comprised four elements: a quality plan, the simplification and updating of the form (a new BAAC-2002 standard was introduced on 1 January 2004), the harmonisation of the data (including a definition of the injury severity), and the decentralisation of the architecture (database shared between local and national levels).
+
+The first problem in quality terms relates to under-reporting: too many accidents are not recorded on a BAAC form. The reason for that may be that police forces have not been informed of the accident: that is the case in particular of minor accidents that do not disrupt the traffic, accidents involving a single vehicle, and accidents involving bicycles ([Amoros et al., 2008\)](#page-8-0).
+
+To improve the degree of under-reporting, the definition of an injured person was restated and clarified: it is a person requiring medical attention. The definition of a seriously injured person was also simplified: before, it was defined as someone who was hospitalised for at least 6 days; now, it is defined as someone who is hospitalised for at least 24 h, making it easier for the police to record him. Lastly, to reduce losses in transmission, the BAAC's indicators are now compared with the quick indicators for the numbers of killed and injured produced each day or each week by the different police forces.
+
+The decentralisation of the information-gathering architecture: in the current architecture, the record is validated at the central level and the corrections made at the local level3 are not used at the national level. In the new computer-based architecture, the mode of transmission is to remain centralised, but the creation of a shared database will enable the departmental level (prefecture, departmental development directorate, local authorities) to dispose of directly exploitable information at the earliest. The idea is to bring the producers (police forces) and consumers (prefecture, DDE, local authorities) closer together in order to improve quality. This BAAC portal has been in use since March 2009.
+
+# 3.1.3. Risk exposure
+
+The number of vehicles times the kilometres driven is the most commonly used indicator of exposure to risk, but its accuracy varies according to road network categories. It can be measured very accurately on motorways and main roads using automatic counting devices, while on departmental roads it can be extrapolated using an abacus on the basis of the number of kilometres driven on the busiest network.4 On the other hand, there is rarely a figure available for traffic on urban roads.
+
+In terms of user category, a reliable risk exposure indicator is obtained from surveys of private motor cars, commercial vehicles and heavy goods vehicles. On the other hand, only a very poor indicator is available for motor cycles, and none at all for moped, bicycles and pedestrians.
+
+# 3.1.4. Speed measurements
+
+For the past few years, the Observatory has been using investigators from a private firm to measure speed and seatbelt or crash helmet use, on the basis of a sampling plan made by INRETS.5 The data represent around 200,000 observations a year and are regularly published, in particular in the Observatory's annual report (ONISR, 2008).
+
+The survey protocol was defined as follows: the only roads retained were straight, level roads without any disruptions to traffic, with no crossroads or traffic lights over a distance of at least one kilometre before and after the measuring point, or a few hundred meters in urban areas. The idea is to choose observation sites where the drivers have no natural limit of speed and can choose their speeds. To measure speed, 362 observation points representative of the French road network were retained (285 during the day and 77 at night). The investigators – around 50 of them – proceeded during half an hour (motorways) or 1 hour (others roads) to all the points in turn to record observations following a predefined breakdown of days of the month and hours of the day, then every 4 months at the same points at the same hour and on the same day of the week. The observations were distributed so they were spread uniformly over the 4-month period and covered every day and every period of the day (between 9.30 am and 4.30 pm in the daytime and between 10.00 pm and 2.00 am at night). Almost all the measurements during the day and all the measurements at night were thus taken outside peak hours. Furthermore, given that each observation point necessitated a sequence of measurements in each direction and in each lane, more than 2000 observation sessions took place each year and more than 200,000 speed measurements were recorded and processed (the year 2008 was incomplete, with 137,507 observations having been recorded during the first 8 months).
+
+#### 3.1.5. Measuring mobile phone use
+
+Measurements were taken by investigators positioned on the roadside at 81 different locations that represented the different types of network: connecting motorways (15 locations), relief
+
+<sup>3</sup> Recovering of some lost accidents, and improving localisation, or some variables' contents (type of vehicle, date of driving licence...).
+
+<sup>4</sup> The statistical department of the ministry of ecology, energy and sustainable development is in charge of statistics for motorways and main roads, ONISR gathers data for secondary roads.
+
+<sup>5</sup> National Institute for Transport and Safety Research.
+
+<span id="page-3-0"></span>motorways (8 locations), interurban roads and country roads (23 locations), and urban roads (35 locations). These measurements were taken between 1 December 2007 and 31 March 2008, on weekdays between 10.00 am and 5.00 pm, and the observation time was 25 min per location. The vehicles observed were motor vehicles with four wheels or more: light vehicles, vans, heavy goods vehicles and buses.
+
+The investigators gathered the following information:
+
+- the driver is holding the telephone to his ear,
+- the driver is holding the telephone in his hand but not to his ear, and
+- the driver is not holding a telephone.
+
+A total of 15,335 vehicles were observed in the whole survey. It was not possible to measure the use of hands-free telephone kits reliably, however, despite the use of an electronic gadget that can detect the utilisation of a mobile phone. Additional tests will be conducted to try and develop a protocol for measuring the use of hands-free mobile phone kits.
+
+#### 3.2. Evaluating the risks
+
+Evaluating risk at a national level entails estimating the risk attributable to a road safety threat in the broadest sense of the term: either a cause, an exacerbating factor or an attenuating factor. It relies on epidemiological methods and covers general factors that are usually taken into account in matters to do with public health, but also factors that are specific to road transport in terms of infrastructure and vehicles. We then turn to a sequential accident model with temporal divisions determined by events (a sequential model), which are more suitable for formulating action plans at local level.
+
+Three factors are taken as examples: two major ones, which are drinking and driving and speeding, and a new one, the use of mobile phones, knowing that other factors could have been retained as safety belt, although the rate of use is very high in France, and in the area of infrastructure, such as the effect of passing from a section of the network in the countryside to a dual-carriageway road network.
+
+### 3.2.1. Risk attributed to alcohol
+
+Starting from 2008 data on the relationship between the amount of alcohol a driver has consumed and the risk of a road accident, we look for estimating the number of human lives that could have been saved if no one had driven with a blood–alcohol level higher than the authorised limit (0.5 g/l) which is equal by definition to the attributable risk.
+
+To do that, one has to know how much alcohol drivers have consumed.
+
+3.2.1.1. Alcohol level of drivers on the road. Little is known about the blood–alcohol level of drivers on the road (which is to say not involved in accidents). The prevalence among drivers stopped at preventive police checks in 2007 was 2.8%, but these drivers cannot be regarded as a representative sample, since the police generally target their checks.
+
+In the BAAC form, the ''person presumed responsible", information filled by the policeman,6 enables us to know the alcohol levels of drivers who are not responsible. One may consider that the characteristics of the drivers who are not responsible are representative
+
+Table 1 Percentage of drivers not responsible who are over the blood–alcohol limit (>0.5 g/l) during the week and at weekends in 2008.
+
+|               | Injury accidents (%) | Fatal accidents (%) |
+|---------------|----------------------|---------------------|
+| In the week   | 0.6                  | 1.6                 |
+| At weekends   | 1.9                  | 8.3                 |
+| All accidents | 0.9                  | 3.25                |
+
+Source: ONISR, accident records.
+
+of the characteristics of all drivers on the road, since these are drivers drawn by chance while driving. Using this method, the prevalence in 2008 was 0.9% in personal injury accidents and 3.25% in fatal accidents, the difference being due to the fact that these accidents did not happen at the same time, with the fatal accidents having tended to take place at night and during the weekend. It can be seen that the rate observed in preventive checks (2.8%) is intermediate between the two, which signifies a high degree of targeting in the checks carried out by the police.
+
+One relies that much more easily on these data insofar as a large number of pointers show that data which only interest the police, such as responsibility or alcohol levels, are very well furnished by police forces.
+
+The percentage of drivers involved in personal injury accidents who are over the blood–alcohol limit is three times greater at weekends than during the week. Furthermore, the percentage of drivers who are over the blood–alcohol limit at the time of fatal accidents is still higher (Table 1). This is attributable to the fact that these accidents happen at certain times and especially at night.
+
+3.2.1.2. Evaluating the number of fatal accidents that could be avoided. To calculate the number of fatal accidents that could be avoided, one starts from accidents in which blood–alcohol levels are known7 thanks to the use of an estimate of the relative risk. When the risk is low, the odds-ratio method is a statistical method for estimating relative risk that is based on the yield of crossover products.
+
+The percentages used are, on the one hand, the previously calculated proportion of drivers who are presumed not to be responsible and, on the other hand, the share of fatal accidents in which alcohol is involved. This is equivalent to the proportion of drivers presumed responsible who are over the blood–alcohol limit, if one makes the assumption that, where a driver presumed responsible is over the blood–alcohol limit, it is the alcohol that is mainly responsible for the accident.
+
+The proportion of drivers who are over the blood–alcohol limit is almost 10 times greater among those presumed responsible than among the reference drivers who are not responsible ([Table 2\)](#page-4-0). We select as reference drivers those who are not responsible at the time of a fatal accident, since we have seen that the day and the hour play a major role in the distribution of injury and fatal accidents.
+
+The relative risk of being responsible for a fatal accident when one has drunk, as estimated by the odds-ratio calculated from accidents with known blood–alcohol levels, is equal to 11.5. One can calculate the ''efficiency" of a driver with a blood–alcohol level below the legal limit in order to ensure that the accident in which he was involved was not fatal.
+
+His ''efficiency" would be:
+
+1 -1=odds-ratio ¼ 91%:
+
+<sup>6</sup> ONISR considers that this variable is correctly filled. In 20% of accidents, the policeman does not indicate any responsible user.
+
+<sup>7</sup> The proportion of fatal accidents with alcohol status known (either no alcohol drivers or at least one positive) is very high: 77%.
+
+<span id="page-4-0"></span>Table 2 Breakdown of drivers presumed not responsible and drivers presumed responsible in fatal accidents according to whether alcohol is present or not.
+
+| Fatal accidents                  | Alcohol (%) | No alcohol (%) |
+|----------------------------------|-------------|----------------|
+| Drivers presumed not responsible | 3.25        | 96.75          |
+| Drivers presumed responsible     | 27.9        | 72.1           |
+
+Hence, the maximum number of fatal accidents that could have been avoided if no driver had driven with a blood–alcohol above the legal limit would be:
+
+878 91.3% = 802, or 25.4% (802/3151) of the fatal accidents where blood–alcohol levels are known.
+
+3.2.1.3. Evaluating the number of human lives saved. The 878 fatal accidents involving drivers with blood–alcohol levels above the legal limit and who are presumed responsible resulted in the deaths of 972 people. In this case, one thus has an average of 1.11 people killed per accident. Applying that multiple to the 802 fatal accidents that could have been avoided, one obtains a potential minimum reduction in deaths caused by drinking and driving of:
+
+802 1.11 = 890, or 26.08% (890/3412) of those killed in fatal accidents where alcohol levels are known.
+
+Extrapolating from all accidents and assuming that accidents with indeterminate or unknown alcohol levels break down into accidents with and without alcohol in exactly the same way as those where alcohol levels are known, one could avoid around 1000 fatal accidents a year and save the lives of 1200 people.
+
+3.2.1.4. Analysing the risk attributed to alcohol. Beyond the calculation of risk, the analysis of this risk can be made: the alcohol impaired drivers represent a very small part of drivers (1%), a different situation from speed impairment (30% of drivers over speed limit and about 10% 10 km/h above speed limit). The average alcohol rate is very high: 1.6 g/l for all accidents and 1.8 g/l for fatal accidents. During the last ten years, despite all the measures taken, there has been no progress in alcohol risk reduction. This leads the expert committee to propose a new set of safety actions: confiscation of the vehicle (confiscation of the driving licence is not enough: alcoholic driver uses to drive without driving licence), improving relationship between medical driving licence committee and the doctors expert on alcohology.
+
+#### 3.2.2. Risk attributed to speeding
+
+In a certain number of cases, it is not known whether a factor of risk existed or not at the time of the accident and the odds-ratio method cannot be used to estimate the relative risk. That is the case, for example, of speeding and the use of mobile phones.
+
+In effect, very little is known about the involvement of speed in individual accidents. What is know about the effect of speed on accidents does not result directly from our knowledge of the role of speed, therefore, but from a statistical analysis of the evolution of accidents on road networks as a result of the actual speeds practised, which may rise or fall over time as a result of a change in regulations.
+
+In such a case, one method for evaluating what is at stake is to use data derived from international scientific literature, obtaining a relative risk factor from analyses of experiments on speed limits around the world.
+
+To the extent that the relationship between average speed and accidents is well known [\(Nilsson, 1974; Cohen et al., 1998; Aarts](#page-8-0) [and van Schagen, 2006\)](#page-8-0) and that it consists of a power of 4 between the variation in average speed and the variation in the rate of fatal accidents, it is possible, by calculating the relative theoretical reduction in average speed if everyone abided by the speed limit, to multiply it by a factor of 4 in order to arrive at the relative fall in fatal accidents.
+
+One could object that this distribution of speed is very theoretical and very far removed from the normal curve that is usually observed. This is what is shown by the chart below, which depicts the development of the distribution of speed on French motorways (Fig. 2). One sees that, even after the installation of speed cameras, there remains a non-negligible proportion of drivers who exceed speed limits, while at the same time a significant proportion of drivers who already abided by speed limits before 2002 reduced their speed in the following years.
+
+However, even if one knows that, whatever measures are taken, the distribution of speeds will remain very Gaussian, a definition of gains in average speed that limits the reductions in speed only to those who exceeded the speed limit seems to us to be an indicator which, although theoretical, is useful for road safety policy. In any event, road safety decision-makers would not understand an ideal objective indicator starting from the principle that there would remain an intransigent fringe when it comes to abiding by speed limits.
+
+Moreover, the same is true of the risk attributable to alcohol: there is no chance that all drivers will abide by legal blood–alcohol limits. In addition, this indicator is not that far removed from reality, since even if it is certain that one will never get all drivers to abide by speed limits, the impact on road safety will be amplified by the reductions in speed of those who already abided by the limits, as we saw in the 2002–2006 period.
+
+Retrospectively, the 10% decrease between 2001 and 2008 of the average speed contributes to a 34.5% decrease of the number of fatalities, which represents nearly three quarters (exactly 72%) of the total decrease of fatalities (48.2%).
+
+![](_page_4_Figure_19.jpeg)
+
+Fig. 2. Share of drivers below a given speed on motorways in 2001 and 2006.
+
+<span id="page-5-0"></span>Prospectively, the average speed would decrease if every driver respects speed limits by 4.8%, which would lead to a decrease of 18% of the number of fatalities, which represents the attributable risk to speed.
+
+3.2.3. Risk attributed to the use of telephones while driving
+
+3.2.3.1. General outline. As far as mobile phones are concerned, we use a method that is similar to the one used for speed, by multiplying the added risk by the risk exposure.
+
+In 2005 an Australian study [\(McEvoy et al., 2005\)](#page-8-0) sounded the alarm about the importance of the extra risk of telephoning while driving: 3.8 for hands-free sets and 4.9 for hand-held phones, thereby corroborating other studies such as the Canadian study ([Redelmeier and Tibshirani, 1997](#page-8-0)).
+
+To evaluate the risk attributable to mobile phones in France, there was a tendency not to go back to this evaluation of the added risk, taking the view that it had been well covered by McEvoy, but rather to look at the prevalence of this risk in France by observing drivers' use of telephones at the wheel.
+
+3.2.3.2. Frequency of use of mobile phones while driving. In terms of types of network, the proportion of drivers observed holding a telephone to their ear varies from 1.8% on country roads and 1.9% on urban streets to 2.6% on connecting motorway network, on which it seems most difficult to monitor this practice. Taking account of the distribution of traffic between the different networks, the average is estimated to 1.9%.
+
+When the driver is holding a telephone in his hand but not to his ear (0.5%), one may assume that it is in one of the following situations: he is reading or writing an SMS, he is dialling a number, or he is using a hands-free telephone or kit.
+
+These findings confirm that the use of handheld mobile phones while driving is not a rare event. Among motoring offences for which points are deducted from driving licences, it is the next most commonly observed one after speeding offences. The fact that a specific measure is going to be available for road traffic will make it possible to improve the monitoring of this practice and better estimate what is at stake for road safety.
+
+It should also be said that these observations were made during the day, between 10.00 am and 5.00 pm. For that reason, the use of handheld telephones may possibly have been overestimated, since one might think that drivers telephone less while driving at night, making the assumption that it is harder to find someone to talk to at that time of day. Nevertheless, as the proportion of night traffic is low (10% of the total), the results would only be marginally altered.
+
+3.2.3.3. Estimate of the potential consequences of using mobile phones while driving. Drawing on the findings of the McEvoy study, the potential consequences of the use of handheld telephones alone represent more than 7% of additional accidents, equal to 1.9% (the proportion of users) multiplied by 4.9 (relative risk) minus 1 (normal risk).
+
+On the other hand, there are more uncertainties when it comes to estimating the implications of using hands-free phone kits, given that it was not possible to measure this practice from the roadside. The results of an opinion survey carried out by the ONISR in March 2008 show that people who use mobile phones the most while driving are generally equipped with hands-free kits. One might thus think that what is at stake is certainly not negligible, and the ONISR is thinking about the best way to proceed in order to gain more reliable knowledge about the proportion of drivers who telephone using hands-free kits.
+
+Lastly, the March 2008 survey showed how the use of SMSs while driving was developing. It found that an SMS was read every 350 km and an SMS sent every 670 km by drivers who said they telephoned while driving.
+
+#### 3.3. Risk management
+
+Risk management is the way to drive the road safety policy from a sound risk assessment process which identifies the main characteristics of the road risks and their degree of acceptability. Different strategies are available to reduce the frequency and the severity of the traffic accidents: prevention, mitigation, risk avoidance, ... Risk management is based on three components:
+
+- monitoring, which makes it possible to track what is happening, once safety options have been implemented, and understand, and even anticipate, the development of the situation;
+- bench-marking, which enables the performance of each department to be compared with that of the others, when the implementation of safety measures is delegated to them, and then to benchmark the results; and
+- policy making which enables the details of a policy and of the safety options to be refined so as to make it more effective.
+
+# 3.3.1. Monitoring: monthly analysis of the situation taking account of the effects of weather and seasonal and time-of-year factors
+
+In view of the random nature of the numbers of accidents and victims, an analysis of time series is recommended to extract the trend and the seasonal effects from the irregular part.
+
+In effect, monthly data are characterised by substantial seasonal variations: traditionally, there are fewer accidents during the winter months, but they are followed by a steady increase during the spring, with the number of accidents rising to a peak during the three summer months and remaining at a high level in the autumn.
+
+These seasonal variations do not make it possible to make a direct comparison between some month and the previous month. As a result, a month is always compared with the same month the year before.
+
+The disadvantage of comparing monthly results at 12-month intervals is that there is no reference level to determine whether it was a ''good" or a ''bad" month. In particular, weather conditions have a considerable influence on the results, mainly as a result of their effect on traffic: generally speaking, good weather conditions bring an increase in traffic and hence a rise in the number of accidents. Furthermore, we do not know whether behaviour during the month in question was good or bad, whereas it would be more logical to compare it directly with the previous month, when behaviour patterns can be supposed to be similar.
+
+To facilitate comparisons between monthly results, the Observatory uses the Giboulée model developed by the SETRA8 and INRETS [\(Bergel et al., 1994](#page-8-0)) which calculates risk indicators corrected for the variations year-of-effects of weather and seasonal and time.
+
+With this correction, the Observatory calculates a monthly risk indicator in the form of an ''annual equivalent", which is interpreted in the following way: for example, given that the annual equivalent for May 2008 is 4520 and assuming that behaviour patterns remain the same during the year and that weather is neutral, the result in May 2010 will be 4520 fatalities, which makes it possible to evaluate the results for each month in comparison with an annual target.
+
+[Fig. 3](#page-6-0) shows that, whereas the results in early 2008 appeared to be positive when compared to 2007, it would be wrong to be optimistic since the outcome for 2008 reflected a bad year-end perfor-
+
+<sup>8</sup> Road and Motorway Research Agency.
+
+<span id="page-6-0"></span>![](_page_6_Figure_2.jpeg)
+
+Fig. 3. Annual equivalent of the number of deaths per month.
+
+mance, and if the same trend were to continue, the number of deaths will have increased by some 3% or 4% by the end of 2009.
+
+To sum up, we used a very sophisticated model but applied it in a very simple and pragmatic manner so as to produce clear conclusions for decision-makers.
+
+# 3.3.2. Bench marking: a method for comparing the performance of each department by standardising the risk
+
+To judge the road safety performance of a department, one traditionally has a choice between two methods: either one tracks developments from year to year, or one compares it with the performance of other departments.
+
+The drawback of the first method is that, not knowing whether the results of the previous year were good or bad, one cannot interpret developments during the current year.
+
+The drawback of the second method is that one cannot be content with a comparison between raw figures (there are large and small departments) and that one has to take account of risk exposure. Population is a totally inadequate indicator of risk exposure, since the number of kilometres driven per inhabitant is known to be very different from one department to another, ranging from 1230 vehicle-kilometres per inhabitant in Paris to 29,380 vehiclekilometres per inhabitant in the Landes ([ONISR, 2009](#page-8-0)).
+
+3.3.2.1. Basic principle of local accident indicators (LAIs). The purpose of LAIs is to provide a departmental indicator that takes account of the volume of traffic and its distribution between the different types of road network (motorways, country roads, urban areas). An LAI compares the level of risk of a department with what it would be if the department had the same levels of risk on its different networks as the whole of France.
+
+From that standpoint, the LAI is based on a classic method of standardisation, since it relates an observed degree of risk to an expected degree of risk that is estimated on the basis of the number of road deaths over five years.
+
+We distinguish between five categories of network: motorways, interurban roads, secondary roads, other country roads, and urban areas.
+
+The risk exposure indicator is the vehicles kilometres travelled or, in the case of urban areas, the population of urban districts of over 5000 inhabitants that have a central town with 5000 inhabitants or more.
+
+An LAI is defined for each department using the following formula, with j the department (from 1 to 96) and i the network (from 1 to 5), such that:
+
+- t(i, j) is the number of deaths on network i in department j;
+- e(i, j) is the risk exposure on network i in department j; and
+- r(i) is the average risk on network i throughout France.
+
+Thus
+
+$$r(i) = \frac{\sum_{j=1}^{96} t(i,j)}{\sum_{j=1}^{96} e(i,j)}$$
+
+$$LAI(j) = \frac{\sum_{j=1}^{5} t(i,j)}{\sum_{j=1}^{5} t(i,j)}$$
+
+One recognises in the LAI the classic relationship between the observed number of deaths and the expected number of deaths. The LAI makes it possible to go from an analysis in terms of an accident rate related to the population to an analysis in terms of an accident rate related to distance, applying the following simplified formula:
+
+LAI ¼ deaths=vehicles kilometres travelled
+
+- ¼ ðdeaths=inhabitantsÞ=ðvehicles
+  - kilometres travelled=inhabitantsÞ
+
+where the vehicles kilometres travelled are a weighting of the vehicles kilometres travelled observed by the average risks by network in France as a whole.
+
+Standardisation by vehicles kilometres travelled (and hence the LAI approach) provides a lot of ''explanations", since the maximum difference falls from 1 to 10 to 1 to 3 and the variance narrows from 0.36 to 0.25.
+
+Interpreting LAIs is more difficult since, to the extent that the distance factor is already taken into account, one has to turn to other explanatory factors. As a first approach, some factors grab the attention immediately. One can see, for example, that among the highest-ranked departments, the majority are departments with very marked urban characteristics and that the best results for the trunk road network are often scored by departments that have the largest networks of fast four-lane dual carriageways ([Fig. 4\)](#page-7-0).
+
+However, one may also notice that, among departments sharing similar characteristics, LAI values differ considerably, whether it is the overall LAI or LAIs by networks. With the distance factor neutralised, other factors have to be sought to interpret the differences. These variables have to be selected for their accidentinducing potential and have to be documented at the departmental level. In the current state of knowledge, the variables on which researchers are working are alcohol, seatbelts, roadside trees and shrubs, motorcycles, and the proportion of traffic on country roads.
+
+## 3.3.3. Policy making
+
+All speed measurements showed the extent to which drivers exceed speed limits in France. At the end of 2001, about 35% of motorists were found to drive at 10 km/h more than the speed limit. This highlighted what was at stake as regards speeding in France and enabled us to understand why the country was so far behind other comparable European countries [\(Delorme and Lassarre,](#page-8-0) [2005](#page-8-0)). In the light of these findings, traffic victims' associations called for tougher speed controls, which led the government to start testing automatic speed cameras in 2001–2002 and then to introduce them from 2003 onwards.
+
+The installation of 1400 fixed cameras and the deployment of 700 mobile cameras brought a substantial reduction in speed: the average speed declined by 10 km/h in 2008, with 10% of drivers driving at 10 km/h more than the speed limit. As a result, we observed a sharp fall in the number of deaths on the road – by 48% between 2001 and 2008. This example shows that knowledge had a particularly powerful impact on policy.
+
+According to the calculation of attributable risks, alcohol has now become the first factor of accidents in France, a fact that impressed the policy-makers. The analysis also underlies the main characteristics of drink driving (very small number of drivers but
+
+<span id="page-7-0"></span>![](_page_7_Figure_2.jpeg)
+
+Fig. 4. Map of the standardised rates of fatalities by department.
+
+very high rate of alcohol) what oriented the propositions of the expert committee.
+
+It's the same for the telephone when driving whose effect was before totally under-evaluated.
+
+#### 4. What governance?
+
+In terms of governance, we view the role played by the Observatory as an interface between experts and decision-makers in the transmission of information of a scientific nature for the purpose of formulating road safety policy. Information is disseminated to the media through press conferences that are programmed as a function of the political agenda. The results of expert studies are debated in more broadly-based organisations, such as the National Scientific Research Centre (CNSR), where other interested parties participate, such as motor manufacturers, insurance companies, victim defence associations and particular categories of user. This led to the decision taken in 2000 to seek to improve the quality of the information gathered and of the risk analyses carried out to guide decision-makers. Two action plans are currently being implemented to improve this process of risk evaluation: data from the road accident victims register of the department of the Rhône are being used to provide more rigorous estimators of the numbers of injured according to seriousness; and research in road safety economics is being encouraged in order to reintroduce monetary profitability criteria into decision-making, criteria that could thus be integrated into a broader, long-term sustainable approach to the road system.
+
+Additionally, the Observatory has developed a programme for evaluating the policies pursued with teams of researchers and technicians from the Ministry, and the resulting reports have been published – one on automatic speed cameras (ONISR, 2008) and one on drinking and driving (ONISR, 2007).
+
+The experience of the past few years has shown the importance of developing simple but rigorously constructed methods and tools, providing telling results for decision-makers and the public.
+
+Nevertheless, the situation is far from perfect. Firstly, these tools are perfectible, and bench-marking the methods promoted by the European Commission as part of projects like SafetyNet ([Thomas et al., 2005](#page-8-0)) will help get them shared more widely.
+
+In terms of risk selection, the Observatory does not cover all the issues, far from it. We are starting to invest in risk factors such as falling asleep at the wheel and taking medicines. The construction of risks is determined in part by networks of experts belonging to the different parties concerned, but will also depend on events, such as serious accidents, and on political and social considerations.
+
+Furthermore, experience shows that, over and beyond the results obtained and the tools used, a permanent concern is getting decision-makers to assimilate and validate them. Road safety managers need to watch out increasingly for the legalisation of the organisational process of risk management in order to preserve their own legitimacy and reputation.
+
+#### Acknowledgements
+
+We thank Nicole Muhlrad (INRETS) for assisting us in improving the english expression.
+
+#### <span id="page-8-0"></span>References
+
+- Aarts, L., van Schagen, I., 2006. Driving speed and the risk of road crashes: a review. Accident Analysis and Prevention 38 (2), 215–224.
+- Amoros, E. et al., 2008. Actual Incidences of Road Casualties, and Their Injury Severity, Modelled from Police and Hospital Data. EJPH, France.
+- Bergel, R., Girard, B., Lassarre, S., Le Breton, P., 1994. Un modèle de désaisonnalisation des indicateurs de sécurité routière. In: Carré, J.R., Lassarre, S., Ramos, M. (Eds.), Modélisation de l'insécurité routière. Tome II. Actes du séminaire 1993. Paradigme, Caen.
+- Chapelon, J., 2006. Impact du contrôle sanction automatisé sur la sécurité routière (2003–2005), ONISR. [<http://www.securiteroutiere.gouv.fr/cnsr/travaux\\_cnsr.](http://www.securiteroutiere.gouv.fr/cnsr/travaux_cnsr.htm) [htm>](http://www.securiteroutiere.gouv.fr/cnsr/travaux_cnsr.htm) (séance du 15 mars 2006).
+- Chapelon, J., Biecheler, M.B., Facy, F., Fontaine, H., Got, C., Perez-Diaz, C., Sibi, P., 2007. L'alcool sur la route: état des lieux et propositions, Comité des experts de la sécurité routière. [<http://www.securiteroutiere.gouv.fr/cnsr/travaux\\_cnsr.](http://www.securiteroutiere.gouv.fr/cnsr/travaux_cnsr.htm)
+- [htm>](http://www.securiteroutiere.gouv.fr/cnsr/travaux_cnsr.htm) (séance du 9 juillet 2007). Cohen, S., Duval, H., Lassarre, S., Orfeuil, J.-P., 1998. Limitations de vitesse – Les décisions publiques et leurs effets. Hermès, Paris.
+- Christensen, C., Elvik, R., 2007. Effects on accidents of periodic motor vehicle inspection in Norway. Accident Analysis and Prevention 39 (1), 47–52.
+- Delorme, R., Lassarre, S. (Eds.), 2005. L'insécurité routière en France dans le miroir de la comparaison internationale. La comparaison entre la France et la Grande-Bretagne. Rapport no. 216, Les collections de l' INRETS, Bron, France.
+- Lassarre, S., Hoyau, P.-A., 2008. Evolution récente du risque routier en France et en Grande-Bretagne. In: Delorme, R., Lassarre, S. (Eds.), Les régimes français et
+
+- britannique de régulation du risque routier: la vitesse d'abord. Synthèse no. 57, Les collections de l' INRETS, Bron, France.
+- Leproust, S., Lagarde, E., Salmi, L.-R., 2008a. Systematic screening for unsafe driving due to medical conditions. BMC Public Health 8, 27.
+- Leproust, S., Lagarde, E., Salmi, L.-R., 2008b. Risks and advantages of detecting individuals unfit to drive: a Markov decision analysis. Journal of General Internal Medicine 23 (11), 1796–1803.
+- McEvoy, S.P., Stevenson, M.R., McCartt, A.T., Woodward, M., Haworth, C., Palamara, P., Cercarelli, R., 2005. Role of mobile phones in motor vehicle crashes resulting in hospital attendance: a case-cross over study. British Medical Journal 331, 428–430.
+- Nilsson, G., 1974. The effects of speed limits on traffic crashes in Sweden. In: Proceedings of the International Symposium on the Effects of Speed Limits on Traffic Crashes and Fuel Consumption, Dublin, Organisation for Economy Cooperation and Development (OECD), Paris.
+- OECD, 2008. Towards Zero: Ambitious Road Safety Targets and the Safe System Approach. Paris.
+- ONISR, 2009. La sécurité routière en France: bilan de l'année 2008. La Documentation Française, Paris.
+- Redelmeier, D., Tibshirani, R., 1997. Associations between cellular–telephone calls and motor vehicle collisions. The New England Journal of Medicine 336 (7), 453–458.
+- Thomas, P. et al., 2005. Designing the European Road Safety Observatory. International Journal of Injury Control and Safety Promotion 12 (4), 251–253.

Zotero/001_artiklid/Road Safety Indicators/chengpoissonweibullgeneralizedlinear2013.md

@@ -0,0 +1,328 @@
+---
+category: literaturenote
+citekey: chengpoissonweibullgeneralizedlinear2013
+title: The Poisson–Weibull generalized linear model for analyzing motor vehicle crash data
+authors: "Cheng, Lingzi; Geedipally, Srinivas Reddy; Lord, Dominique"
+year: 2013
+date: 2013-00-00 2013
+doi: 10.1016/j.ssci.2012.11.002
+publication: Safety Science
+url: "https://doi.org/10.1016/j.ssci.2012.11.002"
+zotero_key: AGS3NFM5
+zotero_storage: N78RI3GX
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "Cheng, Lingzi"
+status: converted
+---
+![](_page_0_Picture_1.jpeg)
+
+Contents lists available at [SciVerse ScienceDirect](http://www.sciencedirect.com/science/journal/09257535)
+
+# Safety Science
+
+journal homepage: [www.elsevier.com/locate/ssci](http://www.elsevier.com/locate/ssci)
+
+![](_page_0_Picture_5.jpeg)
+
+# The Poisson–Weibull generalized linear model for analyzing motor vehicle crash data
+
+Lingzi Cheng <sup>a</sup> , Srinivas Reddy Geedipally b,1 , Dominique Lord a,⇑
+
+<sup>a</sup> Zachry Department of Civil Engineering, Texas A&M University, 3136 TAMU College Station, TX 77843-3136, USA
+
+<sup>b</sup> Texas Transportation Institute, 110N Davis Drive, Suite 101, Room 124, Arlington, TX 76013-1877, USA
+
+#### article info
+
+#### Article history: Received 25 July 2012 Received in revised form 31 August 2012 Accepted 4 November 2012 Available online 23 December 2012
+
+Keywords: Poisson–Weibull Poisson–gamma Generalized linear model Traffic crashes
+
+#### abstract
+
+Over the last 20–30 years, there has been a significant amount of tools and statistical methods that have been proposed for analyzing crash data. Yet, the Poisson–gamma (PG) is still the most commonly used and widely acceptable model. This paper documents the application of the Poisson–Weibull (PW) generalized linear model (GLM) for modeling motor vehicle crashes. The objectives of this study were to evaluate the application of the PW GLM for analyzing this kind of dataset and compare the results with the traditional PG model. To accomplish the objectives of the study, the modeling performance of the PW model was first examined using a simulated dataset and then several PW and PG GLMs were developed and compared using two observed crash datasets. The results of this study show that the PW GLM performs as well as the PG GLM in terms of goodness-of-fit statistics.
+
+> -2012 Elsevier Ltd. All rights reserved.
+
+## 1. Introduction
+
+Over the last 20–30 years, there has been a significant amount of tools and statistical methods that have been proposed for analyzing crash data. These tools are needed because of the nature of the data, which are characterized by the random and (assumed) independent discrete non-negative events. [Lord and Mannering](#page-4-0) [\(2010\)](#page-4-0) have recently documented the latest regression models that have been developed or applied for modeling crash data. Statistical models can be used for various purposes, such as establishing relationships between motor vehicle crashes and different covariates (i.e., understanding the system), predicting values or screening variables.
+
+As documented in the literature, crash data are characterized by unique attributes. They include datasets that contain a limited number of observations which can also be subjected to low sample mean values (see [Lord and Mannering, 2010; Maher and Sum](#page-4-0)[mersgill, 1996](#page-4-0), and references herein). It has been noted that these unique attributes could negatively influence regression models by providing biased estimates of regression coefficients or predicted values ([Lord, 2006](#page-4-0)). As a result, a few researchers have examined the application of alternative regression models that could be used for minimizing these problems. Some of the models include the Poisson–lognormal, the negative binomial (NB) bootstrap maximum likelihood estimation (MLE) method and the NB-Lindley model [\(Miaou et al., 2003; Zhang et al., 2007; Geedipally et al.,](#page-4-0) [2012\)](#page-4-0).
+
+In the line of the discussion above, this paper documents the application of the Poisson–Weibull (PW) regression model for analyzing crash data. Before examining the stability of this model for datasets characterized by small sample sizes and low sample mean values, there is a need to determine whether or not the PW model performs as well as the traditional NB or Poisson–gamma (PG) model. If it does not, there is no need to evaluate it in the context of the issues described above. Although not very popular in traffic safety (due to the complexity of parameterization – described below), the PW model has been applied in the other areas (see, e.g., [Wagner and Steenbakkers, 1989; Phoenix et al., 1997](#page-4-0)). In highway safety, the PW model has only been applied once [\(Maher and](#page-4-0) [Mountain, 2009\)](#page-4-0). Thus, there is a need to fully describe its modeling performance using simulated and observed datasets.
+
+The study objective was accomplished using both simulated and observed datasets. First, the general performance of the PW model was shown using the simulated data. Then the modeling performance of the PW model was compared to the PG model using two observed datasets. Several goodness-of-fit (GOF) measures were used for evaluating the models.
+
+The next section describes the characteristics of the PW distribution and its generalized linear model (GLM).
+
+<sup>⇑</sup> Corresponding author. Tel.: +1 (979) 458 3949; fax: +1 (979) 845 6481. E-mail addresses: [lingzi\\_cheng@tamu.edu](mailto:lingzi_cheng@tamu.edu) (L. Cheng), [srinivas-g@ttimail.tamu.](mailto:srinivas-g@ttimail.tamu. edu) [edu](mailto:srinivas-g@ttimail.tamu. edu) (S.R. Geedipally), [d-lord@tamu.edu](mailto:d-lord@tamu.edu) (D. Lord).
+
+<sup>1</sup> Tel.: +1 (817) 462 0519x11519.
+
+#### <span id="page-1-0"></span>2. Background
+
+This section describes the characteristics and parameterization of the PW GLM. First, the statistical background about the PW is provided. Then, the second part illustrates the parameterization of the PW model.
+
+## 2.1. Characteristics of the PW GLM
+
+The PW distribution is a mixture of Poisson and Weibull distributions, as the name implies. Similar to most Poisson-based distributions (e.g., Poisson–gamma, Poisson–lognormal, etc.), the PW model is also designed to accommodate the over-dispersion ([McCullagh and Nelder, 1993; Raghavachari et al., 1997; Lord](#page-4-0) [et al., 2005; Maher and Mountain, 2009](#page-4-0)).
+
+First, the Poisson and Weibull distributions need to be defined, respectively. Crash data can be characterized as the product of Bernoulli trials with unequal probability of events (also known as Poisson trials). As the number of trials increases the distribution may approximately follow a Poisson process and the amount of dispersion is governed by the characteristics of this process ([Lord](#page-4-0) [et al., 2005\)](#page-4-0). Thus, the number of crashes at ith roadway entity Yi is assumed to be Poisson distributed with mean l<sup>i</sup> and independent over all entities:
+
+$$Y_i | \mu_i \sim \text{Poisson}(\mu_i) \quad i = 1, 2, 3, \dots, I$$
+ (1)
+
+The Poisson mean l<sup>i</sup> is structured as:
+
+$$\mu_i = \hat{\mu}_i \varepsilon_i = f(\mathbf{X}; \mathbf{\beta}) \cdot \varepsilon_i \tag{2}$$
+
+and,
+
+$$\hat{\mu}_i = f(\mathbf{X}; \mathbf{\beta}) = \exp(\beta_0 + \sum_{j=1}^q \beta_j X_j), j = 1, 2, 3, \dots, q$$
+ (3)
+
+where Xs are the independent variables; q represents the total number of independent variables; bs are the regression coefficients; and e<sup>i</sup> is the model error independent of all covariates ([Cameron and](#page-4-0) [Trivedi, 1998; Miaou and Lord, 2003; Lord and Park, 2010\)](#page-4-0).
+
+For the PW model, it is assumed that e<sup>i</sup> is independent of all covariates and Weibull distributed. This is used for capturing the extra variation that the traditional Poisson cannot fully handle. The Weibull probability density function (PDF) is given as follows:
+
+$$f(x) = \frac{k}{\lambda} \left( \frac{x}{\lambda} \right)^{k-1} \exp\left[ -\left( \frac{x}{\lambda} \right)^k \right] \quad x > 0, k > 0, \lambda > 0$$
+ (4)
+
+where k and k are scale and shape parameters, respectively. The PDF of the Weibull distribution has a wide variety of shapes depending on the k values and the shape can be similar to that of the gamma, gamma-like, exponential or approximate normal distributions. This characteristic gives the model a lot of flexibility to fit different kinds of data.
+
+The mean and variance of the Weibull distribution are:
+
+$$E(\varepsilon) = \lambda \Gamma \left(1 + \frac{1}{k}\right)$$
+
+$$Var(\varepsilon) = \lambda^2 \Gamma \left(1 + \frac{2}{k}\right) - \left[\lambda \Gamma \left(1 + \frac{1}{k}\right)\right]^2$$
+(5)
+
+Given the statistical characteristics of Poisson and Weibull distributions, the PW distribution is defined as the mixture of those two distributions such that
+
+$$P(Y = y; \mu, \lambda, k) = \int Poisson(y; \hat{\mu}\varepsilon) Weibull(\varepsilon; \lambda, k) d\varepsilon$$
+ (6)
+
+The mean or expected value of the PW distribution is given as:
+
+$$E(Y) = \hat{\mu}E(\varepsilon) = \hat{\mu} \times \lambda \Gamma\left(1 + \frac{1}{k}\right)$$
+ (7)
+
+and the variance is given by:
+
+$$Var(Y) = \hat{\mu} \times \lambda \Gamma \left( 1 + \frac{1}{k} \right) + \hat{\mu}^2 \times \lambda^2 \Gamma \left( 1 + \frac{2}{k} \right) - \hat{\mu}^2$$
+
+$$\times \left[ \lambda \Gamma \left( 1 + \frac{1}{k} \right) \right]^2$$
+(8)
+
+#### 2.2. Parameter estimation
+
+As discussed above, the likelihood function for the PW GLM was given by Eq. (6). An important characteristic of the PW distribution is that the likelihood function does not have a closed form. However, this can be solved by using a hierarchical representation of this function. As discussed above, the PW model is conditional on the site-specific error term e which explains the additional heterogeneity. Therefore, the PW model can be also written as:
+
+$$P(Y = y; \mu | \varepsilon) = Poisson(y; \hat{\mu}\varepsilon)$$
+  
+ $\varepsilon \sim Weibull(\varepsilon; \lambda, k)$  (9)
+
+The formulation above has a nice Bayesian interpretation and hierarchical structure. Therefore, the parameter estimation and inference can be obtained by using Markov chain Monte Carlo (MCMC) and software such as WinBUGS [\(Spiegelhalter et al.,](#page-4-0) [2003](#page-4-0)). Since the Bayesian formulation requires priors for all unknown parameters, non-informative normal priors for bs and gamma priors for xð¼ 1=k<sup>k</sup> Þ and k were used.
+
+The total number of iterations was determined using the Gelman–Rubin (G–R) statistic ([Gelman and Rubin, 1992; Brooks and](#page-4-0) [Gelman, 1998\)](#page-4-0). The G–R convergence statistic is generally used to verify that the simulation runs converged properly and is based on analyzing multiple simulated MCMC chains (usually 3–5 chains) by comparing the variances within each chain and the variance between chains. A total of three Markov chains were used in the coefficient estimation process so that the G–R diagnostic was performed accurately. For model comparison, it was suggested that convergence was achieved when the G–R statistic was less than 1.2 ([Mitra and Washington, 2007\)](#page-4-0). The first half of iterations was used as burn-in samples and was discarded. Thus, the remaining half of the iterations was used for estimating the coefficients.
+
+# 3. Methodology
+
+This section describes the functional form and the GOF statistics that were used for comparing the PW GLM with the PG GLM. The PG model is one of the most commonly used models in highway safety application ([Hauer, 1997; Lord, 2006; Lord and Mannering,](#page-4-0) [2010](#page-4-0)). The characteristics of the PG GLM can be found in other documents (see, e.g., [Hilbe, 2011](#page-4-0)).
+
+The functional form used for model development is as follows:
+
+$$\hat{\mu}_i = \beta_0 \times L_i \times F_i^{\beta_1} \times y \times e^{j-2} X_{ij} \beta_j$$
+(10)
+
+where l<sup>i</sup> is the estimated number of crashes per year for site i; Fi the vehicles per day (ADT) for segment i; Li the length of segment i in miles; y the number of years of crash data; Xij the a series of covariates (e.g., shoulder width, lane width, etc.) for site i; n the number of covariates; and b<sup>s</sup> is the estimated coefficients.
+
+The GOFs used in this study for comparing the PW and PG GLMs included the Deviance Information Criterion (DIC), the Mean Absolute Deviance (MAD), the Mean Squared Predictive Error (MSPE) and the Pearson Chi-square (v<sup>2</sup> ). The DIC is often used as a GOF measurement when Bayesian estimation method is used ([Mitra](#page-4-0) [and Washington, 2007; Lord and Park, 2010; Geedipally et al.,](#page-4-0) [2012](#page-4-0)). In general, a smaller DIC value refers to a better model fit. As a rule of thumb, differences in the DIC values more than 10 will rule out the model with a higher DIC and a difference between 5 and 10 can be considered substantial [\(Spiegelhalter et al., 2002\)](#page-4-0). However, it is important to point out that the DIC is dependent on the structure of the model. Thus, as discussed by [Mitra and](#page-4-0) [Washington \(2007\)](#page-4-0), and [Lord and Park \(2008\),](#page-4-0) it is recommended to use more than one GOF measure for evaluating regression models.
+
+The MAD, MSPE and Pearson v<sup>2</sup> are three common GOF measurements that are also utilized for assessing how well the model fit the data. Generally, a model with a smaller value shows a better statistical fit. Interested readers are referred to [Oh et al. \(2003\)](#page-4-0) for additional information about these GOF measures.
+
+#### 4. Data description
+
+Two datasets are used in this study for comparing the modeling performance of the PW and PG GLMs. This section describes the characteristics of these two datasets.
+
+## 4.1. Indiana data
+
+Five years (1995–1999) of crash and traffic data collected at 338 rural interstate road segments in the state of Indiana were used for the model development. This dataset was utilized by [Anastasopo](#page-4-0)[ulos et al. \(2008\), Washington et al. \(2011\) and Geedipally et al.](#page-4-0) [\(2012\)](#page-4-0) for developing tobit and NB-Lindley models. Table 1 summarizes the key traffic and geometric variables. For a complete and detailed description of the variables, the interested reader is referred to [Washington et al. \(2011\).](#page-4-0)
+
+### 4.2. Texas data
+
+Crash data from 1997 to 2001 collected at 4-lane rural undivided in Texas were provided by the Texas Department of Public Safety (DPS) and the Texas Department of Transportation (TxDOT). This dataset was used by [Lord et al. \(2008a,b\)](#page-4-0) for the project titled ''NCHRP 17-29: Methodology to Predict the Safety Performance of Rural Multilane Highways'' and the evaluation of the Conway– Maxwell–Poisson GLM, respectively. The final database included 1499 segments (P0.1 mile). [Table 2](#page-3-0) presents the summary statistics of the data.
+
+#### 5. Modeling results
+
+This section presents the modeling results for the PW and PG GLMs based on simulated and observed data.
+
+#### 5.1. Simulated data
+
+This section presents the modeling results for the simulated data that are intended to illustrate the general performance of the PW model. The simulation design was carried out in several steps:
+
+Table 1 Indiana data summary.
+
+| Traffic variable                                       | Minimum | Maximum | Average (std. dev.) | Total  |
+|--------------------------------------------------------|---------|---------|---------------------|--------|
+|                                                        |         |         |                     |        |
+| Crashes (for 5 years)                                  | 0       | 329     | 16.97(36.30)        | 5737   |
+| Average daily traffic (ADT) (veh./day)                 | 9442    | 143,422 | 30237.56(28776.43)  | _      |
+| Minimum friction on road segment (FR) (0–100 scale)    | 15.90   | 48.20   | 30.51(6.67)         | _      |
+| Pavement surface (PS) (asphalt = 1, concrete = 0)      | 0       | 1       | 0.77(0.42)          | _      |
+| Median width (MW) (ft)                                 | 16      | 194.7   | 66.98(34.71)        | _      |
+| Median barrier (MB) (present = 1, absent = 0)          | 0       | 1       | 0.16(0.37)          | _      |
+| Interior rumble strips (IRS) (Present = 1, absent = 0) | 0       | 1       | 0.72(0.45)          | _      |
+| Segment length (L) (miles)                             | 0.009   | 11.53   | 0.89(1.48)          | 300.09 |
+
+(1) Generate a true mean value (qi) for roadway entity i from a fixed sample population mean (d):
+
+$$\rho_i = \delta \tag{11}$$
+
+(2) Generate a value (ei) from a Weibull distribution with parameters k and k. Here, the mean of the Weibull distribution is equal to 1. The values for k and k are determined based on the dispersion parameter (DP) of the NB model (VarðYÞ ¼ l þ al2, where a is the DP) in order to better illustrate the level of dispersion based on a regression model commonly used in highway safety:
+
+$$\varepsilon_i \sim \text{Weibull}(k, \lambda)$$
+ (12)
+
+(3) Calculate the mean ðl<sup>i</sup> Þ for roadway entity i: l<sup>i</sup> ¼ q<sup>i</sup> e<sup>i</sup> ð13Þ
+
+(4) Generate a discrete value ðYiÞ for entity i from a Poisson dis-
+
+tribution with mean equal to 
+$$\mu_i$$
+:  
+ $Y_i \sim \text{Poisson}(\mu_i)$  (14)
+
+(5) Repeat steps 1–4 ''N'' times, where ''N'' is the required number of observations (which is also the sample size).
+
+To avoid the potential bias associated with the small sample size and low sample mean (see [Lord, 2006\)](#page-4-0), the following values were considered:
+
+- (a) Sample size ''N'' = 300.
+- (b) Sample population mean ''d'' = 10.
+- (c) DP ''a'' = 0.5, 1, 2, 3, 5.
+
+The theoretical values for k and k were calculated and labeled as ''true'' parameters for each dispersion level. By following the steps above, crashes or counts are then simulated using the PW distribution. Once the crash dataset was created, the parameters were reestimated using the PW model and then compared with the ''true'' parameters.
+
+[Table 3](#page-3-0) presents the modeling results for the simulated dataset. This table shows that PW model was able to reproduce the ''true'' parameter values. All parameter were statistically significant at the 5% level.
+
+#### 5.2. Indiana data
+
+[Table 4](#page-3-0) summarizes the coefficient estimates and GOF statistics of the PG and PW models for the Indiana data. The segment length was treated as an offset and thus the crash frequency increases linearly with the increase in segment length. For both PG and PW models, the estimated coefficient for the traffic flow is less than 1. This indicates that with the increase in the traffic flow, the crash risk increases as the flow increases. It should be noted that the 95% marginal posterior credible intervals for each coefficient estimate did not include the origin. [Table 4](#page-3-0) shows that all the estimated coefficients between the two models have the same sign, and most of their coefficients are very close. The standard errors for both
+
+<span id="page-3-0"></span>Table 2 Texas data summary.
+
+| Traffic variable                       | Minimum | Maximum | Average (std. dev.) | Total  |
+|----------------------------------------|---------|---------|---------------------|--------|
+| Crashes (for 5 years)                  | 0       | 97      | 2.84(5.69)          | 4253   |
+| Average daily traffic (ADT) (veh./day) | 42      | 24,800  | 6613.61(4010.01)    | _      |
+| Lane width (LW) (ft)                   | 9.75    | 16.5    | 12.57(1.59)         | _      |
+| Total shoulder width (SW) (ft)         | 0       | 40      | 9.96(8.02)          | _      |
+| Curve density (CD) (curves/mile)       | 0       | 18.07   | 1.43(2.35)          | _      |
+| Segment length (L) (miles)             | 0.1     | 6.28    | 0.55(0.67)          | 830.49 |
+
+Table 3 Modeling results for the simulated data.
+
+| Dispersion Level             | a = 0.5 |         | a = 1.0 |         | a = 2.0 |         | a = 3.0 |         | a = 5.0 |         |
+|------------------------------|---------|---------|---------|---------|---------|---------|---------|---------|---------|---------|
+| Parameters                   | k       | x       | k       | x       | k       | x       | k       | x       | k       | x       |
+| Theoretical values           | 1.436   | 0.871   | 1.000   | 1.000   | 0.721   | 0.936   | 0.607   | 0.935   | 0.500   | 1.414   |
+| Estimated values (std. dev.) | 1.446   | 0.873   | 1.000   | 0.993   | 0.731   | 0.931   | 0.607   | 0.936   | 0.506   | 1.414   |
+|                              | (0.080) | (0.061) | (0.053) | (0.065) | (0.038) | (0.060) | (0.032) | (0.061) | (0.029) | (0.084) |
+
+x ¼ 1=k<sup>k</sup> where k; k are the shape and scale parameters respectively in Eq. [\(4\).](#page-1-0) The Weibull distribution was re-parameterized since WinBUGS uses a slightly different parameterization than the one discussed above. This did not influence the model performance.
+
+Table 4 Modeling results for the Indiana data.
+
+| Variable          | PG       |          | PW       |          |  |  |
+|-------------------|----------|----------|----------|----------|--|--|
+|                   | Value    | S.E.     | Value    | S.E.     |  |  |
+| Intercept (ln b0) | 4.627    | 1.354    | 4.022    | 1.377    |  |  |
+| ADT (b1)          | 0.7029   | 0.1254   | 0.6428   | 0.1243   |  |  |
+| FR (b2)           | 0.02589  | 0.01048  | 0.02713  | 0.01128  |  |  |
+| PS (b3)           | 0.4226   | 0.1874   | 0.4267   | 0.1992   |  |  |
+| MW (b4)           | 0.005169 | 0.001906 | 0.005489 | 0.002007 |  |  |
+| MB (b5)           | 3.035    | 0.3047   | 2.99     | 0.3093   |  |  |
+| IRS (b6)          | 0.3901   | 0.1866   | 0.4113   | 0.1987   |  |  |
+| /                 | 1.089    | 0.1392   |          |          |  |  |
+| xa                |          |          | 0.9959   | 0.316    |  |  |
+| k                 |          |          | 0.9805   | 0.07021  |  |  |
+| DIC               | 1486.47  |          | 1450.67  |          |  |  |
+| Pearson v2        | 1009.406 |          | 1003.086 |          |  |  |
+| MAD               | 6.919    |          | 7.014    |          |  |  |
+| MSPE              | 209.909  |          | 231.476  |          |  |  |
+
+<sup>a</sup> x ¼ 1=kk.
+
+models are also very similar. Though the PG and PW model have the same hierarchical structure, there is an extra parameter in the PW model. This is because the shape and scale parameters are assumed to be the same in the PG model, but not for the PW model. However, this extra parameter does not add any additional burden with regards to coding and running the PW model in Win-BUGS [\(Spiegelhalter et al., 2003](#page-4-0)) compared to the PG model.
+
+# 5.3. Texas data
+
+Table 5 summarizes the modeling results for the Texas data. The functional form used is similar to the one used for Indiana dataset. Like the previous dataset, the segment length was considered as an offset in the model. All the coefficients are significant at 5% level. In general, all the estimated coefficients are logical and consistent with the existing literature. The increase in the traffic flow and the horizontal curve density increases the crash risk, whereas the increase in lane width and shoulder width decreases the risk.
+
+# 6. Discussion
+
+There are two relevant points that need to be discussed. First, the results using the simulated data have shown that the PW model was able to reproduce the ''true'' parameters. Second, it was
+
+Table 5 Modeling results for the Texas data.
+
+| Variable          | PG      |        | PW      |        |  |
+|-------------------|---------|--------|---------|--------|--|
+|                   | Value   | S.E.   | Value   | S.E.   |  |
+| Intercept (ln b0) | 6.3590  | 0.3907 | 6.2280  | 0.4298 |  |
+| ADT (b1)          | 0.9770  | 0.0424 | 0.9682  | 0.0430 |  |
+| LW (b2)           | 0.0532  | 0.0169 | 0.0509  | 0.0163 |  |
+| SW (b3)           | 0.0100  | 0.0033 | 0.0101  | 0.0033 |  |
+| CD (b4)           | 0.0674  | 0.0121 | 0.0694  | 0.0122 |  |
+| /                 | 2.5510  | 0.2338 |         |        |  |
+| xa                |         |        | 1.0130  | 0.3068 |  |
+| k                 |         |        | 1.6290  | 0.0817 |  |
+| DIC               | 4784.45 |        | 4771.61 |        |  |
+| Pearson v2        | 1798.14 |        | 1869.32 |        |  |
+| MAD               | 1.70    |        | 1.69    |        |  |
+| MSPE              | 11.24   |        | 11.43   |        |  |
+
+<sup>a</sup> x ¼ 1=kk.
+
+shown that the PW GLM offers potential for modeling traffic crash data and performs as well as the PG model. As detailed in the modeling results for two observed datasets, both models provided similar GOF statistics. In addition, the computational time for both the models in WinBUGS is very similar.
+
+Given the fact that the PW GLM has so far not been applied often, there are many lines of research activities that could be investigated. First, as discussed above, crash data can sometimes be subjected to very low sample mean values or very sample sizes. Consequently, the PG model do not perform well with such datasets since the inverse dispersion parameter can be significantly biased (or mis-estimated). This can negatively influence the standard errors associated with the model's coefficient. Therefore, the further work is needed on examining the stability of the PW model when the data are characterized by low sample mean and small sample size.
+
+Second, since the empirical Bayes (EB) method is now frequently used in highway safety, an EB modeling framework should be development for the PW model. The approach used by [Zou et al.](#page-4-0) [\(2013\)](#page-4-0) to develop the EB framework for the Sichel model could be utilized. Third, the use of the PW GLM to identify hazardous sites should also be investigated. Fourth, even though the analysis was executed by assuming a fixed shape parameter (independent of covariates) in the Weibull distribution, further work should be accomplished to examine the effects of a variable-dependent shape parameter. Finally, a well-defined likelihood function and the <span id="page-4-0"></span>related moments for the PW model should be built. This way, the MLE method could be used for estimating PW GLMs.
+
+#### 7. Summary and conclusions
+
+This paper has described the application of the PW GLM for modeling traffic crashes. Although the PW GLM has been used in other fields, it has only been applied once in traffic safety (Maher and Mountain, 2009). The PW model was developed using a Bayesian framework and its general modeling performance was examined using the simulated dataset. The comparison of the PW and PG models was performed using two observed crash datasets. The comparison analysis was carried out using the most common functional form used by transportation safety analysts, which link crashes to the traffic flows and geometric variables. The results of this study show that the PW GLMs perform as well as the PG model in terms of GOF statistics. If the PW model performs well and offers stability when the data are characterized by low sample mean and small sample size values, then it could potentially offer a better alternative over the PG model for modeling motor vehicle crashes.
+
+#### References
+
+- Anastasopoulos, P., Tarko, A., Mannering, F.L., 2008. Tobit analysis of vehicle accident rates on interstate highways. Accident Analysis and Prevention 40 (2), 768–775.
+- Brooks, S.P., Gelman, A., 1998. General methods for monitoring convergence of iterative simulations. Journal of Computational and Graphical Statistics 7 (4), 434–455.
+- Cameron, A.C., Trivedi, P.K., 1998. Regression Analysis of Count Data. Cambridge University Press, Cambridge, UK.
+- Geedipally, S.R., Lord, D., Dhavala, S.S., 2012. The negative binomial-Lindley generalized linear model: characteristics and application using crash data. Accident Analysis and Prevention 45 (2), 258–265.
+- Gelman, A., Rubin, D.B., 1992. Inference from iterative simulation using multiple sequence. Statistical Science 7 (4), 457–511.
+- Hauer, E., 1997. Observational before-after studies in road safety: estimating the effect of highway and traffic engineering measures on road safety. Elsevier Science Ltd., Oxford.
+- Hilbe, J.M., 2011. Negative Binomial Regression, second ed. Cambridge University Press, Cambridge, UK.
+- Lord, D., 2006. Modeling motor vehicle crashes using Poisson–gamma models: examining the effects of low sample mean values and small sample size on estimation of the fixed dispersion parameter. Accident Analysis and Prevention 38 (4), 751–766.
+- Lord, D., Mannering, F.L., 2010. The statistical analysis of crash frequency data: a review and assessment of methodological alternatives. Transportation Research Part A: Policy and Practice 44 (5), 291–305.
+
+- Lord, D., Park, B.-J., 2010. Appendix D-negative binomial regression models and estimation methods. In: CrimeStat Version 3.3 Update Notes: Part 2: Regression Modeling, The National Institute of Justice, Washington, DC.
+- Lord, D., Geedipally, S.R., Persaud, B.N., Washington, S.P., Schalkwyk, I., Ivan, J.N., Lyon, C., Jonsson, T., 2008a. NCHRP Web-only document 126: methodology to predict the safety performance of rural multilane highways. [<http://](http://www.onlinepubs.trb.org/onlinepubs/nchrp/nchrp_w126.pdf) [onlinepubs.trb.org/onlinepubs/nchrp/nchrp\\_w126.pdf>](http://www.onlinepubs.trb.org/onlinepubs/nchrp/nchrp_w126.pdf).
+- Lord, D., Guikema, S.D., Geedipally, S.R., 2008b. Application of the Conway– Maxwell–Poisson generalized linear model for analyzing motor vehicle crashes. Accident Analysis and Prevention 40 (3), 1123–1134.
+- Lord, D., Park, P.Y.-J., 2008. Investigating the effects of the fixed and varying dispersion parameters of Poisson–gamma models on empirical Bayes estimates. Accident Analysis and Prevention 40 (4), 1441–1457.
+- Lord, D., Washington, S.P., Ivan, J.N., 2005. Poisson, Poisson–gamma and zeroinflated regression models of motor vehicle crashes: balancing statistical fit and theory. Accident Analysis and Prevention 37 (1), 35–46.
+- Maher, M., Mountain, L., 2009. The sensitivity of estimates of regression to the mean. Accident Analysis and Prevention 41 (4), 861–868.
+- Maher, M.J., Summersgill, I., 1996. A comprehensive methodology for the fitting predictive accident models. Accident Analysis and Prevention 28 (3), 281–296. Miaou, S.-P., Song, J.J., Mallick, B.K., 2003. Roadway traffic-crash mapping: a space-
+- time modeling approach. Journal of Transportation and Statistics 6 (1), 33–57. McCullagh, P., Nelder, J.A., 1983. Generalized Liner Models. Chapman and Hall,
+- London, UK. Miaou, S.-P., Lord, D., 2003. Modeling traffic-flow relationships at signalized intersection: dispersion parameter, functional form, and Bayes versus empirical Bayes. Transportation Research Record No.1840, 31–40.
+- Mitra, S., Washington, S., 2007. On the nature of over-dispersion in motor vehicle crash prediction models. Accident Analysis and Prevention 39 (3), 459–468.
+- Oh, J., Lyon, C., Washington, S., Persaud, B., Bared, J., 2003. Validation of FHWA crash models for rural intersections: lessons learned. Transportation Research Record 1840, 41–49.
+- Phoenix, S.L., Ibnabdeljalil, M., Hui, C.-Y., 1997. Size effects in the distribution for strength of brittle matrix fibrous composites. International Journal of Solids Structures 34 (5), 545–568.
+- Raghavachari, M., Srinivasan, A., Sullo, P., 1997. Poisson mixture yield models for integrated circuits: a critical review. Microelectronics Reliability 37 (4), 565– 580.
+- Spiegelhalter, D.J., Best, N.G., Carlin, B.P., Linde, A., 2002. Bayesian measures of model complexity and fit (with discussion). Journal of the Statistical Society: Series B 64 (4), 583–639.
+- Spiegelhalter, D.J., Thomas, A., Best, N.G., Lun, D., 2003. WinBUGS Version 1.4.1 User Manual. MRC Biostatistics Unit, Cambridge. Available from: <http:// www.mrcbsu. cam.ac.uk/bugs/welcome.shtml>.
+- Wagner, H.D., Steenbakkers, L.W., 1989. Stochastic strength and size effect in ultrahigh strength polyethylene fibres. Philosophical Magazine Letters 59 (2), 77–85. Washington, S.P., Karlaftis, M.G., Mannering, F.L., 2011. Statistical and Econometric
+- Methods for Transportation Data Analysis, second ed. Chapman and Hall/CRC, Boca Raton, FL.
+- Zhang, Y., Ye, Z., Lord, D., 2007. Estimating the dispersion parameter of the negative binomial distribution for analyzing crash data using a bootstrapped maximum likelihood method. Transportation Research Record 2019, 15–21.
+- Zou, Y., Lord, D., Zhang, Y., Peng, Y., 2013. Comparison of sichel and negative binomial models in estimating empirical Bayes estimates. Paper 13-2938. Presented at the 92nd Annual Meeting of the Transportation Research Board, 2013, Washington, D.C.

Zotero/001_artiklid/Road Safety Indicators/choidosilverzonesreduce2018.md

@@ -0,0 +1,336 @@
+---
+category: literaturenote
+citekey: choidosilverzonesreduce2018
+title: "Do Silver Zones reduce auto-related elderly pedestrian collisions? Based on a case in Seoul, South Korea"
+authors: "Choi, Yunwon; Yoon, Heeyeun; Jung, Eunah"
+year: 2018
+date: 2018-00-00 2018
+doi: 10.1016/j.aap.2018.07.005
+publication: "Accident Analysis & Prevention"
+url: "https://doi.org/10.1016/j.aap.2018.07.005"
+zotero_key: RGDSQTFM
+zotero_storage: SK96UGPA
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "Choi, Yunwon"
+status: converted
+---
+![](_page_0_Picture_1.jpeg)
+
+Contents lists available at [ScienceDirect](http://www.sciencedirect.com/science/journal/00014575)
+
+# Accident Analysis and Prevention
+
+journal homepage: [www.elsevier.com/locate/aap](https://www.elsevier.com/locate/aap)
+
+![](_page_0_Picture_5.jpeg)
+
+# Do Silver Zones reduce auto-related elderly pedestrian collisions? Based on a case in Seoul, South Korea
+
+![](_page_0_Picture_7.jpeg)
+
+Yunwon Choi[a](#page-0-0) , Heeyeun Yoon[b,](#page-0-1)[c,](#page-0-2) [\\*](#page-0-3), Eunah Jung[c](#page-0-2)
+
+- <span id="page-0-0"></span><sup>a</sup> *Interdisciplinary Program in Landscape Architecture, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-742, Republic of Korea*
+- <span id="page-0-1"></span><sup>b</sup>*Department of Landscape Architecture and Rural Systems Engineering, College of Agriculture and Life Sciences, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-921, Republic of Korea*
+- <span id="page-0-2"></span>c *Research Institute of Agriculture and Life Sciences, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-921, Republic of Korea*
+
+#### ARTICLE INFO
+
+*Keywords:* Silver Zone Pedestrian safety Generalised linear model Difference-in-difference Bivariate Moran's I Kernel density mapping
+
+#### ABSTRACT
+
+Inaugurated in 2007, in Seoul, South Korea, the Silver Zone is a designated pedestrian safety zone for the elderly that adopts speed limit measures such as traffic signage and road surface markings. In this study, we empirically investigate the effectiveness of the Silver Zone in two respects: first, whether the establishment of the Silver Zone has lowered the number of elderly pedestrian collisions, and second, whether Silver Zones are established in the appropriate areas, that is, those with the highest frequency of such collisions. From our quasi-experimental statistical analysis, Difference-in-Difference, we learn that the Silver Zone has no effects on reducing elderly pedestrian collisions. From our spatial statistical analyses—Kernel Density mapping and Bivariate Moran's I—we found a spatial mismatch between the frequency of senior pedestrian-vehicular collisions and the location of Silver Zones. For better performance of the Silver Zone system, we suggest additional types of physical measures to be integrated into the Silver Zone system. Municipal-level comprehensive master plan for Silver Zone system is also necessary, under which local governments should use periodic surveys to inventory and prioritise the locations of highest elderly pedestrian-vehicular collisions.
+
+# **1. Introduction**
+
+As the world's population rapidly ages, with the ratio of the elderl[y1](#page-0-4) growing from the current 11% to 22% of the population by 2050 ([United Nations, 2015](#page-9-0)), many societies have made efforts to create healthier and safer environments for senior citizens ([Zhao, 2014;](#page-9-1) [Li and](#page-8-0) [Zhao, 2015\)](#page-8-0). Improving neighbourhood walkability, as an integral part of daily life, is one strategy towards this goal ([Hahm et al., 2017;](#page-8-1) [Kim](#page-8-2) [et al., 2014](#page-8-2)). Walking is both a means of exercise and transportation for the elderly. As they experience physical and cognitive losses, they forgo driving and taking public transit to avoid collisions, while maintaining physical activity [\(Piatkowski et al., 2015;](#page-8-3) [Burbidge and Goulias, 2009](#page-8-4)).
+
+Elderly pedestrian-vehicular collisions, however, are a serious problem [\(Rosenbloom et al., 2016;](#page-9-2) [Cœugnet et al., 2017\)](#page-8-5). While pedestrian deaths account for 22% of all vehicle-related casualties, approximately 40% of those involve the elderly[2](#page-0-5) [\(International Transport Forum,](#page-8-6) [2014\)](#page-8-6). This number has been increasing along with the aging population in many member countries of the Organization for Economic Cooperation and Development (OECD). Especially, increase of the traffic volume in high-density cities in the East Asia is a threat to elderly pedestrian safety ([Zhao et al., 2014](#page-9-3)). South Korea is no exception. Currently, elderly pedestrian collisions account for 40% of all vehicle-related casualties ([International Transport Forum, 2014;](#page-8-6) [Whi, 2015](#page-9-4)).
+
+In order to protect elderly pedestrians from collisions, the South Korean government established the Silver Zone system in 2007. The system mandates areas as safety zones where speed-limit measures, such as traffic signage and road surface markings, caution drivers about the presence of elderly pedestrians. The similar systems in other countries are Silver Zone[3](#page-0-6) and Green Man Plus system[4](#page-0-7) in Singapore and Safe Routes for Seniors program[5](#page-0-8) in the U.S.A. ([Fwa, 2016;](#page-8-7) [Tan,](#page-9-5)
+
+*E-mail addresses:* [yunwon.choi@snu.ac.kr](mailto:yunwon.choi@snu.ac.kr) (Y. Choi), [hyyoon@snu.ac.kr](mailto:hyyoon@snu.ac.kr) (H. Yoon), [jea0610@snu.ac.kr](mailto:jea0610@snu.ac.kr) (E. Jung). 1Age group of 60+
+
+<span id="page-0-3"></span><sup>⁎</sup> Corresponding author at: Department of Landscape Architecture and Rural Systems Engineering, College of Agriculture and Life Sciences, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-921, Republic of Korea.
+
+<span id="page-0-4"></span>
+
+<span id="page-0-5"></span><sup>2</sup>Age group of 65+
+
+<span id="page-0-6"></span><sup>3</sup> Singapore's National project to enhance road safety for seniors, since 2014.
+
+<span id="page-0-7"></span><sup>4</sup> Technology to help the elderly cross the road more comfortably without adversely affecting the traffic flow by giving more green light time.
+
+<span id="page-0-8"></span><sup>5</sup> City-wide project to improve pedestrian infrastructure for seniors in the U.S.A.
+
+#### [2008;](#page-9-5) [Transportation Alternatives, 2009\)](#page-9-6).
+
+Since the inception and spreading implementation of the Silver Zone, however, questions have been raised about its effectiveness in reducing collisions. Although some analytical research has pointed to the ineffectiveness of these approaches ([Park and Oh, 2011;](#page-8-8) [Lee, 2012](#page-8-9)), and the media has speculated about possible reasons for its failures, the lack of relevant data has prevented a full assessment of its performance. The accumulated number of Silver Zones in Seoul reached 80 in early 2016, but it was not until 2010 that the database on the pedestrian collisions became available by the Korea Road Traffic Authority.
+
+In this study, we empirically investigate the effectiveness of the Silver Zone in two respects: first, whether the establishment of Silver Zones has lowered the number of elderly pedestrian-vehicular collisions, and second, whether Silver Zones were established in the appropriate areas, that is, those with the highest frequency of such collisions. To better evaluate Silver Zone program, we not only focused on the effect of Silver Zone, but also the effect of ten other physical elements in the zone, which may have effects on the frequency of collisions. With the analytical results, we further explore ways to improve the performance of Silver Zones.
+
+For the first question, we use generalised linear modelling: Zero Inflated Poisson (ZIP), Zero Inflated Negative Binomial (ZINB), Zero Truncated Poisson (ZTP) and Zero Truncated Negative Binomial (ZTNB) in Difference-in-Difference, one of the quasi-experimental specifications. To answer the second question, we use spatial statistical analyses, namely, the Kernel Density estimation and Bivariate Local Moran's I.
+
+The present study is the first attempt to investigate the environmental components of the Silver Zones that explain the elderly pedestrian-vehicular collisions, and the spatial alignment of the zones and the collision locations. Our multi-pronged evaluation will provide a more comprehensive understanding of the performance of Silver Zones, and thereby be a useful reference for municipalities wanting to improve the current system.
+
+The structure of this study is as follows. In the next section, we briefly review the literature on Silver Zones in South Korea, followed by a description of our analytical methods. After presenting our analytical design, we describe the results, including an overview of the actual effects of Silver Zones as well as the other environmental factors on pedestrian collisions, and the degree of spatial alignment between the designated Silver Zones and senior pedestrian-vehicular collision spots. The final section discusses the implications of our findings and future research direction.
+
+## **2. Background**
+
+#### *2.1. Pedestrian safety*
+
+Safety zones are purposed to protect pedestrians from vehicles, adopting a number of safety measures and techniques. School Zone and Silver Zone are some of those examples, made for protecting children and the elderly, respectively, and are established in areas where a large volume of such populations gather. School Zones are commonly located around schools and day-care facilities to help children's commuting safer. Silver Zone is relatively newer than the School Zone system, conceived in response to the increasing concern on the aging society. Japan is a pioneer of Silver Zone since 1986, and South Korea and Singapore have adopted the system recently [\(Ibrahim, 2003](#page-8-10); [Fwa,](#page-8-7) [2016;](#page-8-7) [KoRoad, 2012\)](#page-8-11).
+
+Safety Zones adopt traffic calming measures and techniques, to limit the speed of vehicles. In most of the safety zones, cars are not allowed to drive faster than 20mph (30 km/h). To inform drivers about the condition, speed signs are installed in the entrance and the exit of the zone. Within the zones, speed humps, smaller corner radii, pavement treatment, and chicane are deployed to physically and visually deter drivers from speeding. Also, more frequent and brighter lighting and fences are installed to help pedestrians walk with caution. Occasionally, surveillance cameras are operated to warn the drivers and detect the violation ([Lee et al., 2013](#page-8-12)).
+
+#### *2.2. Silver Zone*
+
+In South Korea, to address the increasing elderly pedestrian-vehicular collisions, the Ministry of Government Administration and Home Affairs (MOGAHA) established the legal framework for the Silver Zone system, with the passage of the Road Traffic Act in May 2007. Since then, as of September 2016, a total of 746 zones have been created in South Korea, of which 80 are located in Seoul [\(Ministry of Government](#page-8-13) [Administration and Home Affairs, 2016;](#page-8-13) [Kim, 2015\)](#page-8-14).
+
+The Silver Zone designation is initiated by the requests from the heads of public or private facilities for seniors, such as senior welfare centres, medical institutions, sports centres and parks. Where the request is granted, a safety zone is created with special treatment to vehicular roads within a 300- to 500-metre radius outward from the facility [\(Ministry of Public Administration and Security, 2012](#page-8-15)). The borough, the city government and the police department coordinate efforts to manage the Silver Zones thereafter.
+
+In the Silver Zones, the speed is limited to below 30 km/h, and the zone-designation and speed-limit signage is installed. Road surface is marked with colouring in red-brown and lettering the phrase "Silver Zone". Occasionally, extra measures are added, such as fences, speed bumps, elevated crosswalks, reduced crosswalk slope, realignment to one-way traffic, widened pedestrian pathways, and speed and signal cameras [\(Ministry of Public Administration and Security, 2012\)](#page-8-15).
+
+However, previous studies, using Before-After evaluation methods, suggested that Silver Zones have no or only a slight effect in reducing collisions [\(Lee, 2012](#page-8-9); [Park and Oh, 2011](#page-8-8)). [Lee \(2012\)](#page-8-9) analysed the effects of Silver Zone by types of senior care facility, shapes of Silver Zone boundary (rectangular, T, Y, L, and I shape), and the locations of Silver Zone (at the corner or along the straight road). In [Lee \(2012\)](#page-8-9), Silver Zone was partially effective in reducing collisions at some locations. [Park et al. \(2010\)](#page-8-16) found that Silver Zone is effective in reducing the severity of collision by 9.5% but showed only a slight effect, 1.6%, in reducing the number of collision. Anecdotal evidence points to the impracticality of the speed reduction measures the system currently adopts, and pressing the necessity of more vigorous enforcements such as speed and signal cameras, speed bumps and radar speed signs [\(Kim,](#page-8-17) [2017\)](#page-8-17). Some editorials also argue that the lack of consideration on the previous collision records leads to failure in prioritizing Silver Zones in the collision-prone spots ([Choi, 2015](#page-8-18); [Yoon, 2013;](#page-9-7) [Lim, 2015](#page-8-19); [Lee,](#page-8-20) [2015\)](#page-8-20). Silver Zones are established only when the requests are made, thus locations with high collision rates could have been left untreated if such request was not made ([Busan Ilbo, 2016](#page-8-21); [Park, 2016\)](#page-8-22).
+
+#### *2.3. Analytical methodology*
+
+## *2.3.1. Poisson, negative binomial, ZIP, ZINB, ZTP and ZTNB in differencein-difference approach*
+
+The Difference-in-Difference (DID) approach is one of the quasiexperimental analyses frequently used to evaluate the impact of policy interventions, since it is useful for inferring near-causality in observational studies ([Li et al., 2012;](#page-8-23) [Chabé-Ferret, 2015](#page-8-24); [Dempsey and](#page-8-25) [Plantinga, 2013](#page-8-25); [Wang and Shi, 2012;](#page-9-8) [Pope and Pope, 2012](#page-9-9)). DID estimates the effects of interests by comparing the outcome from the treatment and control groups in two different time periods: usually before and after the treatment. While the treatment group is exposed to the intervention only in the after period, the control group does not receive treatment during either period or receives treatment during both periods. By deducting the difference in the outcomes between the two groups with and without the treatment, in the periods before and after the treatment, we can understand the remaining "difference-indifference" as a pure impact of the treatment, controlling for all other factors that simultaneously affect both groups, in the before and after
+
+#### periods [\(Pope and Pope, 2012\)](#page-9-9).
+
+Data of collisions have special characteristics: The number of collisions per street segment during a certain time period is discrete and generally small or zero. Since collisions are rare events, the count of segments with zero collisions tends to be high. Poisson and Negative Binomial, and their zero-truncated and zero-inflated options are such distribution explaining collision data. The Poisson distribution illustrates the probability of observing discrete numbers of events in a given time [\(Bradshaw et al., 2009](#page-8-26)), and thus, has been adopted in many transportation studies ([Pérez et al., 2007;](#page-8-27) [Dong et al., 2014](#page-8-28); [Lord et al.,](#page-8-29) [2005\)](#page-8-29): The distribution, however, assumes the mean and variance to be identical, and for that to be the case, the probability of an event occurrence is identical and independent throughout the entire time period ([Chang et al., 2014;](#page-8-30) [Hardin and Hilbe, 2012](#page-8-31)). The strict assumption of this single-parameter model is often inappropriate to apply to real-life data. The Negative Binomial distribution relaxes this assumption, and has been used for accommodating the condition of overdispersion ([Wooldridge, 2016;](#page-9-10) [Hardin and Hilbe, 2012](#page-8-31)).
+
+In case of excessive or non-zero counts in data, zero-inflated and zero-truncated specifications of the Poisson or Negative Binomial modelling are adopted. These specifications identify the probability of the outcome value zero, then separate or exclude it, respectively, from the distribution of the rest of the outcome values. In zero-inflated approaches, the model is divided into two parts: first, the binary part to determine whether observations fall in a condition of taking only zero value, and second, the Poisson or Negative Binomial part to predict the rest of the counts. In zero-truncated models, the probability of the outcome value zero is taken out by adjustment on their original–Poisson or Negative Binomial–distribution ([Nelson, 1977;](#page-8-32) [Keeley et al., 1978](#page-8-33); [Hardin and Hilbe, 2012](#page-8-31)).
+
+Transportation and crime research have used these models conventionally. [Tipakornkiat \(2014\)](#page-9-11) used both the Poisson and negative binomial models to find the positive impact of safety rest areas for drivers in reducing the number of road accidents. Because of the overdispersion, the negative binomial model turned out to fit the data better. [Schneider et al. \(2010\)](#page-9-12) also compared the Poisson and negative binomial models in assessing the association between the characteristics of roadway intersections and the risk of pedestrian collisions in Alameda County, California. For the same reason stated above, the negative binomial model outperformed the Poisson model. [Ayati and](#page-8-34) [Abbasi \(2011\)](#page-8-34) also selected the negative binomial over the Poisson model to find the impact of traffic volume in collisions on urban highways.
+
+These two models are often compared with their zero-inflated versions. For example, [Mouatassim and Ezzahid \(2012\)](#page-8-35) compared Poisson and zero-inflated Poisson (ZIP) to model the number of claims from Moroccan private health insurance. As a substantial portion of policyholders had not filed insurance claims during the study period, the ZIP regression performed better. [Kim et al. \(2015\)](#page-8-36), using the ZINB model, suggested that drivers' demographic characteristics and the record of past traffic violations predict the number of collisions in South Korea. Since the data included a large portion of drivers who had never been involved with collisions, the zero-inflated model was a better choice for the dataset. The zero-truncated version of the Poisson and negative binomial models are used when the data do not contain any zero values. For example, [Van Der Heijden et al. \(2003\)](#page-9-13) used ZTP to estimate the size of the criminal population. The crime report, the main dataset of the analysis, listed individuals who had been apprehended at least one time, thus the data did not include a zero value.
+
+# *2.3.2. Spatial analysis: kernel density and bivariate local Moran's I*
+
+Kernel Density Estimation is a non-parametric statistical method used to visualise point patterns of data. By using moving windows focused on data points, so-called kernels, with a specific radius this analytical method generates density surfaces that show where the points are concentrated [\(Bailey and Gatrell, 1995](#page-8-37)). Bivariate Local Moran's I is an analytical tool that examines whether two characteristics are spatially correlated. With bivariate local Moran's I, we can identify the degree of such a correlation in the four categories: first, High–High where both values of the variables are high; second, Low–Low where both are low; and Low–High and High–Low where only one is high, while the other is low. Moran's I index of 1 and -1 represents the perfect positive and negative correlation between the two variables, respectively, with values close to zero implying weak correlations. The absolute value of .3 or higher is considered a fairly strong correlation ([Yoon and Srinivasan, 2014\)](#page-9-14).
+
+## **3. Analytical design**
+
+## *3.1. Study site*
+
+Our study site consists of 80 Silver Zones in Seoul, South Korea. Assuming that the effect of the Silver Zone may extend beyond this immediate area, we include 300-metre buffers around the zones themselves, which implies an average of a 5-minute walking distance ([Azmi et al., 2012](#page-8-38)). For the DID analysis, we analysed 58 zones established either from 2007 to 2009 or from 2011 and 2014. For the DID analysis with the environmental factors, we excluded zones that had no collision incidence and analysed the rest 27 zones. For the spatial analyses, 32 zones established from 2011 to 2015 were considered. [Fig. 1](#page-3-0) describes our study area.
+
+## *3.2. Dataset and sample*
+
+The two primary datasets were Silver Zone data collected by the Seoul Metropolitan Government from 2007 to 2014 and Elderly Pedestrian Vehicular Collision data from the Korea Road Traffic Authority (KoRoad) from 2010 to 2015. The Silver Zone data include locations, configurations and installation dates of each Silver Zone, and the name and type of facilities that it centres on. The Elderly Pedestrian Vehicular Collision dataset provides detailed information on collisions, including locations, dates, times, the age and gender of the injured party and driver, seriousness of the injury/damages, road types and the weather at the time of the incident. The number of elderly pedestrians injured in vehicular collisions totals 3009, with 478 occurring in 2010, 390 in 2011, 549 in 2012, 564 in 2013, 711 in 2014 and 668 in 2015.
+
+For the supplementary information about the physical environments of the zones, we used Daum, a web portal that provides eye-level maps, satellite imageries and street views. We included nine different characteristics: distance from the centre of Silver Zone, percentage of coloured road surface in the entire Silver Zone, the number of lanes, distance from a collision to the nearest crosswalk, speed bump and traffic light, presence and location of fencing, no-sidewalk road signage and land use (e.g., residential and commercial). The descriptive statistics is in Appendix I.
+
+# **4. Analytical plan**
+
+# *4.1. Difference-in-Difference*
+
+With DID approach, we compare the count of collisions in the treatment and control groups before and after their designation as Silver Zones. Our treatment group comprises collisions that occurred in the areas designated as Silver Zones and the 300-metre buffer area in 2011, 2012, 2013 or 2014. Our control group is the collision count in the areas that were designated as Silver Zones and the 300-metre buffer areas in 2007, 2008 or 2009. Control group is supposed to be a group of samples that are closely matched with treatment group, whereby the only difference is whether the treatment was imposed or not. Therefore, the areas designated as a Silver Zone in the earlier years can be a more appropriate control group for the areas designated as such in the later years, than the randomly selected, non-Silver Zone areas. To allow for a
+
+<span id="page-3-0"></span>![](_page_3_Figure_2.jpeg)
+
+**Fig. 1.** Study Site: Seoul, South Korea.
+
+1-year stabilisation period, and to measure the full-year effects of those Silver Zones, the collisions were counted in the year 2010 for the before condition and during 2015 for the after condition.
+
+If the Silver Zone designation improved pedestrian safety, the number of collisions would go down more or show less of an increase from 2010 to 2015 in the treatment group, compared with the number counted in the control group. Since new Silver Zones are advertised to be safer and easier to walk, it has potential to attract more pedestrians. If this were the case, pedestrian collisions would have impacted by the increased exposure. To rule out this possibility, we conducted two sets of *t*-tests to verify whether the changes of the pedestrian volume differ or not in the two groups (control and treatment groups), in the two points of the collision measurement. Due to data availability, we used data of 2009 and 2015. We could conclude that the treatment and control groups have maintained the same level of senior pedestrians in both years, and the level of change between those two years in those two groups are identical. This implies that the exposure of the senior pedestrians to collisions have changed in a similar way in both of the groups. The result of the *t*-test is available from the authors upon request.
+
+The full DID model is shown below:
+
+$$\begin{split} g\left(E(Num\_Collision_i)\right) &= \ \beta_0 + \beta_1 Treatment_i + \beta_2 After_i \\ &+ \ \beta_3 (Treatment_i\_After_i) + \beta X_i \end{split}$$
+
+Function (1) Difference in Differences (DID) model
+
+Our dependent variable, *Num Collision* \_ , is the number of collisions occurred in the each Silver Zone in the aforementioned years (mean: 0.83); *Treatment* is a binary variable indicating whether the collision occurred within the treatment group or the control group (*Treatment* = 1 if established in 2011, 2012, 2013 and 2014 or *Treatment* = 0 if established in 2007, 2008 and 2009). *After* is a binary variable indicating whether the collision occurred in 2015 or in 2010 (*After* = 1 if occurred in 2015 or *After* = 0 if occurred in 2010). By including the interaction term, *Treatment\_After*, as a product of the group and time indicator, we allow differential changes from the before and after periods in the number of pedestrian-vehicular collisions between those two groups. *Xi* is a vector of the aforementioned environmental characteristics of the Silver Zone. The detailed explanation of the variables is in Appendix I.
+
+We fit the ZIP, ZINB, ZTP and ZTNB models: first, ZIP and ZINB with the three aforementioned variables directly relevant to the DID inference, and then ZTP and ZTNB with all other additional variables representing environmental characteristics of the Silver Zone. In the first analysis, all Silver Zone samples are included, and many of them have not accommodated any collision in either 2010 or 2015. Due to the high frequency of zero value, ZIP and ZINB are utilized to handle the data. In the second analysis, on the other hand, the data is zero truncated because the Silver Zones with collision records are included in the sample. ZTP and ZTNB are utilized to address the zero truncated characteristic of the data.
+
+*g(.)* is a link function that relates the expected dependent variable to the linear predictors [\(Fox, 2016](#page-8-39)). For the Poisson and negative binomial family, a canonical link function–natural log is used. Consequently, the relationship between the dependent and independent variables in Poisson, negative binomial models are shown below:
+
+$$ln(E(Num\_Collision_i)) = \beta_0 + \beta_1 Treatment_i + \beta_2 After_i + \beta_3 (Treatment_i\_After_i) + \beta X_i$$
+
+Function (2) Poisson model
+
+For the negative binomial model, as its variance is allowed to differ from the mean, a latent heterogeneity term *<sup>i</sup>* is introduced in the conditional mean of the model, where exp( *<sup>i</sup>*) follows gamma distribution [\(Shankar et al., 1995\)](#page-9-15):
+
+$$\begin{split} ln(E(Num\_Collision_i)) = & \ \beta_0 + \beta_1 Treatment_i + \beta_2 A fter_i \\ & + \beta_3 (Treatment_i\_A fter_i) + \beta X_i + \ \varepsilon_i \end{split}$$
+
+Function (3) Negative binomial model
+
+#### *4.2. Spatial analysis*
+
+We use two spatial analyses, Kernel Density Estimation (KDE) and Bivariate Local Moran's I, to further investigate the geographical relationship between Silver Zones and sites with a high occurrence of senior pedestrian car-related collisions, and to determine whether the collision points and Silver Zone locations overlap.
+
+First, we plotted a series of KDE maps to visualise the locations of the new Silver Zones established in each year from 2011 to 2015, and the locations of frequent senior pedestrian car-related collisions in the prior year. If the Silver Zones were established close to the previous year's sites of highest-frequency collisions, the maps should show a geographical match between them.
+
+To achieve a more rigorous assessment of the degree of spatial match than a visual comparison can provide, we used the Bivariate Local Moran's I analysis. We created the two variables aggregated at the level of the census tract[6](#page-4-0) to measure their correlation in this fashion: first, the cumulative number of senior pedestrian-vehicular collisions from 2010 to 2014, aggregated by census tract, and second, the total number of Silver Zones in the same census tract as of 2015. The bivariate Local Moran's I function is presented below in Function (4):
+
+$$I_i = A_i \times \sum_{i=1}^n \omega S_i$$
+
+Function (4) Bivariate Local Moran's I *Ai* is the number of such collisions in the census tract i (up to n), *Si* is the number of Silver Zones in the same census tract and is a spatial weight matrix. We chose a distance-based weight matrix over contiguity-based ones, since the analytical units vary in size and configuration, thus could not be consistent in defining neighbouring units. We used a threshold distance of 300 m because it represents an average 5-minute walking distance for elderly and could be considered a maximum distance seniors are willing to walk as part of their daily routine.
+
+#### **5. Findings**
+
+*5.1. Result 1: DID*
+
+In [Table 1,](#page-5-0) we present the analytical results of the ZIP, ZINB, ZTP and ZTNB regression.
+
+For the first DID analysis, in order to select the best model for testing the effects of Silver Zone, we conducted two steps of tests; first, we tested zero-inflation with Vuong test to select a model between standard Poisson and ZIP models, and second, we tested overdispersion with a likelihood ratio test to select a model between ZIP and ZINB model ([Desmarais and Harden, 2013](#page-8-40); [Zuur et al., 2009\)](#page-9-16). The Vuong test statistics were significantly positive (z = 6.64, Pr > z = 0.00), led us to ZIP over the standard Poisson model. The likelihood ratio test indicates overdispersion, led us to ZIP over ZINB model. Therefore, we selected ZIP as the final model. Also, smaller AIC for ZIP reaffirmed our decision.
+
+For the second DID analysis, since we excluded all Silver Zones that had no collision history in 2010 or 2015, the data became zero-truncated. To select between ZTP and ZTNB model, we again used the likelihood ratio test and confirmed that our data is not overdispersed, consequently, we selected ZTP as our final model.
+
+From both the ZIP and ZINB models, we learned that the Silver Zone is ineffective in reducing collisions. All variables directly relevant to DID - *After, Treatment* and their interaction, *After\_Treatment* - explain that the change in the number of collisions in the treatment and control groups from the before and after period is not different at 5% significance level.
+
+Among other environmental factors, the *Locational range*–a binary variable indicating whether a collision happened in the Silver Zone, *Distance to traffic lights, Distance to crosswalk* and *Distance to intersections* are demonstrated to be a predictor of senior pedestrian collisions.
+
+First, we found that senior pedestrian collisions are more likely to occur in the Silver Zone compared to their 300-m buffer. The expected number of collisions in the Silver zone is 684% (=exp(1.923)) of that of the 300-m buffered area. The Silver Zone is established in front of senior care facilities where senior pedestrians tend to concentrate, and the chance of collision involving them would increase. In addition, the variable *Distance to traffic lights* suggests that more collisions would occur in locations farther from vehicle traffic lights. When moving 10 m away from the vehicle traffic light, the expected number of collisions is increased by 109.86% (=exp(0.094)) of that of otherwise cases. Longer distance of traffic intervals may encourage drivers to drive faster and also encourage pedestrians to jaywalk.
+
+*Distance to crosswalks* is also a factor related to the number of senior pedestrian-vehicular collisions. When moving 10 m away from crosswalks, the expected number of collisions is reduced to 88% (=exp (-0.117)) of that of the otherwise cases, holding all other variables constant. This means that collisions have occurred more frequently near crosswalks. This result may imply that the areas near crosswalks are relatively unsafe for senior pedestrians due to drivers' frequent violation of traffic signals or their tendency to make sudden stops. However, it could also be true that simply a higher density of pedestrians is exposed to collisions near crosswalks. The variable *Distance to intersections* can be understood in a similar manner: intersections are also collisionprone spots ([Lee and Abdel-Aty, 2005](#page-8-41); [Lee et al., 2017;](#page-8-42) [Miranda-](#page-8-43)[Moreno et al., 2011\)](#page-8-43). When moving 10 m away from intersections, the expected number of collisions is reduced to 97% (=exp(−0.028)) of that of the otherwise cases. In intersections with vehicles coming from many different directions, the chance of collisions naturally increases: where cars make multi-directional turns simultaneously, drivers tend to pay less attention to pedestrians. As mentioned above, it is also possible that increased exposure of the pedestrians in the intersections or crosswalks could have impacted on change in the number of collisions.
+
+<span id="page-4-0"></span><sup>6</sup> In South Korea, the census unit is equivalent to the census tract in the U.S. It is called *Jigyegu*, and contains approximately 500 residents.
+
+<span id="page-5-0"></span>**Table 1** Parameter estimates, standard errors and approximate p-values from the ZIP, ZINB, ZTP and ZTNB models, describing the DID relationships between the number of collisions in treatment and control groups in the before and after period, along with other selected predictors.
+
+|                       | Effects of Silver Zone            |                   |                                             |                   | Effects of Silver Zone and Physical Elements associated with Senior Pedestrian Collisions |                                              |
+|-----------------------|-----------------------------------|-------------------|---------------------------------------------|-------------------|-------------------------------------------------------------------------------------------|----------------------------------------------|
+|                       | Zero Inflated<br>Poisson<br>Model |                   | Zero Inflated<br>Negative Binomial<br>Model |                   | Zero Truncated Poisson<br>Model                                                           | Zero Truncated Negative<br>Binomial<br>Model |
+| Variables             | ZIP with DID                      | inflate           | ZINB with DID                               | inflate           | ZTP with<br>DID and Physical Variables                                                    | ZTNB with<br>DID and Physical Variables      |
+| After                 | 0.265<br>(0.292)                  | −0.287<br>(0.607) | 0.265<br>(0.292)                            | −0.287<br>(0.607) | 0.202<br>(0.390)                                                                          | 0.202<br>(0.390)                             |
+| Treatment             | 0.233<br>(0.368)                  | 1.200*<br>(0.698) | 0.233<br>(0.368)                            | 1.200*<br>(0.698) | 0.241<br>(0.615)                                                                          | 0.241<br>(0.615)                             |
+| After_Treatment       | 0.032<br>(0.461)                  | 0.055<br>(0.947)  | 0.032<br>(0.461)                            | 0.055<br>(0.947)  | 0.082<br>(0.472)                                                                          | 0.082<br>(0.472)                             |
+| Loc_range             | –                                 | –                 | –                                           | –                 | 1.923**<br>(0.757)                                                                        | 1.923**<br>(0.757)                           |
+| Percent_colour        | –                                 | –                 | –                                           | –                 | 0.611<br>(0.685)                                                                          | 0.611<br>(0.685)                             |
+| Number_lane           | –                                 | –                 | –                                           | –                 | 0.371<br>(0.236)                                                                          | 0.371<br>(0.236)                             |
+| Dist_crosswalk        | –                                 | –                 | –                                           | –                 | −0.117**<br>(0.054)                                                                       | −0.117**<br>(0.054)                          |
+| Dist_light            | –                                 | –                 | –                                           | –                 | 0.094***<br>(0.032)                                                                       | 0.094***<br>(0.032)                          |
+| Fence                 | –                                 | –                 | –                                           | –                 | −0.658<br>(0.479)                                                                         | −0.658<br>(0.479)                            |
+| Dist_intersection     | –                                 | –                 | –                                           | –                 | −0.028**<br>(0.0133)                                                                      | −0.028**<br>(0.0133)                         |
+| Speedlimit<br>Signage | –                                 | –                 | –                                           | –                 | −0.0675<br>(0.335)                                                                        | −0.0675<br>(0.335)                           |
+| No_sidewalk           | –                                 | –                 | –                                           | –                 | 0.404<br>(0.896)                                                                          | 0.404<br>(0.896)                             |
+| Residential           | –                                 | –                 | –                                           | –                 | −0.709<br>(0.786)                                                                         | −0.709<br>(0.786)                            |
+| Commercial            | –                                 | –                 | –                                           | –                 | 0.248<br>(0.427)                                                                          | 0.248<br>(0.427)                             |
+| Constant              | 0.985***<br>(0.233)               | 0.706<br>(0.445)  | 0.985***<br>(0.233)                         | 0.706<br>(0.445)  | −0.050<br>(0.952)                                                                         | −0.050<br>(0.952)                            |
+| Observations          | 116                               | 116               | 116                                         | 116               | 27                                                                                        | 27                                           |
+| −2LL                  | −0.0264                           |                   | −0.0264                                     |                   | −0.2345                                                                                   | −0.8303                                      |
+| df                    | 8                                 |                   | 9                                           |                   | 15                                                                                        | 15                                           |
+| AIC                   | 230.4553                          |                   | 232.455                                     |                   | 117.868                                                                                   | 117.868                                      |
+| BIC                   | 252.484                           |                   | 257.238                                     |                   | 137.306                                                                                   | 137.306                                      |
+| Prob > chi2           | 0.4160                            |                   | 0.4160                                      |                   | 0.0404                                                                                    | 0.6987                                       |
+
+Robust standard errors in parentheses.
+
+#### *5.2. Result 2: Spatial analysis with kernel density and bivariate local Moran's I*
+
+From the Kernel Density maps, we found no apparent relationship between the locations of higher numbers of senior pedestrian collisions in a given year and the locations of newly established Silver Zones in the next year. In general, no spatial match is visible except for some small areas. For example, the northwestern area in [Fig. 2\(](#page-6-0)a), and the south western parts in [Fig. 2\(](#page-6-0)c), (d), (e) whereby Silver Zones seem to have been inaugurated at sites of higher collision frequency in the
+
+<sup>\*\*\*</sup> p < 0.01, \*\* p < 0.05, \* p < 0.1.
+
+<span id="page-6-0"></span>![](_page_6_Figure_2.jpeg)
+
+**Fig. 2.** Kernel Density Estimation of Senior Pedestrian-Vehicular Collisions and New Silver Zones.
+
+previous years.
+
+From the Bivariate Local Moran's I analysis, we found a similar result as above. The bivariate local Moran's I value of -0.004 (p = 0.05) implies very little negative or no correlation between the density of senior pedestrian-vehicular collisions and Silver Zone locations ([Fig. 3](#page-7-0)). If Silver Zones had been established where such collisions were the most prevalent, then the areas marked as High–High and Low–Low should be dominant in the map. In our analysis, only 50 are marked as High–High and 1062 are marked as Low–Low out of a total of 16,230 census tracts in Seoul. Indeed, there is a higher occurrence of spatial mismatch: 1,221 are marked as High–Low, meaning Silver Zones were not established at sites that coincided with a higher number of collisions; and 634 were marked as Low–High, meaning the opposite, that Silver Zones were implemented in areas with low rates of elderly pedestrian-vehicular collisions.
+
+We should note that there is a chance of misreading this result as the real effects of the system. If Silver Zones actually reduce the number of collisions, then the census tracts with a higher number of Silver Zones would have fewer collisions, and thus be categorised as Low–High. Therefore, the large number of census tracts in this category presented in our bivariate local Moran's I result could be read as supporting the effectiveness of the Silver Zone system. However, through our carefully designed quasi-experiment, the Difference-in-Difference analysis and the Kernel Density map, we previously demonstrated the ineffectiveness of the Silver Zone system and therefore eliminate the other interpretation of this analytical result.
+
+<span id="page-7-0"></span>![](_page_7_Figure_2.jpeg)
+
+**Fig. 3.** Bivariate Local Moran's I Cluster Map (Threshold 300).
+
+## **6. Conclusion**
+
+In this study, we investigate the effectiveness of the Silver Zone in two respects. First, we assess the changes in the number of elderly pedestrian-vehicular collisions in the two groups through the DID approach, and second, we assess the appropriateness of their locations to address highly collision-prone spots through spatial modelling.
+
+As discussed above, our statistical analyses demonstrate that the Silver Zone, as currently implemented, is an ineffective measure in reducing senior pedestrian-vehicular collisions. The number of collisions increased from 2010 to 2015 without statistical difference in both treatment and control areas; in other words, the Difference-in-Difference was not supported at a statistically significant level. The analysis also highlights which types of physical characteristics contribute to senior pedestrian collisions. Areas bounded as a Silver Zone have more collisions than their 300-metre buffers. In addition, areas farther away from traffic lights and areas closer to crosswalks or intersections invite more of such collisions.
+
+Our analytical results also suggest that current Silver Zone locations do not spatially coincide with areas of higher senior pedestrian-vehicular collisions. The Kernel Density Estimation of senior pedestrian collision density shows that yearly records of such collisions are not closely reflected in new Silver Zone designations the following year. The Bivariate Local Moran's I analysis provides similar results in that the cumulative number of collisions do not overlap with designated Silver Zones. As mentioned in the background of this study, Silver Zones are initiated at the request of individual operators of senior facilities, without a city-level master planning process incorporating collision pattern studies ([Ministry of Public Administration and](#page-8-15) [Security, 2012](#page-8-15)). The current process creates several problems. On the one hand, the city government could easily overlook areas with high rates of elderly pedestrian-vehicular collisions were it not for the request of Silver Zone by the head of senior citizen facilities. Without a more comprehensive system, the city is not able to coordinate individually requested zone designations with other dangerous sites beyond the vicinity of senior facilities, such as the dangers of long distance of traffic intervals, identified above.
+
+Although the system was originally conceived for seniors, Silver Zones could be used for greater pedestrian safety for all age groups. However, for this system to function effectively, a more comprehensive approach is needed, both for locating these special zones and designing their safety measures. Instead of leaving it to civil petition, the city government should take responsibility for inventorying pedestrian collisions, including locations, through periodic surveys. Based on this information they should prioritise the most critical sites for Silver Zone designation. Moreover, in addition to the signage and road marking that currently comprises the system, other design features and measures could be integrated into the system, such as longer green lights for slow pedestrians, fences to prevent jaywalking, high friction pavement, speed cameras, in-roadway warning flashing light (IRWL) systems to slow the speed of vehicles and part-time pedestrianization [\(Park et al.,](#page-8-16) [2010;](#page-8-16) [Abdelrahman et al., 2011](#page-8-44); [Zhang and Ma, 2014](#page-9-17); [Castillo-](#page-8-45)[Manzano et al., 2014](#page-8-45)).
+
+#### **Acknowledgements**
+
+This work was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Science, ICT and Future Planning [grant number NRF-2015R1C1A2A01055615], Social Science Program through the National Research Foundation of Korea funded by the Ministry of Education [grant number NRF-2017S1A3A2066771], the Korea Environmental Industry and Technology Institute (KEITI) [grant number 2014-001-310007] and the Creative-Pioneering Researchers Program in Seoul National University (number 500-20170162).
+
+### **Appendix A. Supplementary data**
+
+Supplementary material related to this article can be found, in the online version, at doi:[https://doi.org/10.1016/j.aap.2018.07.005.](https://doi.org/10.1016/j.aap.2018.07.005)
+
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+- <span id="page-9-16"></span>[Zuur, A.F., Ieno, E.N., Walker, N.J., Saveliev, A.A., Smith, G.M., 2009. Zero-truncated and](http://refhub.elsevier.com/S0001-4575(18)30302-6/sbref0320) [zero-inflated models for count data. Mixed Effects Models and Extensions in Ecology](http://refhub.elsevier.com/S0001-4575(18)30302-6/sbref0320) [With R. Springer, New York, NY, pp. 261–293.](http://refhub.elsevier.com/S0001-4575(18)30302-6/sbref0320)

Zotero/001_artiklid/Road Safety Indicators/corbenstrengtheningroadsafetystrategy2010.md

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+---
+category: literaturenote
+citekey: corbenstrengtheningroadsafetystrategy2010
+title: Strengthening road safety strategy development ‘Towards Zero’ 2008–2020 – Western Australia’s experience scientific research on road safety management SWOV workshop 16 and 17 November 2009
+authors: "Corben, Bruce F.; Logan, David B.; Fanciulli, Lisa; Farley, Roger; Cameron, Iain"
+year: 2010
+date: 2010-00-00 2010
+doi: 10.1016/j.ssci.2009.10.005
+publication: Safety Science
+url: "https://doi.org/10.1016/j.ssci.2009.10.005"
+zotero_key: 4DRNCUW9
+zotero_storage: 5H83CVWN
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "Corben, Bruce F."
+status: converted
+---
+![](_page_0_Picture_1.jpeg)
+
+# Contents lists available at [ScienceDirect](http://www.sciencedirect.com/science/journal/09257535)
+
+# Safety Science
+
+![](_page_0_Picture_4.jpeg)
+
+![](_page_0_Picture_5.jpeg)
+
+# Strengthening road safety strategy development 'Towards Zero' 2008–2020 – Western Australia's experience scientific research on road safety management SWOV workshop 16 and 17 November 2009
+
+Bruce F. Corben a,\*, David B. Logan <sup>a</sup> , Lisa Fanciulli <sup>b</sup> , Roger Farley <sup>b</sup> , Iain Cameron b,1
+
+### article info
+
+Article history: Received 1 July 2009 Received in revised form 24 September 2009 Accepted 4 October 2009
+
+Keywords: Safe System Vision Zero Sustainable Safety Computer modelling Prediction Serious casualties Strategy performance Road safety Community consultation
+
+### abstract
+
+With a significant list of achievements in traffic safety over some 40 years, Australia's most successful initiatives have emerged from consideration of the scientific basis for achieving effective results. Over time, the increasing use of scientific methods has matured to an extent whereby road safety strategies for entire jurisdictions are now being formed and optimised on the basis of evidence-based mathematical modelling of predicted strategy performance over periods of ten or more years ahead. This paper describes the approach used in the State of Western Australia (WA) to support the development of its new strategy, 'Towards Zero', addressing the 12-year period from 2008 to 2020. Also described is the early development of the modelling approach in the State of Victoria, Australia, subsequently applied, refined and adapted to Western Australia. The 'Towards Zero' strategy aims to ensure that road safety policies continue to evolve within a strategic framework, based on Australasia's Safe System framework, which was derived from the best elements of the Swedish Vision Zero and the Dutch Sustainable Safety visions.
+
+The process for the development of the strategy involved a greater degree of community and stakeholder engagement than has been the case previously, based on the fundamental belief that the community should be provided with the best evidence about what works no matter how controversial, so that it can debate and consider the options available to improve safety.
+
+It is equally important to have a strategy based on the best possible evidence. The Monash University Accident Research Centre (MUARC) was appointed by the WA Office of Road Safety to identify, describe and recommend proven counter-measures within the Safe System framework and develop a series of scientifically sound directions and options.
+
+This paper outlines the modelling technique used by MUARC along with results and summarises the community consultation process.
+
+> -2009 Elsevier Ltd. All rights reserved.
+
+# 1. Background
+
+The Western Australian government and Road Safety Council of Western Australia undertook to develop a new road safety strategy for the period 2008–2020 within Australasia's Safe System framework, with the addition of a bold, long term level of aspiration or vision. The Safe System vision had already been formulated from the best elements of the Swedish Vision Zero and the Dutch Sustainable Safety visions, however Western Australia had never before had a long term level of aspiration or vision. Such an approach has rarely been tried around the world. This project, therefore, should be recognised as an ambitious, highly-challenging initiative of the WA government. MUARC was commissioned by the government to provide the objective research basis for the strategy which, subject to successful implementation, can be expected to deliver large and lasting road safety benefits for Western Australia. A key aspect of the approach was to develop a model to estimate the projected benefits of a combination of best-practice Safe System countermeasures. The METS (Macro Estimates for Target Setting) model was developed for Victoria and, with the permission of Victoria's state road authority, VicRoads, the underlying model structure was used as the basis for substantial further development, culminating in the model now known as METS–WA ([Corben et al., 2008](#page-12-0)).
+
+Given the challenge of implementing such an approach, the WA Road Safety Council determined that the strategy should be developed in a consultative and transparent way to maximise
+
+<sup>a</sup> Monash University Accident Research Centre, Building 70 Monash University, Victoria 3800, Australia
+
+<sup>b</sup>Office of Road Safety, Main Roads Western Australia, Government of Western Australia, Perth, Australia
+
+<sup>\*</sup> Corresponding author. Tel.: +61 3 9905 4375; fax: +61 3 9905 4363. E-mail addresses: [Bruce.Corben@muarc.monash.edu.au](mailto:Bruce.Corben@muarc.monash.edu.au) (B.F. Corben), [Lisa.](mailto:<xml_chg_old>Lisa.Fanciulli@dpc.wa.gov.au</xml_chg_old><xml_chg_new>Lisa. Fanciulli@mainroads.wa.gov.au</xml_chg_new>) [Fanciulli@mainroads.wa.gov.au](mailto:<xml_chg_old>Lisa.Fanciulli@dpc.wa.gov.au</xml_chg_old><xml_chg_new>Lisa. Fanciulli@mainroads.wa.gov.au</xml_chg_new>) (L. Fanciulli).
+
+<sup>1</sup> Tel.: +61 8 9222 8781.
+
+stakeholder and community acceptance. As such, the process for the development of the strategy for 2008–2020 involved a greater degree of community and stakeholder consultation than has been the case with previous strategies.
+
+### 2. The Safe System
+
+The adoption of the Safe System road safety philosophy represents a profound shift in thinking and insight in the Australian society's efforts to curb road trauma. Translating the Safe System philosophy and principles into real-world practice is believed to have the potential to deliver major advances in the safety performance of Australia's road-transport system over coming years and decades.
+
+The Safe System framework was created specifically for Australia and New Zealand by combining the best elements of Sweden's Vision Zero and the Netherlands' Sustainable Safety road safety philosophies. Of the highly motorised countries, Sweden and the Netherlands are acknowledged world leaders in road safety performance and have each created and adopted during the 1990s bold, fundamentally new approaches to reducing road trauma. While these philosophies differ in their relative emphases, they are both founded on a strong ethical platform and both acknowledge the vital importance of explicitly recognising the limitations of humans using the road-transport system.
+
+Like its Swedish and Dutch counterparts, Australasia's Safe System philosophy also aspires to eventually eliminating death and serious injury within its road-transport systems. Serious casualties are defined as the sum of deaths and serious injuries. While some will regard this goal as unrealistic, it is important to realise that:
+
+- - Designing and operating a system that tolerates consistently high-levels of serious trauma is both unethical and at risk of perpetuating the acceptance of failure by system designers and operators.
+- - New, fundamentally safe, designs will result from viewing the safety of the road-transport system in this new light. Intrinsically safe designs and protocols for operation can shift system safety a large step forward, in contrast with the incremental progress characterising traditional approaches.
+
+The Safe System is underpinned by four key principles:
+
+- 1. The limits of human performance Traditional approaches to road safety focus heavily on preventing human failures within the system. For example, there has been considerable success with programs targeting drink-driving, speeding, and restraint non-use. However, despite this partial success, these and other forms of human failure, such as poor gap selection at complex or simple intersections or while overtaking, failure to stay within travel lanes, even on high-speed high-standard roads, and driving while fatigued, have so far proven beyond our capabilities to eliminate through behaviour change programs. A guiding philosophy that explicitly acknowledges the limited intrinsic capabilities of humans is essential to future success.
+- 2. The limits of human tolerance to violent forces Humans are limited in their biomechanical tolerance to the violent forces and energy exchanges that commonly occur in traffic crashes. When tolerance limits are exceeded serious injury or death results. The Safe System explicitly acknowledges these scientific facts by seeking to create a road-transport system that is forgiving of human failures within the system, such that any foreseeable collisions occur within the biomechanical limits of the
+
+humans involved. To achieve this in practice, the ability of a vehicle to protect its occupants in common crash types and at typical impact speeds (resulting from legal travel speeds) must be known and taken into account in decisions about system design and operation. It is also vital to understand the biomechanical limits of unprotected road users (e.g., pedestrians, bicyclists and motorcyclists) in collisions across the full range of vehicle types and speed zones.
+
+- 3. Safe road use While the ultimate responsibility for the safety performance of the road-transport system resides with the system designers and operators, it can only be possible to move progressively towards a situation of no deaths or serious injuries in the long-term provided road users comply with key rules such as speed limits, restraint-use, driving unimpaired and in vehicles with good safety features. Thus, under a shared responsibility for road safety, the system designers depend on compliance by road users for achieving a truly Safe System, while individual, complying users depend on inherently safe design standards and operation for their safety.
+- 4. Creating a forgiving road-transport system The road-transport system is, fundamentally, a real-world illustration of the basic laws of nature governing the movement of objects, be they vehicles or humans, relative to the physical environment. How these objects interact is, ultimately, a matter of physics varied in time and space according to human intervention, which is particularly difficult to predict or control.
+
+Safe outcomes are largely determined by the ability of individual road users to control kinetic energy, which is the physical energy gained by an object (most significantly a vehicle) as a result of its motion. Kinetic energy is a function of both the mass of an object, but more importantly, its speed at any instant in time. Unlike mass, which is linearly related to kinetic energy, speed has a squared (i.e. 2nd power) relationship with kinetic energy. A safe road-transport system depends, therefore, on the successful separation of sources of kinetic energy (crash avoidance) and, where this cannot be achieved, the controlled dissipation of kinetic energy to avoid exceeding human biomechanical limits (injury prevention or mitigation). Given the inherent limitations of human performance within the road-transport system, the Safe System seeks to create roads and roadsides that are tolerant of human error and reasonable levels of impairment. This is achieved by ensuring that sources of kinetic energy remain separated or, in worst cases, can be managed within the limits of human tolerance to serious injury.
+
+A major challenge for the future is to identify and implement current initiatives that meet this goal, as well as to generate new initiatives consistent with these Safe System principles.
+
+### 3. Approach to developing the optimal strategy
+
+A key early challenge was to identify a way to apply the Safe System to a large geographic jurisdiction with a low population.
+
+Western Australia has the largest land area of all the Australian States and Territories comprising 2.5 million sq km and 13,000 km of coastline. Of the population of 2.1 million people, some 1.6 million live in the capital city, Perth. The road network is 179,000 km long, of which 126,000 km is unsealed with 227 million vehicle kilometres travelled annually.
+
+In 2007 the fatality rate was 112 per million people, of which about two-thirds were killed on regional roads at a rate of about 220 per million compared to a rate of 50 deaths per million people in Perth. A total of about 3000 people are seriously injured each year on Western Australian roads.
+
+To facilitate the identification of the best mix of initiatives for Western Australia's next road safety strategy, the concept of a ''Safe System Matrix" was created. The matrix aimed to direct attention primarily to a relatively small number of the larger and most severe traffic injury problems, using proven high-impact solutions. This approach still permits other problems of lower priority to be addressed (e.g., where specific user groups are at especially high risk, even though their absolute numbers of injuries may be relatively low), but at a level commensurate with the potential savings in serious trauma.
+
+The Safe System Matrix served two important purposes:
+
+- 1. It provided a systematic, structured approach to identifying strategically important road safety initiatives, consistent with the principles of the Safe System. In particular, it ensured that each of the main components of the Safe System, namely, safe roads and roadsides, safe travel speeds, safe vehicles and safe road use, were comprehensively addressed within the strategy. These main components have become known as the Safe System Cornerstones.
+- 2. The matrix was structured to ensure that the differing road safety problems and priorities between Western Australia's three main geographic areas – Metropolitan Perth, Regional WA and Remote WA – could be more precisely targeted within the strategy to meet these differing needs. 'Regional WA' represents the road network within a 300 km (approximately) radius of metropolitan Perth, while 'Remote WA' encompasses the rest of the state. These divisions were chosen to acknowledge the substantial differences in road, vehicle and other characteristics between each of these areas.
+
+The Safe System Matrix is shown in generic form in Table 1. The matrix does not contain all of the proposed countermeasures, but rather those that are anticipated to have a significant effect upon serious casualties. There are a variety of other worthwhile initiatives, including additional bicycle paths, traffic calming, improved pedestrian separation and lighting (especially in remote areas of WA) included in the final strategy. A brief description of each of the major areas of the matrix follows.
+
+### 3.1. Safe roads and roadsides
+
+The Safe Infrastructure Cornerstone consists of countermeasures aimed at improving the safety of roads and roadsides. It al-
+
+Table 1 The WA Safe System Matrix.
+
+Safe roads and roadsides Safe speeds Safe vehicles Safe road use All of WA Statewide Accident 'Black Spot'<sup>a</sup> program safer roads programs Enhanced speed enforcement Promotion of crash avoidance features Development of aggregate behaviour change programs Review and fine tune speed limits Promotion of advanced crashworthiness features Metro Perth Intersection countermeasures Adjustment of speed limits to complement infrastructure measures No metro-specific countermeasures Development of specific behaviour change for Metro issues Run-off-road countermeasures Regional WA Safe System transformation of strategically important routes radiating from metro boundary Rezone all limits downwards by 10 km/h Specific promotion of ESC in 4WDs Development of specific behaviour change programs for regional issues Promote ESC selection/fitment to heavy vehicles Remote WA Safe System transformation of strategically important routes around remote centres Rezone all limits downwards by 10 km/h Specific promotion of ESC in 4WDs Development of specific behaviour change programs for issues in remote areas Promote ESC selection/fitment to heavy vehicles
+
+lows for the continuation of existing Accident Black Spot and Safer Roads programs across the whole of WA, provided the selected sites and routes do not overlap with the specific regional and remote treatments detailed below.
+
+One of the key countermeasures for Metro Perth is a 'Safe System Transformation' of intersections. This would involve the implementation of such measures as roundabouts, full control of right-turns at signals, combination red light/speed cameras and others at key intersections. Sites would be selected on the basis of numbers of serious casualties, regardless of exposure, in order to maximise the potential savings in serious casualties as a result of countermeasures being implemented. The use of serious casualties, normalised for traffic volume, may redirect attention away from locations with the worst safety records in terms of absolute numbers of deaths and serious injuries. Run-off-road crashes are also a significant problem in urban areas, but few effective solutions currently exist. Ongoing research should be conducted into the development of new barrier solutions for urban applications, especially on higher speed roads such as those zoned at or above 70 km/h. For roads currently zoned at 60 km/h, reduced speed limits, coupled with enhanced enforcement, have the potential to address this problem without the need for barrier solutions.
+
+In addition to the whole of WA programs, a Safe System Transformation was proposed for routes radiating from Perth. This aimed to address the run-off-road and potentially, head-on crash problem on key strategic routes from the Metro Perth boundary as far out into regional WA as practicable. A similar strategy could be adopted for key rural centres. Traditionally, specific road sections would be treated piecemeal on the basis of crash history. In the case of a Safe System Transformation, however, the goal is to start from the metropolitan end of each route (where crash densities tend to be higher) and work outwards 'injury-proofing' entire road lengths rather than individual sections.
+
+### 3.2. Safe speeds
+
+Reducing travel speeds across Western Australia is one area where significant serious casualty savings are possible at relatively low cost. This potential has been demonstrated clearly through Nilsson's power laws ([Nilsson, 2004](#page-12-0)) reinforced with a variety of evaluations of reduced speeds conducted internationally (e.g. [Aarts](#page-12-0) [and van Schagen, 2006](#page-12-0) and references therein). This is particularly true for a very large, sparsely populated jurisdiction like Western Australia where it will be practically impossible in the foreseeable future to provide best-practice infrastructure solutions across much of the state. For the whole of WA, a program of enhanced
+
+<sup>a</sup> In Australasia, 'Black Spot' has a similar meaning to high crash location/high risk location, commonly used internationally.
+
+enforcement of speed limits was recommended, involving measures such as better-targeted police coverage and increased use of speed cameras. It was also recommended that a systematic program of 'fine tuning' of existing speed limits be pursued, particularly in metropolitan Perth as well as regional and remote centres. This involved redefining a change in speed limit so as to incorporate nearby known hazardous locations, such as intersections or high-risk curves, within the lower speed limit.
+
+In addition to the above measures, two speed-related countermeasures were recommended for Metro Perth. The first of these was to reduce urban speed limits from 60 km/h to 50 km/h. Currently 27% of all serious casualties occur in 60 km/h speed zones within the metropolitan area and even small reductions in travel speed can be expected to lead to significant serious casualty savings. Another situation where lower speed limits can bring about significant trauma reductions is in areas of high pedestrian activity such as Perth's central business district and urban strip shopping centres. It was therefore recommended that these areas be rezoned either to 40 or 30 km/h to improve Safe System compatibility in both avoiding and mitigating pedestrian-vehicle conflicts.
+
+In regional WA, it was recommended that speed limits be reduced by 10 km/h, with progressive reinstatement possible as the Safe System Transformation program is completed along the selected key routes. It was also deemed highly desirable for WA's open road speed limit to be reduced from 110 km/h to 100 km/h, where the vast majority of roads may never be practically able to be lifted to Safe System standards.
+
+#### 3.3. Safe vehicles
+
+This Safe System Cornerstone aimed to capitalise on the proven safety performance of a number of vehicle safety features that, in general, are not currently-fitted as standard on many vehicles available on the Australian market. These features include electronic stability control (ESC) and Intelligent Speed Adaptation (ISA), which help to prevent crashes occurring and side-impact and curtain air bags, and active head restraints, which help to reduce occupant injury severity when a crash occurs. This initiative aimed to accelerate the introduction and rate of penetration of these features into Western Australia's vehicle population by requiring government fleet purchasers to specify selected features when renewing the government fleet and by encouraging corporate fleet purchasers to do likewise. Not only will this approach accelerate the take-up of these proven features in WA's vehicle fleets, it will also put much-needed pressure on vehicle manufacturers to provide these features as standard in new vehicles, or at least as options that can be specified as stand-alone features in their base models. These benefits will flow on to WA's private vehicle purchasers as government and fleet vehicles are sold into the general fleet.
+
+Based on current and proposed levels of availability of these features, a timeline for their introduction to government and corporate fleet purchases was proposed as follows:
+
+- -ESC from Year 1.
+- -Curtain and side-impact airbags from Year 1.
+- -Intelligent Speed Adaptation from Year 3.
+- -Active head restraints from Year 5.
+
+### 3.4. Safe road use
+
+For a best-practice strategy for WA, the Safe Road Use Cornerstone would involve the creation of an integrated suite of campaigns that present and promote the Safe System road safety philosophy as well as targeting traditional and new problem areas. The main features would include:
+
+- - An emphasis on the Safe System being a new, ambitious approach capable of achieving major improvements in traffic safety over the next decade and beyond.
+- - The importance of shared responsibility, with road users to comply with key laws including drink-driving, drug-driving, seat belt use, fatigue-driving, etc. Correspondingly, the obligation of the system designers and operators to create a low-risk road-transport system would also be reinforced.
+- - A series of problem-specific education, promotion and publicity campaigns targeting key problem types amenable to improvement through behaviour change programs including drink-driving, drug-driving, speeding, restraint-use, distraction/inattention, fatigue-driving, etc. Furthermore, as part of each issue-specific campaign ongoing reinforcement of Safe System principles and the concept of shared responsibility.
+
+### 4. Modelling strategy performance
+
+Central to the overall approach to developing an optimal road safety strategy for Western Australia was the modelling of strategy performance using evidence-based estimates of the effectiveness of the individual road safety initiatives described in the previous section as well as combinations of initiatives. The modelling approach operates at a macro-level and so includes only those initiatives expected to have a sizeable impact on the reduction in severe road trauma. Using evidence-based estimates of effectiveness and actual crash data for Western Australia over recent years, the model used mathematical methods to forecast future savings in serious casualties in each year of the 12-year period from 2008 to 2020. These predicted savings in serious casualties were summed over the strategy life for each individual initiative, assuming it alone was implemented. These savings were also summed for combinations of initiatives implemented as part of a strategy, allowing differentiation between options in terms of their potential contribution to preventing road fatalities and serious injuries. The principal measure of worth of a strategy option is the total number of serious casualties prevented over the strategy life.
+
+These savings are estimated relative to the level of serious casualties that could be expected to occur in the absence of a significant road safety strategy.
+
+Forecasting future road trauma occurrence and trends is a challenging exercise, characterised by uncertainty and assumptions about the nature of the road-transport system, now and in the future. However, to plan for success, it is necessary to follow such a path, while reducing as far as practicable, the potential for error. The approach taken with modelling for the WA strategy has attempted to account for two main, whole-of-system, influences.
+
+- - Future growth in serious casualties as a result of increasing exposure, reflected by vehicle kilometres travelled (VKT). This figure was estimated at 2.6% per annum for the life of the strategy, based on growth between 2001 and 2005, and could be an underestimate depending upon the duration and size of the economic boom experienced by WA at the time of modelling.
+- - Future improvement in serious casualty rates due to the gradual effects of increasing motorisation (e.g. [Jacobs et al.,](#page-12-0) [2000](#page-12-0)). This value was estimated at 1.6% per annum for WA, derived from the trend in serious casualties per vehicle-kilometre travelled using annual police-reported data for the period 1990–1996.
+
+<span id="page-4-0"></span>These two influences, while tending to counteract each other, resulted in a forecast general upward trend of an average 1.0% per annum in serious casualties through to 2020 due to the higher rate of traffic growth than decline in serious casualties associated with motorisation. Together, the combined effect of traffic growth and serious casualty reduction with increasing motorisation was used to define a continuous point of reference against which potential savings in serious casualties due to the proposed strategy and its individual elements were estimated.
+
+The model produces two principal outputs:
+
+- 1. The estimated total number of serious casualties saved over the life of the strategy (relative to the forecast numbers of serious casualties in the absence of a significant strategy).
+- 2. The percentage reduction in serious casualties in the final year of the strategy compared with a selected baseline period, which would be the most recent year, or an average of the most recent three years (if substantially different from the most recent year) for which full serious casualty data were available. The total number of serious casualties saved over the life of a strategy can be used to identify the most effective strategy, while the percentage reduction in the final year of the strategy (Year 12) provides a target for achievement by the end of the strategy (and at intermediate milestones throughout).
+
+The model also produces a number of additional output measures for each initiative and each strategy option. These included the estimated cost (in present-day values), as provided by agencies responsible for implementation, allowing the average cost of implementation per serious casualty saved, predicted numbers of fatalities and serious injuries in the final year of the strategy, among others to be estimated.
+
+# 5. Model structure
+
+### 5.1. Description
+
+The METS (Macro Estimates for Target Setting) model was originally developed over a period of 16 months from early 2006, funded by VicRoads as part of the development of the next Victorian road safety strategy. Although the Western Australian version was based on the latest version of METS, METS-WA has undergone extensive development and customisation with the aim of tailoring it to the Western Australian road safety environment, as well as incorporating significant improvements to the underlying model. The model is a numerical implementation of concepts developed in the late 1990s by MUARC researchers Peter Vulcan and Bruce Corben (e.g. [Vulcan and Corben, 1998](#page-12-0)). It starts with a base number of annual serious casualties (killed and hospitalised) derived from police-reported data. The effectiveness of individual countermeasures in reducing the proportion of total serious casualties is used to predict serious casualty numbers from the effects of the countermeasure in isolation for each year for the duration of the strategy. Underlying trends are also taken into account as detailed above. Individual countermeasures are then combined into strategy 'packages', either additively or multiplicatively, the latter avoiding double-counting of savings when different initiatives act upon the same 'pool' of serious casualties.
+
+# 5.2. Estimating scope for reduction in serious casualties
+
+This section presents a brief overview of the mathematical basis for estimating the reductions in serious casualties possible from specific initiatives. In essence, this section summarises the work of [Vulcan and Corben \(1998\),](#page-12-0) adapting it to the present application. As noted above, fatalities and serious injuries can be reduced by initiatives undertaken within the four Safe System Cornerstones. If no improvements are made in any of these areas, it is considered reasonable to assume that total fatalities (and serious injuries) would change according to an annual average serious casualty growth factor, g, defined as the percentage growth in traffic minus underlying rate of improvement due to the general effects of increased motorisation. As with [Vulcan](#page-12-0) [and Corben \(1998\),](#page-12-0) the effects of traffic congestion and differential growth on different parts of the road network were neglected.
+
+$$SC_t = SC_0 \left( 1 + \frac{g}{100} \right)^t \tag{1}$$
+
+where SC<sup>t</sup> = serious casualties in year t, SC0 = serious casualties in base year, g = annual average serious casualty growth factor, as defined above.
+
+To take account of the empirical finding that even in the absence of any additional road safety measures, fatality rate gradually decreases as motorisation (vehicles per head of population) increases and the road, vehicles and the road user population ''matures". While such effects are difficult to measure allowance has been made for this effect.
+
+Then if the total percentage reduction in fatalities and serious injuries resulting from all safety measures combined is R percent
+
+$$SC_R = SC_t \left( 1 - \frac{R}{100} \right) \tag{2}$$
+
+where SC<sup>R</sup> = number of serious casualties in the final year of the strategy (of duration t years) during which all the safety measures were applied.
+
+To ensure that savings in serious casualties are not counted more than once, they are either added or multiplied together, depending upon the actual mechanisms for achieving the savings. As described earlier, some initiatives act on the same set of crashes as other initiatives and therefore the savings need to be combined multiplicatively, while other initiatives can act on separate crash sets and so have been combined additively. [Vulcan and Corben](#page-12-0) [\(1998\)](#page-12-0) present a number of examples to illustrate this point, namely:
+
+$$1 - \frac{R}{100} = \left(1 - \frac{r_b}{100}\right) \left(1 - \frac{r_s}{100}\right) \tag{3}$$
+
+where rb = percent reduction from better vehicle brakes, rs = percent reduction from increased seat belt wearing, R = total percent reduction from these two measures.
+
+Similarly, if there are four sets of measures (r1–r4), the formula for calculating the total percentage reduction from all measures R is
+
+$$1 - \frac{R}{100} = \left(1 - \frac{r_1}{100}\right) \left(1 - \frac{r_2}{100}\right) \left(1 - \frac{r_3}{100}\right) \left(1 - \frac{r_4}{100}\right) \tag{4a}$$
+
+where r<sup>1</sup> = percentage reduction from all safer vehicle measures, r<sup>2</sup> = percentage reduction from all safer road measures, r<sup>3</sup> = percentage reduction from all safer road user measures, r<sup>4</sup> = percentage reduction from improved emergency medical services.
+
+Or, more generally, for n road safety countermeasures, each resulting in a percentage reduction, rn:
+
+$$1 - \frac{R}{100} = \prod_{i=1}^{n} \left( 1 - \frac{r_n}{100} \right) \tag{4b}$$
+
+Interactions between these four categories of measures have been ignored.
+
+Each of the above four percentage reductions represents the net effect of several measures some of which are additive, some are multiplicative and some of which overlap or interact (e.g. speeding and drink-driving enforcement).
+
+It can be seen from Eq. [\(1\)](#page-4-0) that the extent to which a reduction in fatality rate translates to a reduction in the number of fatalities also depends on traffic growth. Thus influencing the rate of growth or fall in road use also represents scope for further improvements in road safety as well as vehicle emissions.
+
+A unique feature of METS-WA is its ability to allow different levels and combinations of initiatives to be relatively easily compared.
+
+# 5.3. Key assumptions
+
+METS uses a worksheet with more than 150 input variables, both user-defined and calculated. Variables are separated into general parameters as well as parameters relating to each of the Safe System Cornerstones, namely infrastructure (safe roads and roadsides), speed, vehicles and behaviour (safe road use). Where possible, input variables were derived from either reliable agency-supplied statistical data or the results of sound research. For a number of minor variables, however, neither of these sources was able to provide the specific data required. Where this was the case, conservative consensus estimates were used, based on the best evidence currently available.
+
+#### 5.4. Outputs
+
+The two principal outputs of the model are: (a) cumulative numbers of serious casualties saved over the life of the strategy and (b) performance of the strategy in its final year, as well as selected milestone points. Strategy performance was measured as the percentage reduction in the number of serious casualties in the selected year compared with the chosen baseline period (as defined earlier), usually the most recent year for which full serious casualty data are available. The number of cumulative serious casualties saved is a relative figure calculated by projecting the future state of baseline serious casualties in the absence of a specific strategy. Although it is a somewhat arbitrary baseline, it allows different strategy options to be compared with one another. Moreover, cumulative savings are important to consider, as strategy performance in a single year may give little indication of overall strategy performance.
+
+Where the costs of implementing initiatives were provided, the model also provides approximate indications of: (a) total strategy cost, (b) cost per serious casualty saved, (c) the monetary valuation by society resulting from the serious casualty savings, and (d) the ratio of this monetary valuation to strategy cost. Costs are all expressed in present-day values, with future cost increases not taken into account.
+
+To illustrate the use of the equations presented in Section [5.2](#page-4-0) (refer to [Vulcan and Corben, 1998](#page-12-0) for original explanation), consider the case of initiatives being assessed to improve road infrastructure safety, accelerate the take-up of proven vehicle safety features and strengthen speed management. Set out below are three charts which show the estimated annual savings in serious casualties from each of the above initiatives, as well as the yearby-year build-up in the cumulative savings in serious casualties over the period of the 12-year strategy developed for WA. These savings were calculated using the above equations, from knowledge of the:
+
+- average annual number of serious casualties in the chosen base period;
+- effectiveness of individual initiatives in reducing serious casualties; in some cases it is important to distinguish between the different levels of effectiveness of initiatives on fatalities and on serious injuries;
+
+- annual growth in traffic over the strategy life;
+- annual reduction in the rate of serious casualties per vehicle kilometre of travel over the strategy life;
+- extent of implementation of the initiative, either as a onceonly decision or in terms of the annual (or other periodic) level of implementation;
+- timing and the means by which the initiative has its effect, especially with respect to the cumulative effects over time (this is described more fully below).
+
+# 5.5. Example 1 – Safe Roads and Roadsides Cornerstone
+
+The effectiveness of black spot and other safety-based road investment undertaken in Australia over many years were used to estimate savings in serious casualties from improving road and roadside safety. Estimates of effectiveness of these types of program were obtained from local evaluations. Applying these findings to the WA trauma problem ([Meuleners et al., 2005\)](#page-12-0), and adjusting for the actual level of investment each year across a number of safe infrastructure investment options, it was estimated that 58 serious casualties would be prevented each year if \$135 million (in present-day values) is invested annually over the life of the strategy. The estimated annual savings of 58 serious casualties for an annual investment of \$135 million is calculated from a weighted average of the individual levels of effectiveness of different types of infrastructure investment (i.e., accident black spot program, safer roads program, Safe System Transformation of metropolitan intersections, and regional and remote routes).
+
+Because infrastructure programs of this scale require a significant lead time to reach full implementation capacity, no savings were allowed in the first two years of the strategy and only half of annual savings were counted in the third year, before building to full delivery of annual savings from Year 4 for the life of the strategy. Such assumptions attempt to be both realistic about potential savings in serious casualties and conservative in nature, so that implementing agencies are confident they are not being asked to perform beyond their true capacity.
+
+A major feature of investment in safe infrastructure is that savings in serious casualties gained in the first year continue to accrue in each of subsequent years until the theoretical, useful lives of these projects have expired. During this period the savings which accrued from investment in the Years 2, 3, 4, etc. also accrue in the same basic way so that the net effect is a rapidly building profile of savings in serious casualties that actually extend well beyond the 12-year life of the strategy. Because only the savings accrued during the life of the strategy are counted in the strategy assessment method, the model is quite conservative in its estimation of strategy benefits. It is, however, assumed that the effectiveness of safety measures implemented within this cornerstone remain fully effective throughout the life of the strategy (see [Fig. 1](#page-6-0)).
+
+# 5.6. Example 2 – Safe Vehicles Cornerstone
+
+The individual estimates of effectiveness of proven vehicle safety features are used to estimate the rate of accumulation of savings in serious casualties resulting from these features finding their way into a jurisdiction's vehicle fleet. For example, it has been found that Electronic Stability Control (ESC) reduces single-vehicle serious casualties involving passenger vehicles by 35% (after [Lie et al. \(2006\)](#page-12-0), and [Scully and Newstead, 2008\)](#page-12-0), while curtain airbags are effective in reducing all serious casualties from side-impacts and rollovers involving passenger vehicles by 20% (reference: MUARC estimate). Similarly, research has found that Intelligent Speed Adaptation (ISA) is effective in
+
+<span id="page-6-0"></span>![](_page_6_Figure_2.jpeg)
+
+Fig. 1. Estimated cumulative serious casualty savings by year compared with ''business as usual" for the modelled package of infrastructure investment.
+
+reducing all serious casualties involving passenger vehicles by an estimated 10% [\(Regan et al., 2006](#page-12-0)) and that Active Head Restraints are effective in reducing all serious casualties from rear-impacts involving passenger vehicles by 15% (MUARC estimate). These estimates of effectiveness were then applied to actual Western Australian data on each target crash type to estimate savings in serious casualties for a given rate of introduction of the various technologies.
+
+The rates of penetration of the technologies into the WA fleet was based on the assumption that from a specified date for each technology, government and corporate vehicle purchasing policies and practices will change to ensure that such features would always be specified from the assumed start date forward. It was therefore also necessary to obtain information on the current rate of purchase and sale of government and corporate fleet vehicles, and project these rates throughout the 12-year life of the strategy.
+
+In order to maintain an acceptable degree of conservatism in the setting of an overall strategy target, the start dates for each vehicle safety feature were chosen to enable adequate time for implementing agencies to prepare for the required changes in fleet purchasing policy. For largely practical reasons, it was assumed that take-up of both ESC and side/curtain airbags would increase from actual 2008 levels to 100% by 2011 and 2012 respectively, ISA from Year 3 and active head restraints from Year 7, and that only 80% of purchased vehicles in first year of implementation would have the specified safety features, 90% in second year of implementation and 100% thereafter. It was also hoped that the collective actions of fleet purchasers would be sufficient to bring about a change in the policy of many vehicle manufacturers to make these features standard in base models so that from that time forward the occupants of all new vehicles would enjoy the safety benefits possible from these features. The added savings in serious casualties derivable, should such a decision be taken by the manufacturers of vehicles sold in Australia, have not been counted in the total benefits possible during the life of the strategy.
+
+Likewise, in keeping with the conservative nature of this modelling approach, savings in serious casualties from private purchases have not been counted; such savings are regarded as a bonus to overall strategy performance. Notwithstanding, ongoing efforts should be made to promote the purchase by private buyers of vehicles with these proven features. Similarly, the benefits able to be derived from improved vehicle designs offering greater protection in impacts with pedestrians and cyclists, while strongly supported, have not been quantified (see Fig. 2).
+
+### 5.7. Example 3 – Safe Speeds Cornerstone
+
+Two main initiatives were considered under the Safe Speeds Cornerstone; first, achieving improved driver and rider compliance with existing speed limits and, secondly, reducing speed limits on selected types of road. The methods used to estimate savings in serious casualties by implementing the latter of these two initiatives are presented here to illustrate the approach taken.
+
+The work of [Nilsson \(2004\)](#page-12-0) and [Elvik et al. \(2004\)](#page-12-0) resulted in the establishment and widespread use of scientifically robust relationships between changes in mean travel speeds and changes in the incidence of fatalities, serious injuries and other injuries. In essence, Nilsson found that a decrease in mean travel speeds resulted in decreases in the incidence of fatalities, serious injuries and other injuries according to power functions. The decrease in injuries is a function of the decrease in mean speed raised to the fourth, third and second powers, for fatalities, serious injuries and other injuries, respectively.
+
+To estimate the potential savings in serious casualties as a result of reducing the speed limits in existing 60 km/h zones to 50 km/h, Nilsson's relationships were applied to actual injury data for WA, on the basis that this potential reduction in speed limit would reduce the mean speed in 60 km/h zones from 40 km/h to 37 km/h. This estimate was based on actual mean travel speed data and previous research by [Haworth et al. \(2001\)](#page-12-0) which estimated that such a speed limit reduction would produce a 3 km/ h reduction in mean speeds. No additional enforcement is expected to be needed in order to achieve this reduction in mean speeds. These assumptions resulted in the calculation of an overall serious casualty reduction factor of 0.21, derived as a weighted average of the fourth power exponent applied to the actual average annual number of fatalities and the third power exponent applied to the actual average annual number of serious injuries occurring throughout WA's 60 km/h speed zones. It was also assumed that this change in speed limits would not take place until Year 5 of the strategy to enable agencies to prepare for the change, including supporting the somewhat controversial initiative (refer to the section on community consultation) with appropriate education and publicity in advance of the change. The model also included a reduction in 110 km/h posted speed limits to 100 km/h (Year 5) as well as the remainder of state speed limits being reduced by 10 km/h in Year 8 (see [Fig. 3](#page-7-0)).
+
+![](_page_6_Figure_12.jpeg)
+
+Fig. 2. Estimated cumulative serious casualty savings by year compared with ''business as usual" for the modelled package of vehicle safety countermeasures.
+
+<span id="page-7-0"></span>![](_page_7_Figure_2.jpeg)
+
+Fig. 3. Estimated cumulative serious casualty savings by year with respect to ''business as usual" for a reduction of 60 km/h speed limits to 50 km/h and 110 km/ h posted speed limits to 100 km/h in Year 5, with the remainder of state speed limits reduced by 10 km/h in Year 8.
+
+# 5.8. Combining the effects of all initiatives
+
+As noted earlier, if initiatives target the same crashes, then the total savings from the combined effects may be estimated by multiplying together the individual estimates, whereas when the initiatives target different crashes, then the savings may be added to estimate the overall effect.
+
+In the case of the initiatives illustrated above, all vehicle safety features except for ISA target different crash types and therefore their combined effect can be estimated by adding the individual effects. ISA, on the other hand, targets all crash types and so the total savings in serious casualties from all vehicle safety features would be estimated by multiplying the sum of the other three vehicle safety initiatives by the reduction factor for serious casualties from ISA. The overall saving from the initiatives spanning the three Safe System Cornerstones would then be estimated by multiplying the total savings from vehicle safety features by the reduction factors for serious injuries for the infrastructure investment initiative and for the speed limit reduction initiative, as these latter initiatives act on the same crashes.
+
+### 6. Results
+
+### 6.1. MUARC's recommended Safe System strategy
+
+Fig. 4 shows the relative performance of each of the groups of initiatives (as shown in the WA Safe System Matrix section) that were selected for consideration for inclusion in the strategy. From left to right, the bars represent the projected cumulative serious casualties estimated over the 12-year life of the strategy for infrastructure (safer roads and roadsides), enhanced enforcement, speed limit reductions, vehicle safety measures and an aggregate behaviour change program.
+
+The above initiatives were combined to create what was called the 'Optimum' Safe System Option (OSSO). Here, 'optimum' is defined as a pragmatic optimum, derived from consultation with representatives from responsible agencies in WA. Defining this optimum had regard for what would be realistic levels of input from agencies within each cornerstone, while still recognising practical constraints on agency delivery, levels of maturity of new vehicle technology and the influences of political and community views. The OSSO was estimated to yield cumulative savings of 16,000 serious casualties over the 12-year duration of the strategy, reducing annual serious casualties from 2962 in
+
+![](_page_7_Figure_11.jpeg)
+
+Fig. 4. Performance of individual initiatives, if implemented in isolation.
+
+2006 to around 1420 serious casualties per annum by Year 12 in 2020. This represents a 52% reduction in serious casualties compared with 2006. It is estimated that by the conclusion of Year 12 the number of state-wide fatalities annually could reach as low as 100 (c.f. an average annual base level of 202 for the 3 year period from 2005 to 2007).
+
+As traffic growth has a significant influence on model outputs, as well as being somewhat variable, a range of traffic growth figures were investigated. The results, shown in [Table 2](#page-8-0), demonstrate how the model is easily able to show how serious casualty outcomes might change with movements in other variables. The effect of lower traffic growth is to improve the performance of the strategy, while higher traffic growth results in greater cumulative serious casualty savings, but worse strategy performance overall, highlighting the potential risks in strategy implementation.
+
+## 6.2. Strategy alternatives
+
+Several variations to the Safe System strategy were modelled, to investigate the effects of some of the compromises that might be considered for each of the main Safe System initiative groups. Each change was modelled while keeping the others at levels specified by the OSSO. The following delays were examined:
+
+- - Infrastructure: reduce annual investment by 30% (found to result in a similar number of savings in serious casualties forgone as if the investment in infrastructure were delayed by 2 years).
+- - Speed: delay 60–50 km/h, 110–100 km/h until Year 5 (from Year 1); delay 10 km/h reduction until Year 7 (from Year 3).
+- - Enforcement: delay enhanced enforcement until Year 5 (from Year 1).
+- - Vehicles: delay ESC, side/curtain airbags until Year 3 (from Year 1); delay ISA until Year 7 (from Year 3); no change for Active Head Restraints (Year 5)
+
+No changes were made to the aggregate behaviour change program. [Fig. 5](#page-8-0) shows the results of each change, based on the effects of delaying one initiative at a time. Should multiple delays occur, the cumulative effects on serious casualty savings would be considerably greater.
+
+# 6.3. Limitations of modelling approach
+
+With any form of forecasting, there will potentially be a degree of uncertainty about the direction, magnitude and sustainability of predicted change. The modelling method described
+
+<span id="page-8-0"></span>Table 2 Effects of varying traffic growth on model outputs.
+
+| Output estimate                                                               | Traffic growth |        |        |
+|-------------------------------------------------------------------------------|----------------|--------|--------|
+|                                                                               | 2.6%<br>(base) | 2.0%   | 3.0%   |
+| Cumulative serious casualty savings over 12<br>years (rounded to nearest 500) | 16,000         | 15,500 | 17,000 |
+| Percentage reduction in Year 12                                               | 52%            | 57%    | 49%    |
+| Estimated serious casualties in Year 12 (rounded<br>to nearest 10)            | 1420           | 1290   | 1520   |
+| Estimated fatalities in Year 12 (rounded to<br>nearest 10)                    | 100            | 90     | 110    |
+
+![](_page_8_Figure_4.jpeg)
+
+Fig. 5. Effects of varying initiative commitment on cumulative serious casualties saved.
+
+here clearly has a number of limitations on its reliability and accuracy. Some of the main limitations are discussed briefly below, though a full discussion of the effects of these limitations is not practical here.
+
+- quality and consistency of reported crash data describing fatalities and serious injuries;
+- accuracy of estimates of effectiveness of initiatives and countermeasures being modelled, including the transferability of non-local research findings to other jurisdictions;
+- quality of other, non-safety, data such as traffic growth, vehicle sales and future investment in general road improvements;
+- expectations that historical trends in society in general and the transport system in particular will continue to be highly influential in defining future trends;
+- future trauma savings due to infrastructure investment are substantially underestimated as only the savings accrued during the life of the strategy (usually 10–12 years) are counted, whereas much of the infrastructure investment will continue to deliver trauma savings for up to 30 years. A similar argument applies to vehicle safety, though the average life of a passenger vehicle is about 10–12 years, thereby limiting this effect as it relates to vehicles.
+
+To date, the model has not been developed to investigate the effects of shifts in travel mode, such as the growth in motorcycling, walking and public transport use, for example. New projects are currently exploring these possibilities.
+
+To address these and other concerns, the modelling approach has been highly conservative in estimating savings in severe trauma. For example, the general philosophy of the modelling process assumes:
+
+- lower levels of effectiveness of initiatives;
+- slower implementation/take-up of initiatives;
+- higher costs to achieve the predicted savings;
+- sensitivity testing of predicted traffic growth, generally adopting conservative values.
+
+The overall effect of this typically conservative approach has been to ensure governments are not unwittingly promising to deliver more than is realistically possible for an agreed level of investment. In jurisdictions with highly ambitious aspirations, modelling can readily be undertaken in a way that would genuinely 'stretch' the available resources to maximise the achievement of trauma reductions. There appears to be no single correct approach; instead, the modelling can be carried out to suit the aspirational preferences of a particular jurisdiction.
+
+Finally, it is important to recognise that the greater value of this form of modelling lies in establishing the relative benefits of alternative strategy options rather their absolute values. The METS modelling approach is presented as a macro-level approach rather than creating the unjustified 'illusion of precision' ([Sherwood, 2009](#page-12-0)). As a result, there are many road safety initiatives that were not modelled explicitly, primarily because, individually, the predicted savings are small and therefore incompatible with the 'macro' nature of the overall approach. Their aggregate effect, however, can be significant, yet is not counted here and instead is regarded as a 'bonus' contribution to the adopted strategy. In the case of continuing initiatives in place prior to the strategy, some of these benefits will be implicit in the adjustments made for the effects of increased motorisation.
+
+### 7. The community consultation
+
+To promote community, stakeholder and government acceptance of the ambitious approach taken to the development of the strategy, the Road Safety Council (RSC) undertook an extensive consultation process parallel to MUARC's modelling work. The consultation had as its basis the fundamental belief that the community should be provided with the best evidence about what works no matter how controversial that may be so that it can debate and consider the options available to improve safety. This approach was strongly supported by the Road Safety Minister.
+
+### 7.1. Process
+
+The RSC called on the expertise of community engagement specialists Estill and Associates and market research company Synovate to develop, undertake and analyse the community consultation. Over 4000 people directly participated in the consultation.
+
+The consultation process involved three phases:
+
+- - Phase 1 gathered the community's views on road safety and introduced it to the Safe System philosophy and the concept of shared responsibility through a series of community forums hosted by local Members of Parliament in their constituencies and an online survey.
+- - Phase 2 presents the findings of the first phase of consultation and the recommended package of initiatives developed by MUARC to the community for comment through a discussion paper (with online and paper based feedback options), community forums and a survey of a scientifically representative sample of the broader population.
+- - Phase 3 involves the communication of the endorsed strategy to the public, stakeholders and the Parliament.
+
+A bipartisan Parliamentary Reference Group with an independent chairperson was also established and consulted in each phase.
+
+The three phases of the consultation process are further detailed in Appendix A.
+
+### 7.2. Results
+
+It was considered likely that the people who took the time to attend a forum or complete the online or paper-based questionnaire would have a stronger interest in the road safety initiatives proposed by MUARC than would the wider community. It was possible that they would be either more strongly in favour or more strongly against them. In contrast, the representative population sample was selected to be representative of the broader community's age, gender and geographical location and was considered to more accurately reflect the opinions held about road safety by the population at large. On the whole, as shown in Table 3, both groups supported the majority of the strategy proposals made by MUARC.
+
+The research showed that the community was highly concerned about reducing death and serious injury on our roads and recognised that this is a shared responsibility of the entire community. The majority of the community supported MUARC's recommended road safety strategy; however, the level of support varied for individual initiatives and amongst different demographics. In particular there was strong support for initiatives aimed at maximising compliance with the road rules among road users, improving Western Australia's road network and enhancing the safety of vehicles travelling on our roads.
+
+The representative sample indicates that the community was more divided on reducing speed limits in regional, urban and shopping areas, though it was far less resistant towards these changes than the group that completed the available, open survey. To add further complexity to the issue, approximately half of those who did not support speed limit reductions still believe these changes would be at least somewhat effective in reducing death and serious injury on the roads. Support for speed limit reductions is higher among women and those with dependents and lower among men, people without dependents and motorcyclists.
+
+There is a statistically significant difference between the views of the representative population sample and the views of those with an existing interest in road safety who attended the forums or completed the open questionnaire. It appears that those with a passion for road safety are actually less open to speed reductions than the general population.
+
+The community's main concerns surrounding speed limits changes were that irresponsible road users would continue to speed without better enforcement, while responsible road users would feel the impact of reduced travel times.
+
+# 7.3. Implications of community consultation results for MUARC's recommended strategy
+
+In light of the scientific evidence the RSC was convinced that the initiatives recommended by MUARC would effectively reduce the level of death and serious injuries on WA roads. With the high level of community support for MUARC's recommended initiatives to improve road user behaviour, the safety of roads and roadsides, the enforcement of speeding and vehicle safety, the RSC endorsed those initiatives as recommended by MUARC. In addition, the RSC endorsed additional research and evaluation projects for each of the cornerstones and undertaking to acknowledge and encourage some of the programs the community would like to see (such as, first aid training and attitude enhancement programs), provided they are not measures with proven negative impacts.
+
+However, in responding to the divided community views on the desirability of speed limit reduction, the RSC did not adopt MUARC's recommendation to reduce most of the state's speed limits by 10 km/h. Instead, the RSC determined that it should undertake a range of demonstration projects to illustrate the effects of speed limit reductions; adjust speed limits to complement road infrastructure; introduce more consistent speed limits and develop a community education program to enhance community understanding of the benefits of speed limit reduction.
+
+MUARC found that this amendment to its Optimal Safe System Option will reduce the strategy's potential to save people from being killed or seriously injured on WA roads from 12,600 to 11,000 over the 12 year life of the strategy. Nonetheless, by being able to clearly demonstrate the benefits and community views on this recommended initiative, the RSC has been able to give the Government and Parliament a high level of assurance that the strategy will be widely supported by the community which has led them to be more receptive and supportive of it.
+
+Following a change of Government in September 2008, the Minister for Road Safety announced the new Government's endorsement of the policy direction established in Towards Zero in Parliament on 19 March 2009 and received bipartisan support. Implementation is now progressing with widespread community and political support.
+
+Table 3 Snapshot of results of community consultation<sup>a</sup> .
+
+| Safe road use                                                              | Safe roads and roadsides                                                                                                                                                                                                                                                                        | Safe speeds – enforcement                                                                                                                                                                                                                                                                                             | Safe vehicles                                                                                 |
+|----------------------------------------------------------------------------|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------|
+| 94% supported or strongly supported<br>education programs                  | 95% supported or strongly supported<br>improving intersections                                                                                                                                                                                                                                  | 74% supported or highly supported this initiative<br>(with an additional 18% somewhat supporting<br>the measure)                                                                                                                                                                                                      | 90% supported or strongly<br>supported the ongoing<br>promotion of vehicle safety<br>features |
+| 86% supported or strongly supported<br>improved policing of the road rules | 91% supported or strongly supported<br>improving lengths of road or roadsides<br>and black spots<br>74% supported or strongly supported<br>building roadside barriers<br>68% thought that improving the roads<br>would be an effective or highly effective<br>approach to improving road safety | Safe speeds – limit reductions<br>48% supported or strongly supported reducing<br>speed limits near shopping centres<br>40% supported or strongly supported reducing<br>regional speed limits from 110 km/h to 100 km/h<br>40% supported or strongly supported reducing<br>urban speed limits from 60 km/h to 50 km/h | 79% supported or strongly<br>supported safety features on<br>all Government vehicles          |
+|                                                                            |                                                                                                                                                                                                                                                                                                 | 31% believed speed limit reductions would be<br>effective or highly effective (with an additional<br>27% thinking it would be somewhat effective).                                                                                                                                                                    |                                                                                               |
+
+<sup>a</sup> Unless otherwise specified, the percentages shown represent the responses of the representative population group – who were randomly sampled by Synovate. The full report outlining the results of the community consultation can be found at: <http://www.officeofroadsafety.wa.gov.au>.
+
+### 8. Conclusion
+
+The Western Australian government decided to take an ambitious approach by developing a new road safety strategy in accordance with the principles of the Safe System, rarely attempted elsewhere. Based on the underlying structure of a mathematical model developed by the Monash University Accident Research Centre in Melbourne, Australia, the METS–WA model allowed comparisons in terms of cumulative serious casualties saved to be made between the various elements of the Safe System, including the Cornerstones incorporating safe roads and roadsides, safe speeds, safe vehicles and safe road use. METS–WA was also used to combine these initiatives to predict overall road safety strategy performance over its 12-year duration and investigate the effects of delays in implementation or changes in predicted traffic growth.
+
+The strategy subsequently developed aimed to represent the best-practice solution achievable and has the potential to result in large reductions in severe trauma in Western Australia if adopted fully, with annual serious casualties estimated to be reduced by around 50% over 2006 levels ([Office of Road Safety, 2008\)](#page-12-0).
+
+This is the first time Western Australia has conducted widespread community consultation during the development of a road safety strategy and it is regarded as crucial to establishing the foundations for endorsement and implementation.
+
+To promote community acceptance of the Safe System philosophy and a bold, long term vision for road safety, it has been important to share the research with the community and listen to its views. The views of the community and the scientists on reducing road trauma were important considerations for Government in endorsing the recommended Towards Zero strategy.
+
+The successful adoption of the Safe System framework depends upon all participants in the road-transport system accepting their share of the responsibility for its safe operation. This community and stakeholder consultation process increases the chance that those objectives will be met as Western Australia now begins to build its capacity to implement Towards Zero.
+
+#### Acknowledgements
+
+The development of the original METS model was funded by VicRoads. Its permission to use the underlying model in Western Australia is gratefully acknowledged, as is the permission of the Western Australia Office of Road Safety to publish this paper.
+
+### Appendix A. Summary of community consultation
+
+| What                             | Purpose                                                                                                                                                                                                                                                                                                                                            | How                                                                                                                                                                                                                                                          | Where                                                | Respondents | Note                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
+|----------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|------------------------------------------------------|-------------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
+| Community<br>forums<br>(phase 1) | To inform the<br>participants of road<br>safety statistics in<br>their local area and<br>help participants<br>gauge their own<br>awareness of local<br>road safety issues and<br>driving behaviours<br>In addition the<br>workshops allowed<br>for community<br>debate on road safety<br>and promoted<br>community<br>engagement in road<br>safety | Hosted by members of<br>state Parliament in<br>their constituencies –<br>all members of the<br>community were<br>invited to attend<br>through media,<br>advertising and direct<br>invitations (from the<br>MP)                                               | 36 forums<br>were<br>conducted<br>in 19<br>locations | 1326        | Two workshops were held in most<br>of the locations. The morning<br>session was for community<br>representatives (mainly students<br>and apprentices). The afternoon<br>session was for community leaders<br>and 'influences', including those<br>that, as employers, have some<br>responsibility for the safety of their<br>employees. Handheld electronic<br>devices, which ensured anonymity,<br>were used to record (and capture)<br>participants' responses                                                                                                                                                                                                                                           |
+| Online survey<br>(phase 1)       | This was an internet<br>based version of the<br>questionnaire<br>presented at the<br>phase 1 community<br>forums, allowing<br>interested people<br>who had not been<br>able to attend a<br>forum to still have<br>input to the first<br>phase of community<br>consultation                                                                         | Advertisements were<br>placed in The West<br>Australian and the<br>details were emailed<br>to an extensive<br>database of people<br>who had previously<br>indicated an interest<br>in road safety<br>The survey also<br>received extensive<br>media coverage | Online                                               | 1188        | Of the respondents 71% were male.<br>The majority of the sample (43%)<br>was aged between 40 and 59. A<br>large proportion held a motorcycle<br>licence (40%). This group cannot be<br>considered a representative sample<br>as there are too many males, too<br>many respondents in full-time<br>employment and the age groups do<br>not represent the wider community<br>However, the fact that the<br>respondents took the trouble to<br>complete the online survey suggests<br>that they hold considered opinions<br>and are concerned about road<br>safety. Hence, while not a<br>representative sample of the<br>broader population, their views are<br>being considered<br>(continued on next page) |
+
+## Appendix A (continued)
+
+| What                                                                                                                                                                                  | Purpose                                                                                                                                                                                 | How                                                                                                                                                                                                                                                   | Where                                                                                                                                                                                              | Respondents             | Note                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
+|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-------------------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
+| Community and<br>stakeholder<br>forums (phase<br>2)                                                                                                                                   | This phase involved the<br>community and<br>stakeholders in providing<br>feedback on the MUARC<br>recommendations, which<br>were presented as the<br>Toward Zero draft                  | Advertisements<br>and some articles<br>were placed in<br>local newspapers.<br>Invites were sent<br>to stakeholders<br>and relevant                                                                                                                    | In eight locations<br>across the state<br>(metropolitan,<br>regional and<br>remote)                                                                                                                | 807                     | The attendees of these<br>forums were largely<br>stakeholders directly<br>involved and<br>concerned about road<br>safety                                                                                                                                                                                                                                                                                                                                                                   |
+| Online feedback<br>on 'Towards<br>Zero' – MUARC's                                                                                                                                     | discussion paper<br>recommendations<br>(phase 2)                                                                                                                                        | database contacts<br>The Towards Zero<br>draft discussion<br>paper was<br>presented online,<br>together with the<br>feedback form<br>allowing people<br>who were unable<br>to attend the<br>community<br>forums to submit<br>their feedback<br>online | Advertisements<br>and some articles<br>were placed in<br>local newspapers.<br>Details were sent<br>to stakeholders<br>and relevant<br>database contacts.<br>Promoted at the<br>community<br>forums | Online                  |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |
+| This was an open<br>'survey'. Any<br>interested<br>person could<br>complete it                                                                                                        |                                                                                                                                                                                         |                                                                                                                                                                                                                                                       |                                                                                                                                                                                                    |                         |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |
+| Independent<br>representative<br>sample                                                                                                                                               | The primary purpose of<br>this research was to<br>obtain feedback from the<br>larger community and not<br>just from those with an<br>interest or with strong<br>opinions on road safety | Recruited via a<br>phone survey<br>conducted<br>through an<br>independent social<br>research company<br>– Synovate                                                                                                                                    | Respondents were<br>randomly<br>contacted by<br>phone and were<br>given the option to<br>receive and then<br>submit their<br>feedback online or<br>as a hard copy via<br>post                      | 649 (correct to<br>±3%) | The independent<br>research company<br>ensured this sample<br>was representative of<br>the community gender<br>and age spread and<br>included metro,<br>regional and remote<br>participants<br>This representative<br>community survey<br>ensured a balanced<br>view from across the<br>community and all<br>voices are heard – not<br>only the loudest<br>This is considered to be<br>the most reliable<br>representation of the<br>thoughts and opinions<br>of the general<br>population |
+| Additional specific<br>forums<br>(industry<br>leaders, special<br>interest groups<br>(including<br>cyclists and<br>pedestrians)<br>and Road Safety<br>Council agency<br>stakeholders) | These forums encouraged<br>direct feedback from<br>specific groups including<br>vulnerable road users<br>such as motorcyclists, the<br>police and representatives<br>of large companies | Invitations were<br>sent to specific<br>groups,<br>companies,<br>organisations, etc.                                                                                                                                                                  | Perth convention<br>and Exhibition<br>centre                                                                                                                                                       | 200                     |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |
+
+### <span id="page-12-0"></span>References
+
+- Aarts, L., Van Schagen, I., 2006. Driving speed and the risk of road crashes: a review. Accident Analysis and Prevention 38, 215–224.
+- Corben, B.F., Logan, D.B, Johnston, I.R., Vulcan, A.P., 2008. Development of a New Road Safety Strategy for Western Australia 2008–2020, Report Number 282, Monash University Accident Research Centre, June.
+- Elvik, R., Christensen, P., Amundsen, A., 2004 Speed and road accidents: an evaluation of the Power Model. Oslo.
+- Haworth, N., Ungers, R., Vulcan, A.P., Corben, B.F., 2001. Evaluation of a 50 km/h Default Urban Speed Limit for Australia. Monash University Accident Research Centre, Melbourne.
+- Jacobs, G., Aeron-Thomas, A., Astrop, A., 2000. Estimating global road fatalities. TRL Report 445. Transport Research Laboratory, Berkshire, UK.
+- Lie, A., Tingvall, C., Krafft, M., Kullgren, A., 2006. The effectiveness of electronic stability control (ESC) in reducing real life crashes and injuries. Traffic Injury Prevention 7, 38–43.
+- Meuleners, L., Hendrie, D., Legge, M., Cercarelli, L.R., 2005. An Evaluation of the Effectiveness of the Black Spot Programs in Western Australia, 2000–2002.
+
+- Injury Research Centre, School of Population Health, The University of Western Australia, RR155. Crawley, WA.
+- Nilsson, G., 2004. Traffic safety dimensions and the power model to describe the effect of speed on safety, Doctoral thesis, Department of Technology and Society, Traffic Engineering, Lund, Sweden. [http://www.lub.lu.se/luft/diss/](http://www.lub.lu.se/luft/diss/tec_733/tec_733.pdf) [tec\\_733/tec\\_733.pdf](http://www.lub.lu.se/luft/diss/tec_733/tec_733.pdf) [30.6.09].
+- Office of Road Safety, W.A., 2008. Towards Zero Recommended Strategy. Perth, Western Australia.
+- Regan, M.A., Triggs, T.J., Young, K.L., Tomasevic, N., Mitsopoulos, E., Stephan, K., Tingvall, C., 2006 On-Road evaluation of Intelligent Speed Adaptation, Following Distance Warning and seatbelt reminder systems: final results of the TAC Safecar project. IN CENTRE, M.U.A.R. (Ed.) MUARC Report Series, Clayton, Monash University Accident Research Centre.
+- Scully, J., Newstead, S., 2008. Evaluation of electronic stability control effectiveness in Australasia. Accident Analysis & Prevention 40, 2050–2057.
+- Sherwood, O., 2009. ''The illusion of precision". Personal communication, 8 April.
+- Vulcan, A.P., Corben, B.F., 1998. Prediction of Australian road fatalities for the year 2010. Presented to: National Road Safety Summit, Canberra, ACT.

Zotero/001_artiklid/Road Safety Indicators/cottrillevaluatingpedestriancrashesareas2010.md

@@ -0,0 +1,376 @@
+---
+category: literaturenote
+citekey: cottrillevaluatingpedestriancrashesareas2010
+title: Evaluating pedestrian crashes in areas with high low-income or minority populations
+authors: "Cottrill, Caitlin D.; Thakuriah, Piyushimita (Vonu)"
+year: 2010
+date: 2010-00-00 2010
+doi: 10.1016/j.aap.2010.04.012
+publication: "Accident Analysis & Prevention"
+url: "https://doi.org/10.1016/j.aap.2010.04.012"
+zotero_key: PFMRW59R
+zotero_storage: S997TRUT
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "Cottrill, Caitlin D."
+status: converted
+---
+Contents lists available at [ScienceDirect](http://www.sciencedirect.com/science/journal/00014575)
+
+## Accident Analysis and Prevention
+
+journal homepage: [www.elsevier.com/locate/aap](http://www.elsevier.com/locate/aap)
+
+![](_page_0_Picture_5.jpeg)
+
+# Evaluating pedestrian crashes in areas with high low-income or minority populations
+
+Caitlin D. Cottrill <sup>a</sup>,∗, Piyushimita (Vonu) Thakuriah<sup>b</sup>,<sup>1</sup>
+
+- <sup>a</sup> Urban Transportation Center, University of Illinois, Chicago, 412 South Peoria Street, Suite 340, Chicago, IL 60607-7036, United States
+- <sup>b</sup> Department of Urban Planning and Policy, University of Illinois, Chicago, 412 South Peoria Street, Suite 340, Chicago, IL 60607-7036, United States
+
+#### article info
+
+Article history: Received 14 May 2009 Received in revised form 26 April 2010 Accepted 29 April 2010
+
+Keywords: Pedestrian Crash Income Minority Crime Transit
+
+### abstract
+
+In this paper, we present an analysis of the relationship between pedestrian–vehicle crashes and characteristics of areas with high low-income and minority populations in the Chicago metropolitan area (also called environmental justice or EJ areas in the United States). While related research has indicated that pedestrian crashes occur more frequently in these areas than in non-EJ areas, this paper attempts to relate the incidence to environmental characteristics and behavioral factors through a better understanding of the contributing factors present in crash occurrences in EJ versus non-EJ areas. Specially constructed small-area factors from a Spatial Decision Support System (SDSS) are used to explain pedestrian–vehicle crashes.
+
+Using a Poisson model that corrects for underreporting, we find that pedestrian crash incidents in EJ areas are related to variables of exposure (including the suitability of the area for walking and transit accessibility), crime rates, transit availability, and general population demographics such as income and presence of children. Results suggest that it may be necessary to better incorporate a safety perspective or measures of safety improvements in pedestrian and transit improvements and expansion programs within EJ areas.
+
+© 2010 Elsevier Ltd. All rights reserved.
+
+#### **1. Introduction**
+
+In 2005, motor-vehicle crashes killed 4881 pedestrians in traffic in the United States and sent 120,815 pedestrians to emergency medical departments (National Highway Traffic Safety Administration [\[NHTSA\], 2006\).](#page-10-0) While the contributing causal factors to these crashes vary widely, previous studies have indicated that certain factors relating to the socio-demographics and the physical environment of neighborhoods may heighten the risk of pedestrian–vehicle crashes. These initial indications are particularly relevant in regards to environmental justice (EJ) guidelines which broadly require each U.S. federal agency to make the alleviation of inequitable environmental burden a part of its mission by identifying and addressing, as appropriate, disproportionately high and adverse human health or environmental effects of its programs, policies, and activities on minority and low-income populations (Environmental Protection Agency, [EPA, Executive Order, 1994\).](#page-10-0) This paper is intended to specifically address pedestrian–vehicle crashes within the framework of EJ guidance to determine if pedestrian safety is an issue that should be specifically addressed within EJ activities.
+
+Several authors have noted that there is an increased incidence of pedestrian–vehicle crashes in EJ areas [\(Mid-America Regional](#page-10-0) [Council, 2007; Murtha, 2005\).](#page-10-0) EJ areas are those with high proportions of minority and low-income households (the specific definition used in this paper is given in Section [3.1\).](#page-2-0) While numbers gathered from these evaluations are of interest, what is notable is that occurrences of crashes are often cited while paying little attention to the question of general exposure to risk, including such factors as mixture of land uses, the number of potential pedestrians in an area, or the overall character of the surrounding environment and whether it is inviting to and safe for pedestrian travel.
+
+The current study more extensively explores some geographic correlates of pedestrian–vehicle crashes, through an analysis of data from the Chicago metropolitan area in the State of Illinois, USA, with particular emphasis on spatial variations on these events by EJ versus non-EJ area. We examine 2005 Chicago vehicle–pedestrian crash data, gathered from the [Illinois Department of Transportation](#page-10-0) [\(IDOT\)](#page-10-0) as a case study in order to hold factors beyond socio-demographics constant and to provide information relating to risk levels in environmental justice areas. Statistical evidence, as presented below, shows that an elevated risk is
+
+<sup>∗</sup> Corresponding author. Tel.: +1 312 996 4820; fax: +1 312 413 0006.
+
+E-mail addresses: [ccottr2@uic.edu](mailto:ccottr2@uic.edu)(C.D. Cottrill), [vonu-pt@uic.edu](mailto:vonu-pt@uic.edu)(P. Thakuriah).
+
+<sup>1</sup> Tel.: +1 312 996 4820; fax: +1 312 413 0006.
+
+present, perhaps indicating that policies and programs addressing pedestrian–vehicle crashes in these areas should be targeted to those factors that are likely to account for such increases in risk.
+
+The objective of the paper is to report on a comparative analysis of motor-vehicle–pedestrian crashes in EJ versus non-EJ areas and to understand which factors contribute to variations in pedestrian crashes in those areas. We have taken the view that two groups of geographic factors can potentially affect observed differences – those relating to the physical environment (called environmental factors) of the areas and those relating to social behaviors, cognitive and demographics (called behavioral factors) of the residents of the areas. These measures are a part of an ongoing research project to develop a Spatial Decision Support System on the Chicago metro area for planning purposes by the authors' research team. The construction and potential use of these measures in accident analysis are described. The importance of these factors in explaining EJ versus non-EJ differences in pedestrian crashes are demonstrated using exploratory methods as well as regression. An issue of concern that is addressed in the paper is underreporting of pedestrian crashes – we have adopted a statistical approach to address potential underreporting in the Chicago vehicle–pedestrian crash data.
+
+The paper is organized as follows: prior literature on environmental justice and pedestrian crashes is reviewed in Section 2. The study area, the method by which EJ areas were determined and the environmental and behavioral factors considered are presented in Section [3. S](#page-2-0)ection [4](#page-3-0) presents an exploratory analysis of crash trends in EJ versus non-EJ areas and reports summary statistics on the factors and on crash patterns in the two types of areas. Statistical models of pedestrian crashes are given in Section [5. S](#page-7-0)ummary and conclusions are drawn in Section [6.](#page-9-0)
+
+#### **2. Background and prior literature**
+
+In 1994, President Clinton signed Executive Order 12898, "Federal Actions to Address Environmental Justice in Minority Populations and Low-Income Populations". As part of this order, it was required that, "each Federal agency shall make achieving environmental justice part of its mission by identifying and addressing, as appropriate, disproportionately high and adverse human health or environmental effects of its programs, policies, and activities on minority populations and low-income populations..." (1994). Partially in response to this order, and partially in response to growing awareness by residents and activists in environmental justice communities, pedestrian issues in low-income and minority areas have of late been gaining increased visibility and dialogue.
+
+Several authors have examined geographic variations in pedestrian crash rates at both a macro (state or regional) level as well as a micro (intra-regional) level. For example, [Paulozzi \(2006\)](#page-10-0) found that the highest pedestrian fatality rates concentrate in Sunbelt states that have experienced rapid population growth in the past 50 years. This pattern may result from at least three features of these states: (a) a high percentage of urban vehicle miles traveled; (b) urban sprawl; and (c) a high prevalence of alcohol use—especially heavy use—among Sunbelt pedestrians. [Beck et al.](#page-10-0) [\(2007\), i](#page-10-0)n a comparison of the Atlanta metro region with the rest of the U.S., reported that from 2000 to 2004, pedestrian fatality rates declined in the United States, but the Atlanta metropolitan statistical area did not experience the same decline. Pedestrian fatality rates for males, Hispanics, and the 15–34 and 35–54 year age groups were higher in Atlanta than in the United States overall.
+
+Of direct relevance to this paper is a stream of literature on intra-regional variations in pedestrian crash rates. [Dougherty et al.](#page-10-0) [\(1990\)](#page-10-0) found that for Montreal, neighborhoods with income levels in the lowest quintile had death and accident rates that were at least four times the rates for children living in the least disadvantaged neighborhoods. Several authors have written about the complex interaction of factors that put pedestrians in poor neighborhoods, especially child pedestrians, at greater risk from moving vehicles ([Padilla et al., 1976; Brown and Davidson, 1978;](#page-10-0) [Bijur et al., 1986; Lyons et al., 2008; Guyer et al., 1985\)](#page-10-0) including "the lack of secure play space; dwellings adjacent to busy traffic flows; hazardous journeys to school and other facilities; less developed cognitive skills, which would imply risk-taking; and greater stress (physiological, social, and psychological)." ([Bagley,](#page-10-0) [1992\)](#page-10-0) [LaScala et al. \(2004\), u](#page-10-0)sing data from four California communities, found that annual numbers of pedestrian injuries were greater in areas with higher youth population densities, more unemployment, fewer high-income households, and greater traffic flow.
+
+[Loukaitou-Sideris and Liggett \(2007\)](#page-10-0) evaluated pedestrian accidents in Los Angeles in the context of socio-demographic and land use characteristics, eventually concluding that, "The coefficients on these variables [percent of the population below poverty and percent Latino] in each model were positive, supporting the assumption that pedestrian accidents are more likely to occur in low-income, minority neighborhoods once other aspects of risk are controlled for." Similar results were found in Nassau County, New York (pertaining to risk of hospitalization for pedestrian injuries). Additionally, the Surface Transportation Policy Project's (STPP) report, Mean Streets 2002 [\(STPP, 2002\) s](#page-10-0)tated that,
+
+Nationwide, non-Hispanic whites comprise 69 percent of the population. However, only 60 percent of pedestrian deaths for which ethnicity is known are non-Hispanic whites. In contrast, African-Americans make up more than one in five (20 percent) pedestrian deaths, though they represent only 12 percent of the total U.S. population. Likewise, Latino pedestrians comprise 13.5 percent of deaths, but only 12.5 percent of the total U.S. population. However, although the current literature includes studies of individual and environmental characteristics related to injury rates, there exist only a handful of neighborhood studies that introduce specific geographic components with general applicability across communities [\(LaScala et al., 2000, 2001, 2004\).](#page-10-0)
+
+While it is not necessarily the case that these pedestrian deaths took place near the location of residence, it is critical to evaluate the potential that the socio-demographics and the nature of the built environment of the home location may play a part in the relative imbalance of the ethnicity of crash victims.
+
+Several international studies have also indicated a relationship between pedestrian crashes and areas of high low-income and/or minority populations. For example, in a scan of literature addressing the issue from a number of countries, including the US, the United Kingdom, and Australia, among others, [Laflamme and](#page-10-0) [Diderichsen \(2000\)](#page-10-0) found that for most types of traffic injuries, including pedestrian injuries, "...mortality and morbidity are often higher among children from lower social positions and in more deprived socio-economic areas." In a study of English and Welsh families, [Edwards et al. \(2006\)](#page-10-0) found that the pedestrian death rate of children of parents classified as long-term unemployed or never employed was 20.6 times higher than that of children of parents in higher managerial or professional occupations. Finally, a study of traffic crashes involving Maoris in New Zealand conducted by [Sargent et al. \(2004\)](#page-10-0) found a higher proportion of traffic casualties and injuries for all crashes (including pedestrian) for those Maoris living in areas of higher relative deprivation. These findings indicate that potential linkages between socio-economic variables such as income and race and pedestrian crashes are a worldwide phenomena and require additional study.
+
+#### <span id="page-2-0"></span>**3. Study area**
+
+In 2005, the [Illinois Department of Transportation \(IDOT\)](#page-10-0) reported 4886 vehicle crashes in the Chicago region in which a pedestrian was involved. Of those crashes, 120 (or about 3%) resulted in the death of the pedestrian. [Fig. 1](#page-3-0) shows the distribution of vehicle–pedestrian crashes in the six-county Chicago metro area (consisting of Cook, McHenry, Kane, Will, Lake, and DuPage counties; Cook county includes the City of Chicago). Overall, pedestrian–vehicle crashes accounted for about 1% of all 2005 Illinois crashes and about 2% of all crashes in the Chicago region. [Fig. 1](#page-3-0) shows that the distribution of pedestrian–vehicle crashes are not random throughout the region; rather, it appears that crashes are concentrated in the downtown business district (the "Loop") and areas in south and west Chicago. The goal of this paper is to utilize the Chicago region as a case study to analyze pedestrian–vehicle crashes, focusing on those factors that are considered under environmental justice regulations and to determine if issues beyond pedestrian exposure play a part in influencing pedestrian–vehicle crash rates.
+
+#### 3.1. Determination of EJ areas
+
+EJ and non-EJ areas are defined at the level of census tracts. There are several pros and cons in using census tracts as the spatial unit for equity studies. Census tracts have a relatively homogeneous population of about 4000 and are delimited by local persons and thus "reflect the structure of the metropolis as viewed by those most familiar with it" ([Bogue, 1985\).](#page-10-0) They are small enough to reduce the possibility of "aggregation errors" and "ecological fallacies" [\(Anderton et al., 1994\) b](#page-9-0)ut large enough to potentially avoid impacts that spill over beyond smaller spatial units such as block or block groups ([Been, 1994\),](#page-10-0) although other authors have noted that impact areas may run well beyond the boundaries of individual tracts in metropolitan areas [\(Mohai, 1995\).](#page-10-0) Further, it is the most commonly used geographic unit of analysis [\(Anderton](#page-9-0) [et al., 1994\)](#page-9-0) – in our case, the spatial level corresponds to the unit of analysis in the Chicago area Spatial Decision Support System and it is deemed to be a reasonable approximation of the concept of a neighborhood ([Denton and Massey, 1991\).](#page-10-0) Although there are several studies that compare outcomes related to mobility and transportation conditions in EJ versus non-EJ areas, there is no consistency among studies about how EJ areas are defined. In safety research, [Wier et al. \(2009\)](#page-10-0) recently used census tracts in the San Francisco area to determine the relationship between street, land use, and population characteristics, including commute behaviors and census tract-level pedestrian–vehicle injury collisions.
+
+The use of census tracts as the level of analysis also introduces the need to examine the way in which population exposure is evaluated. Because, as noted above, census tracts are fairly homogenous in population size, for purposes of this analysis we have chosen to use population density as a measure of exposure. While the use of actual pedestrian counts would be useful, such information is not generally available on an area-wide basis. The use of density in this calculation is consistent with methods proposed by such entities as the [FHWA \(1999\), w](#page-10-0)hich suggests population density as a method of evaluating potential travel behavior from a contextoriented perspective, and such researchers as [Wedagama et al.](#page-10-0) [\(2006\)](#page-10-0) and [Graham and Glaister \(2003\), w](#page-10-0)ho use population density as an explanatory variable in models of crash frequencies and who suggest that increased urban density may be both an indicator of deprivation, which has been shown as influencing pedestrian crashes, and as an influence on traffic volumes and speed, which may also have an influence. [Raford and Ragland \(2003\), a](#page-10-0)dditionally state that, "Physical factors such as residential population density, mixed land use, street connectivity, and adequate pedestrian facilities have been identified as key physical variables that influence the number and types of walking trips." By using density, we are able to better represent the relative distribution of pedestrian crashes across the Chicagoland region. As the region includes a large variety of census tract types (ranging from rural to highly urban), the spatial area of each tract also varies greatly. It may be misleading to directly compare incidents of pedestrian crashes in highly rural tracts with those in highly urban tracts, as the spatial density will vary greatly. By using population density, we are better able to perform comparative analyses.
+
+The definition of EJ areas adopted here replicates the rule given in [Sriraj et al. \(2003\). E](#page-10-0)J neighborhood criteria are determined in this paper by computing demographic and economic information for Cook County, and basing the threshold analysis for EJ census tracts on the results. Using this method, the following rules are determined to define EJ tracts: (a) Black – according to the 2000 Census, 26% of all residents of Cook County are Black. All census tracts with a Black population greater than 26% qualify as EJ neighborhoods; (b) Hispanic – according to the 2000 Census, 20% of all residents of Cook County are Hispanic. All census tracts with a Hispanic population greater than 20% qualify as EJ neighborhoods; (c) low-income – all households that are within 150% of the poverty threshold are considered low-income. Using the reference area technique, this population is 21.5% of the total population in Cook County. Accordingly, census tracts that have more than 21.5% of their population within the low-income threshold, qualify as EJ neighborhoods.
+
+#### 3.2. Environmental and behavioral factors relating to pedestrian crashes
+
+The Chicago area Spatial Decision Support System (SDSS) integrates a Multi-Criteria Decision-Making (MCDM) environment with small-area spatial data to integrate transportation decision-making with housing, community development, economic development and physical planning. Using a variety of data sources and transportation modeling outputs, it consists of a number of indicators on traffic and transportation, accessibility measures, regional employment opportunities, small-area employment estimates based on forecasted job openings and actual jobs, affordable housing, school quality, crime, health, land use and the built environment.
+
+The factors within the SDSS, which were used in this study, can be categorized into two groups: the first group of factors relate to the physical environment of the area including the level of vehicular traffic flow, quality and complexity of the walking environment, pedestrian crowding possibilities (at transit stations or commercial developments), road crossing opportunities which present possibilities of conflict with vehicular traffic, population density and the extent of crime (called environmental factors). The second group of factors relate to social behaviors, cognitive and demographics (called behavioral factors), which lead to variations in the ability to cope effectively with these hazards, including percent of population with little or no English-speaking ability as indicators of unfamiliarity with the environment, percent of school-going children and percent of carless households.
+
+[Table 1](#page-4-0) presents the indicators used with a brief explanation of each indicator. Indicators were chosen mostly on the basis of prior, published research as well as local knowledge derived from professionals in the Chicago metro area, who work in the area of transportation, safety and public health. Using a methodologically rigorous approach to ensure that all possible factors that account for systematic differences between EJ and non-EJ tracts and omitted variable bias, is left for future research.
+
+<span id="page-3-0"></span>![](_page_3_Figure_2.jpeg)
+
+**Fig. 1.** Map showing 2005 pedestrian crashes in the Chicago metro area.
+
+### **4. Exploratory analysis of pedestrian crashes in EJ versus non-EJ areas**
+
+[Tables 2 and 3](#page-4-0) show summary statistics on variables that are of importance in the analysis. [Table 2](#page-4-0) shows that the number of pedestrian crashes in EJ areas are well over twice that in non-EJ areas and that the pedestrian crash rate per 1000 population is 9.66 in EJ areas compared to 3.37 in non-EJ areas. Large differences do not exist in the proportion of injuries of different types between EJ and non-EJ areas. Injuries are classified as follows [\(IDOT Crash](#page-10-0) [Report Data Dictionary, 2005\):](#page-10-0)
+
+- - A Injuries: incapacitating but not fatal injuries, including those which prevent the injured party from walking, driving, or normally continuing the activities her or she was capable of performing before the injury occurred.
+- - B Injuries: nonincapacitating and non-fatal injuries, evident to observers at the crash scene.
+
+- C Injuries: possible injuries, which are not classified as type A or B above.
+
+Fatal crashes are 2.2% of all crashes in EJ areas compared to 3% in non-EJ areas.
+
+Pedestrian crash victims tend to be younger in EJ areas (close to 28% of pedestrians involved in crashes in EJ areas are less than 16 years of age, compared to about 10% of pedestrians in non-EJ areas) and where the gender of the crash victim is known, involve a slightly larger share of males (56% compared to 55%). [Table 3](#page-5-0) shows that the median household income in EJ areas is \$36,274.79 compared to \$61,414 in non-EJ areas. A larger proportion of EJ area residents have "low" levels of English-speaking ability and also a greater share of school-age children (30% compared to 26% in non-EJ areas). About 24% of households in EJ areas have no cars, compared to only 8% of households in non-EJ areas.
+
+[Table 3](#page-5-0) shows that the mean pedestrian crash rate in EJ tracts is 3.26 and that in non-EJ tracts is 1.94, with a difference of 1.32.
+
+<span id="page-4-0"></span>**Table 1** Environmental and behavioral Indicators used in the study.
+
+| Indicator                                               | Description                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           |
+|---------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
+| Environmental Indicators at census tract-level          |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
+| Transit availability index (TAI)                        | Composite index giving the extent to which residents have access to transit (bus and rail); based<br>on three input measures – frequency (person-minutes served), hours of service (number of hours)<br>and service coverage (percentage of census tract area covered). See Minocha et al. (2008) for more<br>details                                                                                                                                                                                                 |
+| Pedestrian accessibility index (PED)                    | Composite index ranking tract suitability for pedestrian travel; based on input values of<br>population, income, number of households, amount of commercial and residential land uses as a<br>percentage of census tracts, weighted trip origins and destinations, and Pedestrian Environment<br>Factor (PEF) values, where PEF's are the average number of blocks for the quarter section within<br>each census tract and the eight adjacent quarter sections. See Cottrill and Thakuriah (2008) for<br>more details |
+| Sum of annual average daily traffic (SUM AADT)          | Total annual average daily traffic on links of all highway functional classes within census tract;<br>output from regional traffic assignment model and GIS                                                                                                                                                                                                                                                                                                                                                           |
+| Total miles of roads (SUM LENGTH)                       | Total miles of roads of all functional classifications within census tract; output from GIS                                                                                                                                                                                                                                                                                                                                                                                                                           |
+| Total number of schools (NO SCHOOLS)                    | Count of all schools within census tract                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |
+| Crime rate (CRIME)                                      | Total violent and non-violent crimes in census tracts                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |
+| Behavioral indicators at census tract-level             |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
+| Median household income (MEDINC)                        | Median household income; based on census 2000                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |
+| Population density (POP SQMILE)                         | Population per square mile in census tract (census 2000 population)                                                                                                                                                                                                                                                                                                                                                                                                                                                   |
+| Percent with no cars (PERNOCAR)                         | Percentage of population without access to a vehicle (census 2000 data)                                                                                                                                                                                                                                                                                                                                                                                                                                               |
+| Percent commercial (PER COMM)                           | Percentage of census tract used for commercial purposes (based on CATS land use 1990 file)                                                                                                                                                                                                                                                                                                                                                                                                                            |
+| Percent children (PERCHILDREN)                          | Percentage of population under the age of 16 (census 2000 data)                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
+| Percent who speak limited or no English (PERLOWENGLISH) | Percentage of persons who speak no English or limited English (Census 2000 data)                                                                                                                                                                                                                                                                                                                                                                                                                                      |
+
+Our objective in Section [5](#page-7-0) is to examine if and how much, ceteris paribus, environmental and behavioral factors explain the crash rate difference between EJ and non-EJ areas.
+
+The built environment in EJ areas differs from that in non-EJ areas in significant ways. EJ areas are of much higher density (13,910 population per square mile versus 7111 per square mile in non-EJ areas) but have fewer schools per census tract (1.89 on the average, compared to 2.68 in non-EJ areas). EJ tracts are estimated to have lower Average Annual Daily Traffic (with a SUM AADT value of 229,599 miles) compared to 340,739 miles in non-EJ areas. EJ areas also have lower highway length (with a SUM LENGTH value about 3.5 miles on the average per census tract) compared to non-EJ areas (with an average of 9.84 miles).
+
+The average pedestrian accessibility rank (PED) is slightly higher in EJ areas (the t-test of difference between PED in EJ versus non-EJ areas is significant only at the .10 level). The transit availability
+
+**Table 2** Comparison of EJ and non-EJ tracts on pedestrian crash victim socio-demographics and injury severity.
+
+|                           | EJ tract  |         | Non-EJ tract |         | All tracts |         |
+|---------------------------|-----------|---------|--------------|---------|------------|---------|
+|                           | Number    | Percent | Number       | Percent | Total      | Percent |
+| Crash totals              | 3367.00   | 100.00% | 1501.00      | 100.00% | 4868.00    | 100.00% |
+| Crash rates               |           |         |              |         |            |         |
+| Pop 2001 Census Est.      | 3,486,832 |         | 4,458,285    |         | 4,458,285  |         |
+| Count of Ped crashes      | 3367      |         | 1501         |         | 4868       |         |
+| Crash rate                | 0.000966  |         | 0.000336677  |         | 0.000337   |         |
+| Crashes/10,000            | 9.66      |         | 3.37         |         | 6.13       |         |
+| Injury severity           |           |         |              |         |            |         |
+| A Injury crash*           | 664       | 19.72%  | 331          | 22.05%  | 995        | 20.44%  |
+| B Injury crash**          | 1717      | 50.99%  | 746          | 49.70%  | 2463       | 50.60%  |
+| C Injury crash***         | 875       | 25.99%  | 371          | 24.72%  | 1246       | 25.60%  |
+| Fatal crash               | 74        | 2.20%   | 45           | 3.00%   | 119        | 2.44%   |
+| No injuries               | 37        | 1.10%   | 8            | 0.53%   | 45         | 0.92%   |
+| Hit and run               |           |         |              |         |            |         |
+| No                        | 2276      | 67.60%  | 1190         | 79.28%  | 3466       | 71.20%  |
+| Yes                       | 1091      | 32.40%  | 311          | 20.72%  | 1402       | 28.80%  |
+| Age (in years) of victims |           |         |              |         |            |         |
+| 0–5                       | 132       | 3.92%   | 26           | 1.75%   | 158        | 3.26%   |
+| 6–16                      | 824       | 24.47%  | 247          | 16.61%  | 1071       | 22.06%  |
+| 17–35                     | 899       | 26.70%  | 485          | 32.62%  | 1384       | 28.51%  |
+| 36–50                     | 666       | 19.78%  | 313          | 21.05%  | 979        | 20.17%  |
+| 51–70                     | 446       | 13.25%  | 262          | 17.62%  | 708        | 14.59%  |
+| 71 and more               | 400       | 11.88%  | 154          | 10.36%  | 554        | 11.41%  |
+| Gender                    |           |         |              |         |            |         |
+| Female                    | 1314      | 39.03%  | 624          | 41.57%  | 1938       | 39.81%  |
+| Male                      | 1709      | 50.76%  | 774          | 51.57%  | 2483       | 51.01%  |
+| Unknown                   | 344       | 10.22%  | 103          | 6.86%   | 447        | 9.18%   |
+
+<sup>\*</sup> A Injuries: Incapacitating but not fatal injuries, including those which prevent the injured party from walking, driving, or normally continuing the activities her or she was capable of performing before the injury occurred.
+
+<sup>\*\*</sup> B Injuries: Nonincapacitating and non-fatal injuries, evident to observers at the crash scene.
+
+<sup>\*\*\*</sup> C Injuries: Possible injuries, which are not classified as type A or B above.
+
+<span id="page-5-0"></span>**Table 3** Variables utilized in the analysis, tests of significance, effect size and correlations.
+
+| Variable              | EJ tract                                                                  |                    |          | Test of significance and effect size |          |
+|-----------------------|---------------------------------------------------------------------------|--------------------|----------|--------------------------------------|----------|
+|                       | "No"  d  ≤ .20: small; .20 <  d  ≤ .50: medium;<br>.50 <  d  ≤ .80: large | "Yes"<br>(N = 946) | t value* | Cohen's d**                          |          |
+|                       | (N = 886)                                                                 |                    |          |                                      |          |
+|                       | Mean                                                                      | Mean               |          |                                      |          |
+| PED CRASH             | 1.94                                                                      | 3.26               | −7.87    | 0.37                                 |          |
+| Environmental factors |                                                                           |                    |          |                                      |          |
+| TAI                   | 0.61                                                                      | 0.67               | −10.86   | 0.51                                 | 0.20206  |
+| PED LOW (binary)      | 0.26                                                                      | 0.25               | 0.47     | −0.02                                | −0.03654 |
+| SUM AADT              | 340,739.10                                                                | 229,599.87         | 5.44     | −0.26                                | 0.03028  |
+| SUM LENGTH            | 9.84                                                                      | 3.49               | 11.7     | −0.56                                | −0.12138 |
+| NOOFSCHOOLS           | 2.68                                                                      | 1.89               | 6.83     | −0.32                                | 0.29065  |
+| POP00 SQMI            | 7,111.12                                                                  | 13,910.09          | −14.26   | 0.67                                 | 0.29913  |
+| PERCRIME              | 3.03                                                                      | 4.91               | −22.16   | 0.74                                 | 0.27328  |
+| PED                   | 35.31                                                                     | 36.23              | −1.8     | 0.68                                 | 0.31226  |
+| Behavioral factors    |                                                                           |                    |          |                                      |          |
+| WLKTOWRK              | 79.25                                                                     | 52.59              | 3.24     | −0.15                                | 0.29943  |
+| MEDHHINC99            | 67,414.06                                                                 | 36,274.79          | 32.85    | −0.78                                | −0.20477 |
+| PERNOCAR              | 0.08                                                                      | 0.24               | −24.05   | 1.12                                 | 0.31196  |
+| PER COMM              | 0.04                                                                      | 0.09               | −9.08    | 0.42                                 | 0.21792  |
+| PERCHILDREN           | 0.26                                                                      | 0.30               | −10.19   | 0.48                                 | 0.00721  |
+| PERLOWENGLISH         | 0.25                                                                      | 0.43               | −12.41   | 0.57                                 | 0.10207  |
+
+<sup>\*</sup> Italicized and bold estimates are significant at the .01 level.
+
+index (TAI) is significantly larger in EJ areas, indicating that the built environment, land uses and transit access levels may be more conducive to walking in the EJ areas. Figs. 2 and 3 show Trellis plots of variations in pedestrian crashes by EJ and non-EJ census tract, for different levels of TAI and PED. The top panel of the Trellis plots in Fig. 2 shows variations in pedestrian crashes by EJ versus non-EJ census tracts for "High" levels of TAI (a TAI value of "High" indicates census tracts with the top 25% of values of transit availability, "Medium High" indicates census tracts with the second highest 25% of TAI values and so on). [Fig. 3](#page-6-0) displays similar information on PED. The plots also show the mean pedestrian crash rates for each TAI/PED and EJ condition.
+
+Overall, the mean pedestrian crash rates for both EJ and non-EJ tracts decrease with decrease in TAI levels. In the case of non-EJ
+
+![](_page_5_Figure_10.jpeg)
+
+**Fig. 2.** Trellis plot of variations in count of crashes by census tract for combinations of EJ and transit availability index (TAI).
+
+<sup>\*\*</sup> The interpretation of effect sizes given by Cohen's d for difference in means with pooled variance is generally difficult due to "the low level of consciousness of the magnitude of phenomenon" ([Cohen, 1992\),](#page-10-0) but may be interpreted generally as follows: <sup>|</sup>d| ≤ .20: small; .20 < <sup>|</sup>d| ≤ .50: medium; .50 < <sup>|</sup>d| ≤ .80: large. # Correlation with PED CRASH.
+
+<span id="page-6-0"></span>![](_page_6_Figure_2.jpeg)
+
+**Fig. 3.** Trellis plots of variations in counts of crashes by census tracts for combinations of pedestrian accessibility (PED) and EJ status of census tract.
+
+tracts with High TAI levels (on the left hand side of the top panel), the mean crash rate is 3.75, decreasing to 1.37 in the case of tracts with Low TAI levels. The mean crash rates for each TAI condition is higher for EJ tracts compared to non-EJ tracts; but in the case of EJ tracts too, the mean pedestrian crash rate decreases from 3.94 in the case of tracts with HIGH TAI levels to a mean of 2.56 in the case of EJ tracts with Low TAI levels. The difference between the mean crash rates of EJ and non-EJ tracts is substantially greater for tracts with Low–Medium and Low levels of TAI compared to tracts with High and High–Medium TAI levels.
+
+Further, the percent of both non-EJ and EJ tracts with zero crashes increases with decrease in their TAI level. The percent of non-EJ tracts that have zero pedestrian crashes increases from 15% of all non-EJ tracts that have High TAI levels, to about 26% for tracts with High–Medium TAI levels, to approximately 42% for tracts with Low–Medium TAI levels and leveling off at about 40% of non-EJ tracts with Low levels of TAI with zero crashes. The percent of EJ tracts (on the right hand side of the top panel) that have zero pedestrian crashes also share a similar relationship to TAI levels; the percent of EJ tracts with High TAI levels that have zero recorded pedestrian crashes is close to 15% and increases to about 24% for EJ tracts with Low TAI levels. The percent of non-EJ tracts with low levels of pedestrian crashes (1–3 crashes) remains constant (at about 32–45% of all non-EJ tracts) for each TAI level; the same trend can be noticed for EJ tracts (between 32 and 42% of EJ census tracts have 1–3 crashes, irrespective of TAI levels). However, the percent of both EJ and non-EJ tracts with High or Very High crash rates (over 9) occur only where TAI levels are High or High–Medium. For each TAI level, the percent of EJ tracts with Low crashes is lower than in non-EJ tracts while the percent of EJ tracts with High–Medium crashes is greater than in non-EJ tracts.
+
+[Table 3](#page-5-0) also shows the effect sizes of the environmental and behavioral factors, as measured by Cohen's d index ([Cohen, 1992\).](#page-10-0) Based on this measure, the following environmental factors – TAI, SUM LENGTH, POP00 SQMI, PERCRIME and PED – have large differences between pedestrian crashes in EJ and non-EJ tracts. Among behavioral factors, MEDHHINC99 and PERNOCAR have large differences between EJ and non-EJ areas.
+
+The table also shows that the environmental measures TAI, PER-CRIME and PED with large effect sizes are positively correlated with PED CRASH. Finally, MEDHHINC99 is negatively correlated, whereas PERNOCAR is positively correlated with PED CRASH.
+
+The relationship of the pedestrian accessibility index (PED) to pedestrian crashes is similar to that of TAIto crashes and can be seen in the Fig. 3. The mean pedestrian crash rates for both EJ and non-EJ tracts decrease with decrease in PED levels. In the case of non-EJ tracts with High PED levels (on the left hand side of the bottom panel), the mean crash rate is 3.60, decreasing to 1.21 in the case of tracts with Low PED levels. The mean crash rates for each PED condition is higher for EJ tracts compared to non-EJ tracts; but in the case of EJ tracts too, the mean pedestrian crash rate decreases from 5.13 in the case of tracts with HIGH PED levels to a mean of 1.84 in the case of EJ tracts with Low PED levels. Overall, in both EJ and non-EJ tracts, there is an increase in the percent of census tracts with zero recorded crashes as PED levels decrease. However, in contrast to the case of TAI, the percent of both EJ and non-EJ tracts with High or Very High crash rates (over 9) mostly occur only where PED levels are High, with just a minimal percentage of tracts in the High–Medium and Low PED categories, in which such crash rates were experienced.
+
+In summary, the mean crash rate of EJ tracts is estimated to be higher than in non-EJ tracts by 1.32, however, large differences do not exist between the two types of areas in the proportion of injuries of different types and in the proportion of fatalities. The mean crash rate and the percent of both non-EJ and EJ tracts with zero pedestrian crashes increase with decrease in their TAI and PED levels, and are highest in cases of tracts with High levels of TAI and PED. Further, the mean crash rates for each TAI and PED condition is higher for EJ tracts compared to non-EJ tracts. For each TAI and PED level, the percent of EJ tracts with Low crashes is lower <span id="page-7-0"></span>than in comparable non-EJ tracts while the percent of EJ tracts with High–Medium crashes is greater than in non-EJ tracts.
+
+#### **5. Statistical models of pedestrian crash counts**
+
+The basic form of the statistical models considered is PED CRASHj = f(EJ TRACT, environmental factors, behavioral factors)<sup>i</sup> where PED CRASHj is the count of motor-vehicle–pedestrian crashes in the jth tract and EJ TRACTj is a binary variable taking the value of 1 if the jth tract is considered to be an EJ tract based on the rules given in Section [3.1](#page-2-0) and the environmental and behavioral factors are as described in Section [3.2.](#page-2-0)
+
+The crash data considered in this paper poses several methodological challenges including (i) the possibility of variations in the estimated effects of models arising from the choice of census tracts as the spatial unit, (ii) the presence of spatial autocorrelation in safety data, (iii) presence of overdispersion and heterogeneity and (iv) underreporting of crashes. Several different models were estimated in an attempt to address these different aspects of the data. The final results presented in Table 4 are from a Poisson regression with heterogeneity and a Poisson regression with heterogeneity which accounts for exogenous underreporting that are most relevant in explaining the distribution of PED CRASH with census tract-level environmental and behavioral factors.
+
+Variations in the estimated model effects can arise from the choice of census tracts as the areal unit rather than zip code or some other spatial unit; this is referred to as the modifiable areal unit problem (MAUP) ([Openshaw, 1979; Holt et al., 1996; Anselin et al.,](#page-10-0) [2000\).](#page-10-0) Aside from the reasons given in Section [3.1, o](#page-2-0)ur preference behind using census tracts in this analysis is that most EJ analysis have used this unit ([Mid-America Regional Council, 2007; US](#page-10-0) [EPA, 2009\)](#page-10-0) and our results extend safety research into the emerging area of environmental justice analysis. The extent to which the model parameters are sensitive to the choice of this analysis is left for future research.
+
+The presence of spatial autocorrelation can violate the independence assumption made by many statistical models [\(LeSage and](#page-10-0) [Pace, 2004\).](#page-10-0) A Local Indicators of Spatial Association (LISA) significance map of PED CRASH locations (as shown in Fig. 4) provides an indication of the existence of clusters in the spatial arrangement of pedestrian crashes. The similarity of the maps after both 1 and 199 permutations indicates that the sensitivity is fairly low, and supports the existence of spatial clusters. A visual review of the residual versus predicted PED CRASH values from the OLS model also supports the presence of spatial autocorrelation, indicating that crashes tend to be overpredicted in some suburban locations, and underpredicted in the Chicago downtown business district (the "Loop") and in southern areas of the city of Chicago. The calculated Moran's I value of 0.3984 was also significant, indicating that
+
+**Table 4** Alternative models, parameter estimates and measures of fit.
+
+| Variable              | Model I                                          |                                                             |  |  |
+|-----------------------|--------------------------------------------------|-------------------------------------------------------------|--|--|
+|                       | Poisson with<br>heterogeneity<br>Marginal effect | Poisson with exogenous<br>underreporting<br>Marginal effect |  |  |
+| Intercept             | −4.21***                                         | −2.13***                                                    |  |  |
+| EJ TRACT (1 = "Yes")  | 0.65***                                          | 0.33***                                                     |  |  |
+| Environmental factors |                                                  |                                                             |  |  |
+| TAI2                  | 2.01***                                          | 1.01***                                                     |  |  |
+| PED LOW               | 1.61***                                          | 0.59***                                                     |  |  |
+| SUM AADT2             | 0.48e−06***                                      | 0.24e−06***                                                 |  |  |
+| SUM LENGTH2           | −0.28e−03***                                     | −0.14e−03***                                                |  |  |
+| NO SCHOOLS            | 0.19**                                           | 0.09**                                                      |  |  |
+| POP SQMILE            | 0.91e−05                                         | 0.46e−03                                                    |  |  |
+| PERCRIME              | 0.24**                                           | 0.12**                                                      |  |  |
+| PED                   | 0.09***                                          | 0.05***                                                     |  |  |
+| Behavioral factors    |                                                  |                                                             |  |  |
+| WLKTOWRK              | 0.0008***                                        | 0.0009                                                      |  |  |
+| MEDHHINC99            | −0.22e−06                                        | −0.11e−05                                                   |  |  |
+| PERNOCAR              | 2.60**                                           | 1.31**                                                      |  |  |
+| PER COMM              | 1.37                                             | 0.69                                                        |  |  |
+| PERCHILDREN           | −2.09                                            | −1.05                                                       |  |  |
+| PERLOWENGLISH         | 0.21                                             | −0.10                                                       |  |  |
+|                       |                                                  | Probit reporting equation                                   |  |  |
+| Intercept             |                                                  | 0.54e−07                                                    |  |  |
+| COUNTY (1 = "Cook")   |                                                  | 0.018**                                                     |  |  |
+| R2                    | 0.58#                                            | 0.61#                                                       |  |  |
+| Log–likelihood        | −1763.25                                         | −1511.36                                                    |  |  |
+| 2/df                  | 136.8                                            | 93.76                                                       |  |  |
+| Vuong's statistic     | –                                                | −60.75                                                      |  |  |
+|                       | 0.13 (p < 0.0001)                                | 0.18 (p < 0.517)                                            |  |  |
+|                       | –                                                | 0.00                                                        |  |  |
+
+<sup>\*\*</sup> Significant at 0.05. \*\*\* Significant at 0.01.
+
+there is spatial autocorrelation in the residuals. While accounting for such spatial autocorrelation is important for this problem and a spatial autoregressive model was presented in an earlier version of this paper [\(Cottrill and Thakuriah, 2008\),](#page-10-0) that model was limited in that the distribution of PED CRASH was assumed to be normal and further work is necessary to develop a spatial model with the appropriate distributional assumption for PED CRASH. Since there is, simultaneously, evidence of spatial autocorrelation, underreporting and heterogeneity in the count data under consideration in this paper, in the most ideal case, our requirement is to use a count data model that explicitly takes into account the spatial structure, underreporting and evidence of heterogeneity. In the model con-
+
+![](_page_7_Figure_13.jpeg)
+
+**Fig. 4.** LISA cluster map: pedestrian crashes.
+
+<sup>#</sup> Pearson's R<sup>2</sup> given as R<sup>2</sup> <sup>p</sup> = 1 − -J j=1 yj ln(yj/j)/ J j=1 yj ln(yj/y¯) 
+
+sidered here, we account for three out of the four requirements – and leave the explicit introduction of spatial dependence in count models of PED CRASH with heterogeneity and underreporting for future research.
+
+[Table 4](#page-7-0) reports the marginal effects of a Poisson regression that accounts for heterogeneity and a Poisson regression that accounts for both heterogeneity and potential underreporting of crashes. Associated statistics and measures of fit are also presented. Diagnosis of a preliminary OLS model showed there was no evidence of multicollinearity, which may be due to combining many different individual factors into the composite indices, in contrast to introducing them as separate effects. Partial residual plots suggested that several variables need transformation; in particular, TAI, and SUM AADT were squared, leading to improvement in model fit; SUM LENGTH, NO SCHOOLS and RANKTOT were also candidates for transformation, but we chose not to, as the parameter estimates and model fit did not substantially change with the transformations.
+
+Poisson regression is typically used to model crash counts. However, the presence of overdispersion in the data led us to estimate a Negative Binomial model. In the incremental model development process, we estimated Poisson and Negative Binomial models with heterogeneity, of which, on the basis of three measures: Pearson's R2, log-likelihood and 2/df-statistic, we keep the Poisson Model with heterogeneity in [Table 4](#page-7-0) (under Model 1) for further consideration. The Poisson model with heterogeneity has a mean of exp(xˇ + ε) where ε∼N(0, -2) where ˇ's are parameters to be estimated, x's are exploratory variables explaining PED CRASHES and ε's are unobserved heterogeneity that are normally distributed across the individual data with mean 0 and standard deviation -The estimate of is 0.13 and is statistically significant at the .01 level. However, an additional issue, that of underreporting, was taken into account in the final model development step, which leads to Model II in [Table 4.](#page-7-0)
+
+Underreporting in low-income neighborhoods has been noted to be important in several studies. For example, [Sciortino et](#page-10-0) [al. \(2005\)](#page-10-0) found that the California Statewide Integrated Traffic Reporting System (SWITRS) under-reported San Francisco pedestrian injuries by 21% (using San Francisco General Hospital medical records as a gold standard), with African-Americans and males less likely to have a SWITRS-reported injury; [Stutts et al. \(1998\)](#page-10-0) reported on the basis of specially-collected bicycle and pedestrian injury data from emergency hospitals that overall, 70% of the reported bicycle injury events and 64% of the reported pedestrian injury events did not involve a motor-vehicle.
+
+From a modeling perspective, count data models that take heterogeneity and underreporting into account have been given by [Winkelmann and Zimmermann \(1993\)](#page-10-0) and applied to safety data by [Kumara and Chin \(2005\). S](#page-10-0)uchmodels acknowledge that only a subset of the actual number of crashes that occurred are reported and that the count of reported accidents is smaller than the total number of events. Let y\* be the unobserved number of accidents and let y denote the recorded number of accidents. Let y\*|ε have a Poisson distribution with mean E(y∗|x, ε) = exp(x ˇ + ε), where, as before, ˇ's are parameters to be estimated, x's are exploratory variables explaining PED CRASHES and ε's are unobserved heterogeneity that are normally distributed across the individual data with mean 0 and standard deviation -. Further, let ci denote a binary variable which is 1 if the net utility from reporting the ith crash is positive; ci is determined by a reporting process such that c<sup>∗</sup> <sup>i</sup> = zi + ui and ci = 1 iff c<sup>∗</sup> <sup>i</sup> > 0. Hence the number of reported crashes in census tract <sup>j</sup> is yj <sup>=</sup> <sup>y</sup><sup>∗</sup> <sup>i</sup>=<sup>1</sup>ci.
+
+The vector **z** represents exploratory variables that determine the reporting mechanism; in the current case, the feasibility of several variables was examined, based on the literature. Ultimately, COUNTY, a binary variable, which is 1 in the case of Cook County, the most populous county, which includes the City of Chicago and includes over 88% of the EJ tracts, was included in **z**. The vector are parameters to be estimated and with a normality assumption for the ui's, we have a probit model for the selection mechanism. The Poisson probabilities in this model (Poisson with endogenous reporting), with the modified mean ¯ , are given by:
+
+$$\begin{split} P(Y_j = y_j | \varepsilon_j) &= \frac{\exp^{-\tilde{\lambda}_j} \tilde{\lambda}_j^{y_j}}{y_j!} \\ \text{where} \quad \tilde{\lambda}_j &= \exp(x_j \beta + \varepsilon_j) \times \varPhi\left(\frac{z_j \gamma + (\rho | \sigma) \varepsilon_j}{\sqrt{1 - \rho^2}}\right) \end{split}$$
+
+where ˚ is the CDF of the standard normal distribution, is the correlation between ε and u, i.e. is the correlation between the variables relating to crash occurrence and reporting. If = 0, i.e., if reporting is independent from crash occurrence, we have a case of a Poisson model with exogenous underreporting with the conditional mean function:
+
+$$\bar{\lambda}_j = \exp(x_j \beta + \varepsilon_j) \times \Phi(z_j \gamma)$$
+
+The Poisson model with endogenous underreporting led to an estimate of which is small and not significant at any reasonable level of significance. On this basis, we estimated a Poisson model with exogenous underreporting, the results of which are shown as Model II in [Table 4.](#page-7-0) In deciding whether to favor Model II or III, we use Vuong's test, along with three other measures of fit, including Pearson's R2, log-likelihood and 2/df. The Vuong's test statistic (V) is distributed as a standard normal variate and hence its value is comparable to the critical value of the standard normal distribution. Consequently, V > 1.96 favors the Poisson underreporting models, whereas V ≤ 1.96 favors the parent Poisson models. In the case of Model II, V = −60.75, which leads to the conclusion that Model II should be favored. Nevertheless, on the basis of the other measures: we explore the results of Model III further, since it leads to useful insights regarding underreporting and otherwise is a better fit compared to Model I (on the basis of the log-likelihood value at convergence, the Pearson's R<sup>2</sup> and the2/df value).
+
+The reporting equation estimates that crashes in non-Cook County are likely to be under-reported by 1.8% points more than in Cook county. Since most EJ tracts are in Cook county, this result is contradictory with previous literature, which reports pedestrian crashes are more likely to be under-reported by minority and lowincome populations. We believe that this contradictory finding has to do with differences in the nature of the crashes and the severity of the crashes in Cook versus the suburban counties (here referred to as "collar counties"). Whereas crashes per capita are higher in Cook County, compared to collar counties, minor crashes (those without fatalities, incapacitating injuries or with other notable injuries) as a percent of all crashes is higher in collar counties compared to Cook. Minor crashes as a percent of all crashes are higher in EJ tracts than non-EJ tracts in collar counties. This is in contrast to Cook County, where this quantity is lower for EJ tracts than for non-EJ tracts. It is possible that minor crashes that are reported in EJ tracts in collar counties are only a subset of the total number of such crashes occurring there.
+
+It may be recalled that the difference between mean PED CRASHES in EJ tracts and mean PED CRASHES in non-EJ tracts is 1.32. Controlling for environmental and behavioral factors, the OLS model estimates that this difference in average PED CRASH rates drops to 0.65. Across almost all the different models tested, the coefficient for EJ TRACT remains remarkably constant – between 0.62 to 0.67 – and statistically significant, indicating that holding the environmental and behavioral factors constant reduces the difference in PED CRASH between EJ and non-EJ tracts by about half.
+
+<span id="page-9-0"></span>With Model II, however, which corrects for underreporting, the estimate of the differences drops to 0.33. The discussion above, which attempts to relate differential reporting in EJ tracts between Cook and collar county, partly answers this reduction – once underreporting in non-Cook county tracts are accounted for, the difference in PED CRASH between EJ and non-EJ tracts reduces further.
+
+The coefficients for TAI merit further discussion. The TAI estimates are significant in the three models shown in [Table 4.](#page-7-0) In keeping with the Trellis plots in [Figs. 2 and 3](#page-5-0), as the value of these indicators increase, PED CRASH is estimated to increase. This finding implies that TAI is a potentially useful proxy measure to direct measurements on pedestrian exposure by tracts. PERCRIME is also an important predictor of PED CRASH; pedestrian crashes increase with recorded crime in the census tract. The exact mechanism of why this is so merits further research. It would also be interesting to find out whether some of the pedestrians involved in crashes in areas which are unsafe from a personal security perspective were in the process of avoiding crime being committed, or became careless with respect to the traffic environment, in attempts to deal with perceived unsafe situation that theymay have suddenly faced. This would require researchers to access detailed crime data from police department. The coefficient for SUM AADT<sup>2</sup> is as expected; however, the coefficient for SUM LENGTH<sup>2</sup> is negative, possibly because of the presence of freeway links in some of the census tracts, where there little possibility of walking. Whereas the coefficient of NO SCHOOLS is positive, as expected, that of PERCHIL-DREN is negative, indicating that child pedestrians may be more vulnerable to crashes in areas that are not within the immediate vicinity of their residential locations. WLKTOWRK is not significant at any level of significance. It is also likely that the effect of the density variable, POP00 SQMI, was explained by the variable EJ TRACT.
+
+#### **6. Summary and conclusions**
+
+This paper evaluates the incidence of pedestrian–vehicle crashes in high low-income and minority population (EJ) census tracts as compared to pedestrian–vehicle crashes in non-EJ tracts in the Chicago metropolitan area. The summary statistics presented above, primarily the overall incidence, are generally supportive of the finding that pedestrian–vehicle crashes are more prevalent in EJ census tracts, as indicated in previous research. By taking a two-pronged approach to the data set and addressing the issue from the standpoints of environmental characteristics and behavioral factors, these general findings may be expanded upon and more targeted methods of addressing this issue may be developed. While earlier studies have indicated an increased number of pedestrian–vehicle crashes in areas of high minority or low-income populations in comparison to those areas that do not meet these criteria, less attention has been paid to ascertaining contributing factors to this disparity. This paper has attempted to test both environmental and behavioral factors for their contributions to the perceived heightened incidence of these crashes in order to provide better guidance for potential needs for interventions and further study.
+
+In general, the summary statistics indicate that the pattern of pedestrian–vehicle crashes in EJ and non-EJ tracts as evaluated in relation to environmental conditions are broadly similar, with comparable patterns obtained when evaluating these crashes against the transit availability index (TAI) and the pedestrian accessibility index (PED). These findings indicate that the general geographic characteristics of the pedestrian environment have roughly similar impacts on the likelihood of pedestrian–vehicle crashes in terms of rate, if not incidence. The relationship between TAI and pedestrian crashes may be especially significant, as it would suggest that expansions of and improvements to pedestrian-accessed transit stops should be planned and implemented in conjunction with pedestrian safety improvements in order to reduce the risk of incidents. Additionally, the relationship between PED and crashes may indicate the need to more thoroughly address the safety impacts of pedestrian improvements, particularly in the relationship between potential pedestrian and vehicle interactions, in order to more safely encourage walking. These findings are especially relevant in the domain of EJ regulations, as the environmental analysis indicates that EJ tracts tend to have higher levels of both TAI and PED, indicating the potential for more crashes.
+
+The statistical analysis presented reveals a number of interesting relationships. First, the connection between crash underreporting and injury category within the collar counties surrounding the primary urban county in the metropolitan area suggests that there may be differences in these crashes unaccounted for in the model. Potential variables that may impact this underreporting and should be explored further include distance to police or hospital services and general insurance rates and coverage. It is possible, for example, that minor crashes in collar counties are less likely to impact travel flow or be observed by law enforcement, and so are not reported at the time of occurrence. Additionally, if either the driver or pedestrian is uninsured, it may be to their advantage to take care of the crash impacts outside of legal boundaries if the injuries are minor, or if no injury occurred. These and other potentially related variables should be explored further.
+
+A second relationship of note is related to proxies for exposure rates. As noted above, high TAI and PED scores were related to an increase in crash incidence, which may indicate that they reveal areas of increased pedestrianism, thus increased exposure. Two other variables that may also be related to exposure rates are RANKTOTAL and PERCRIME, increases of which were also related to an increased number of crashes. For RANKTOTAL, the relationship is fairly clear, as this variable represents a ranking of census tracts by those factors that are typically associated with high pedestrian rates. PERCRIME, on the other hand, presents a less clear relationship, as noted in Section [5. F](#page-7-0)urther analysis of pedestrian and driver behavior in areas of high crime levels should be conducted to more clearly evaluate how increased levels of crime impact pedestrian–vehicle crashes. Finally, the general spatial analysis presented here reveals the presence of spatial autocorrelation, indicating that a more thorough spatial analysis of the data should be conducted. Results from the initial spatial error model improved overall model performance, indicating that controlling spatial dependence would likely result in better overall model fit.
+
+The implications of the findings of the analysis are fairly wideranging. As noted, further examination of a number of relationships is needed; however, it is evident that a number of factors related to pedestrian–vehicle crashes in EJ areas should be addressed. First, pedestrian and transit improvements and expansions should better incorporate safety considerations at locations of potential pedestrian–vehicle interaction. The raised incidence of pedestrian crashes in areas that rank highly for pedestrian amenities indicates that further analysis of safety requirements is needed, beyond the current practices. Secondly, further analysis of pedestrian and driver behavior in areas of high crime rates should be conducted in order to encourage more safe behavior in these areas. Finally, environmental justice analyses should include a review of how pedestrian–vehicle crash rates may be impacted by projects or programs developed for these areas.
+
+## **References**
+
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+- Laflamme, L., Diderichsen, F., 2000. Social differences in the traffic injury risks in childhood and youth—a literature review and a research agenda. Injury Prevention 6, 293–298.
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+- LeSage, J.P., Pace, R.K., 2004.Models for spatially dependentmissing data. The Journal of Real Estate Finance and Economics 29 (2), 233–254.
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+- Loukaitou-Sideris, A., Liggett, R., 2007. Death on the crosswalk: a study of pedestrian accidents in Los Angeles. Funded by a UCTC year 16 research grant. Journal of Planning Education and Research.
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+- Mid-America Regional Council, 2007. Transportation Improvement Program 2008-2012: Environmental Justice Analysis., http://www.marc.org/ transportation/tip/TIP08-12.htm.
+- Minocha, I., Sriraj, P.S., Metaxatos, P., Thakuriah, P., 2008. Analysis of transit quality of service and employment accessibility for the greater Chicago, Illinois, region. Transportation Research Record: the Journal of the Transportation Research Board 2048, 20–29.
+- Mohai, P., 1995. Methodological Issues: The Demographics of Dumping Revisited: Examining the Impact of Alternate Methodologies in Environmental Justice Research. Copyright (c) 1995 Virginia Environmental Law Journal Association Virginia Environmental Law Journal.
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+- Openshaw, S., 1979. A million or so correlation coefficients: three experiments on the modifiable areal unit problem. In: Wrigley, N. (Ed.), Statistical Methods in the Spatial Sciences. Pion, London.
+- Padilla, E.R., Rohsenow, D.J., Bergman, A.B., 1976. Predicting accident frequency in children. Pediatrics 58.2, 223–226.
+- Paulozzi, L.J., 2006. Is it safe to walk in the Sunbelt? Geographic variation among pedestrian fatalities in the United States, 1999–2003. Journal of Safety Research 37, 453–459.
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+- Sargent, M., Begg, D., Broughton, J., Stephenson, S., Wright, C., Baxter, J., 2004. Motor vehicle traffic crashes involving Maori. Journal of the New Zealand Medical Association. 117 (January (1188)).
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Zotero/001_artiklid/Road Safety Indicators/coutonotemodelingroadaccident2011.md

@@ -0,0 +1,350 @@
+---
+category: literaturenote
+citekey: coutonotemodelingroadaccident2011
+title: "A note on modeling road accident frequency: A flexible elasticity model"
+authors: "Couto, António; Ferreira, Sara"
+year: 2011
+date: 2011-00-00 2011
+doi: 10.1016/j.aap.2011.05.033
+publication: "Accident Analysis & Prevention"
+url: "https://doi.org/10.1016/j.aap.2011.05.033"
+zotero_key: F4KGU2P8
+zotero_storage: DHB3GHBT
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "Couto, António"
+status: converted
+---
+![](_page_0_Picture_1.jpeg)
+
+Contents lists available at [ScienceDirect](http://www.sciencedirect.com/science/journal/00014575)
+
+## Accident Analysis and Prevention
+
+j ou rnal home page: [www.elsevier.com/locate/aap](http://www.elsevier.com/locate/aap)
+
+![](_page_0_Picture_5.jpeg)
+
+# A note on modeling road accident frequency: A flexible elasticity model
+
+## António Couto∗, Sara Ferreira
+
+Civil Engineering Department, School of Engineering, Porto University, Rua Dr. Roberto Frias 4200-465 Porto, Portugal
+
+#### a r t i c l e i n f o
+
+Article history: Received 24 January 2011 Received in revised form 24 May 2011 Accepted 25 May 2011
+
+Keywords: Translog function Negative binomial Road accident models Regression models
+
+### a b s t r a c t
+
+Count data models and their variants have been widely applied in accident modeling. The traditional log-linear function is used to represent the relationship between explanatory variables and the dependent variable (accident frequency). However, this function assumes constant elasticity for the estimation parameters, which is a limitation in the analysis of the effects of explanatory variables on accident risk. Although interaction effects between explanatory variables have been studied in the road safety context (where they are normally assessed by logistic regression), no one has yet examined the possibility of using a flexible function form allowing non-constant elasticity values. This paper seeks to explore the use of the translog function usually used in the economics context to allow the elasticity to vary with the values of other explanatory variables. Therefore, the objective of this study was to evaluate the application of the translog function to accident modeling and to compare the results with those of the traditional log-linear function negative binomial (NB) model. The results show that, in terms of goodness-of-fit statistics and residual analysis, the NB model with the translog function performs better than the traditional NB model. Additional evaluations in terms of predictive performance, hotspot identification and uncertainty associated with the estimated values were taken into account. Although this study is exploratory in nature, it suggests that the translog function has considerable potential for modeling accident observations. It is hoped that this novel accident modeling methodology will open the door to the reliable interpretation and evaluation of the influence of explanatory variables on accident frequency.
+
+© 2011 Elsevier Ltd. All rights reserved.
+
+### **1. Introduction**
+
+In recent decades, there has been considerable research conducted on the development of accident prediction models, usually using generalized linear models (GLMs) to describe the influence of explanatory variables on road accidents ([Fridstrom](#page-7-0) et [al.,](#page-7-0) [1995;](#page-7-0) [Poch](#page-7-0) [and](#page-7-0) [Mannering,](#page-7-0) [1996;](#page-7-0) [Sawalha](#page-7-0) [and](#page-7-0) [Sayed,](#page-7-0) [2001;](#page-7-0) [Greibe,](#page-7-0) [2003;](#page-7-0) [Lord](#page-7-0) [and](#page-7-0) [Persaud,](#page-7-0) [2004\).](#page-7-0) To better understand the factors determining accidentfrequencies, additionaltechniques have been applied recently to the modeling of accidents, such as randomparameters count models. These particular models account for the presence of heterogeneity across observations by allowing some or all parameters to vary according to a random distribution [\(Anastasopoulos](#page-7-0) [and](#page-7-0) [Mannering,](#page-7-0) [2009\).](#page-7-0) Other studies using a modeling framework, such as zero-inflated negative binomial models [\(Carson](#page-7-0) [and](#page-7-0) [Mannering,](#page-7-0) [2001;](#page-7-0) [Lee](#page-7-0) [and](#page-7-0) [Mannering,](#page-7-0) [2002;](#page-7-0) [Kumara](#page-7-0) [and](#page-7-0) [Chin,](#page-7-0) [2003\),](#page-7-0) Conway–Maxwell–Poisson generalized linear models [\(Lord](#page-7-0) et [al.,](#page-7-0) [2008\)](#page-7-0) and generalized negative binomial models [\(Mitra](#page-7-0) [and](#page-7-0) [Washington,](#page-7-0) [2007;](#page-7-0) [Lord](#page-7-0) [and](#page-7-0) [Park,](#page-7-0) [2008\),](#page-7-0) have focused on the performance of the models.
+
+The GLM usually used to model accidents applies a logarithmic transformation to linearize the multiplicative equation and can be referred to as a log-linear function model. As is well known, these log-linear function models assume constant elasticity for the estimation parameters, and this can be a limitation to represent the relationships between explanatory variables and accident frequency. Moreover, why has traffic flow elasticity been assumed to be the same for both long and short segments? Additionally, why must the effect on accident risk of a percentage increase in traffic flow be the same in contexts of both high and low traffic flows?
+
+Infact, studies ([Lord,](#page-7-0) [2000;](#page-7-0) [LordandPark,](#page-7-0) [2008;Hadayeghi](#page-7-0) et [al.,](#page-7-0) [2010\)](#page-7-0) that have applied the CURE method proposed by [Hauer](#page-7-0) [and](#page-7-0) [Bamfo](#page-7-0) [\(1997\)t](#page-7-0)o analyze the cumulative residuals for each explanatory variable have revealed that for high values of traffic flow the model did not perform well (i.e., the cumulative residual curves were larger than the +2.0 boundary and/or did not end near the zero-residual line). Moreover, [Lord](#page-7-0) [\(2000\)](#page-7-0) suggested that separate models could be developed when the cumulative residuals indicate a change from a possible underestimation of accidents to an overestimation of accidents. This solution assumed different elasticities for the traffic volume. Nonetheless, if the model has more than one variable, then this is not an achievable solution.
+
+Although interaction effects between some explanatory variables have been used in many road safety studies ([Yannis](#page-7-0) et [al.,](#page-7-0) [2005;](#page-7-0) [Hill](#page-7-0) [and](#page-7-0) [Boyle,](#page-7-0) [2006;](#page-7-0) [Liu,](#page-7-0) [2007;](#page-7-0) [Sze](#page-7-0) [and](#page-7-0) [Wong,](#page-7-0) [2007;](#page-7-0) [Rhodes](#page-7-0)
+
+<sup>∗</sup> Corresponding author. Tel.: +351 225 082 110. E-mail addresses: [fcouto@fe.up.pt](mailto:fcouto@fe.up.pt) (A. Couto), [sara@fe.up.pt](mailto:sara@fe.up.pt) (S. Ferreira).
+
+[and](#page-7-0) [Pivik,](#page-7-0) [2011\),](#page-7-0) the purpose was only to analyze the difference in risk for two or more populations as they move from one condition to another. For instance, in the case of segment length, it is understandable that this factor can influence the impact of traffic flow on accident frequency. Indeed, traffic flow can have a different impact on accident frequency depending on whether the segment is longer or shorter. This interaction can be modeled by a flexible functional form instead of the constant elasticity model usually used to represent the effects of explanatory variables. Thus, even though the interaction effects of explanatory variables were not the main focus of this study, the flexible function form takes them into account. Because the main objective of this study is to assess the possibility that explanatory variables have non-constant elasticity, it is expected that the assumption adopted in this study will outperform the mathematical limitations of some popular function forms because the flexible function can allow for the free variation of elasticity and thus provides a well-structured function and better fitting performance.
+
+Flexible function forms are frequently used in econometrics ([Caves](#page-7-0) et [al.,](#page-7-0) [1980;](#page-7-0) [Diewert](#page-7-0) [and](#page-7-0) [Wales,](#page-7-0) [1987;](#page-7-0) [Oum](#page-7-0) [and](#page-7-0) [Tretheway,](#page-7-0) [1989;](#page-7-0) [Couto](#page-7-0) [and](#page-7-0) [Graham,](#page-7-0) [2009\)](#page-7-0) because they allow analysts to model second-order effects, such as elasticities of substitution, which are functions of the second derivatives of production, cost or utility functions ([Greene,](#page-7-0) [2008\).](#page-7-0) The most popular flexible functional form is the translog function originated in [Christensen](#page-7-0) et [al.](#page-7-0) [\(1973\).](#page-7-0) This function has been extensively applied in transportation research, especially in logistics and policy studies based on transportation costs ([Karlaftis](#page-7-0) [and](#page-7-0) [Mccarthy,](#page-7-0) [2002;](#page-7-0) [Link,](#page-7-0) [2006;](#page-7-0) [Satar](#page-7-0) [and](#page-7-0) [Peoples,](#page-7-0) [2010\).](#page-7-0)
+
+The translog function form can generalize negative binomial (NB) and Poisson models through the estimation of quadratic "cross variables," thereby allowing the elasticity to vary with the values of other explanatory variables.
+
+By using a flexible function, this paper provides a new interpretation of the relationship between explanatory variables and the dependent variable, and it tests the potential of this function form by applying it to accident modeling. To accomplish this objective, an NB model with a traditional log-linear functional form and an NB model with a translog function were developed and compared using a segment dataset. This dataset contains accident data collected at segments in Porto, Portugal, over a 5-year period. The models developed in this study consider two of the most widely used explanatory variables besides traffic flow (often referred to as general annual average daily traffic or AADT): segment length and the number of minor intersections per segment length. These explanatory variables are usually used to homogenize the segment and are easy to determine at all road safety study stages. The study will show that the model with a translog function performs better than the traditional log-linear function, producing statistically significant "cross variable" parameters.
+
+The next section presents a brief background related to the traditional log-linear functional form and the translog function. The third section describes the methodology used for estimating and comparing the NB model with and withoutthe second-order terms. The data and estimation results are summarized in the fourth and fifth sections, respectively. The last section presents a summary and conclusions of the analysis performed in this work.
+
+#### **2. Background**
+
+Count-data modeling techniques are commonly used for accident frequency analysis because the number of accidents on roadway segments per unit oftime is a non-negative integer. Count data are generally modeled with a Poisson regression. One requirement of the Poisson distribution is that the mean of the count process equals its variance.When the variance is significantly larger than the mean, the data are said to be overdispersed. Accident data have been shown to exhibit over-dispersion [\(Sawalha](#page-7-0) [and](#page-7-0) [Sayed,](#page-7-0) [2001;](#page-7-0) [Lord](#page-7-0) et [al.,](#page-7-0) [2005;](#page-7-0) [Caliendo](#page-7-0) et [al.,](#page-7-0) [2007\).](#page-7-0) In many cases, overdispersion count data are successfully modeled using an NB model ([Washington](#page-7-0) et [al.,](#page-7-0) [2003\).](#page-7-0)
+
+The probability density function of the NB distribution can be defined as:
+
+$$P(Y = y_i | \mu_i, \alpha) = \frac{\Gamma(y_i + (1/\alpha))}{\Gamma(1/\alpha) \cdot y_i!} \cdot \left(\frac{1/\alpha}{(1/\alpha) + \mu_i}\right)^{1/\alpha} \times \left(\frac{\mu_i}{(1/\alpha) + \mu_i}\right)^{y_i}$$
+(1)
+
+where ˛ is the dispersion parameter (when ˛<sup>=</sup> 1/ is equal to zero that is →∞, the NB distribution reverts back to the Poisson distribution) and (.) is <sup>a</sup> gamma function. Thus, the mean <sup>i</sup> <sup>=</sup> <sup>E</sup>{Y} can be smaller than the variance Var{Y} <sup>=</sup> <sup>i</sup> <sup>+</sup>˛<sup>i</sup> 2.
+
+In addition, the mean is linked to a vector of explanatory variables by a log-linear function:
+
+$$\mu_i = \exp(\beta X_i)$$
+ or, equivalently  $\ln(\mu_i) = \beta X_i$ 
+
+where Xi is <sup>a</sup> vector of explanatory variables and <sup>ˇ</sup> is <sup>a</sup> vector of estimable parameters. In this formulation, the expected number of events per period is given by <sup>E</sup>[yi] <sup>=</sup> <sup>i</sup> <sup>=</sup> exp(ˇXi). The estimated parameters ˇ are used to make inferences about the explanatory variables thought to impact the accident process. To analyze the parameter estimation results, elasticities are determined to provide an estimate of the impact of a variable on the expected frequency, and they can be interpreted as the effect of a 10% change in the variable on the expected frequency <sup>i</sup> ([Washington](#page-7-0) et [al.,](#page-7-0) [2003\).](#page-7-0) The elasticity of frequency <sup>i</sup> is defined as
+
+$$E_{x_{ik}}^{\mu_i} = \frac{\partial \mu_i}{\mu_i} \times \frac{x_{ik}}{\partial x_{ik}} = \beta_k x_{ik} \tag{2}$$
+
+where E represents the elasticity, xik is the value of the kth explanatory variable for observation <sup>i</sup>, <sup>ˇ</sup><sup>k</sup> is the estimated parameter for the <sup>k</sup>th explanatory variable and <sup>i</sup> is the expected frequency for observation i.
+
+However, the traditional NB model (with a log-linear function) assumes constant elasticity. This limitation can bias the interpretation of the relationship between the explanatory variables and the expected accident frequency. Hence, a flexible function form has been considered to model second-order effects.
+
+The translog function originated in [Christensen](#page-7-0) et [al.](#page-7-0) [\(1973\)](#page-7-0) has become enormously popular in the economics context probably because itis easier to estimate and interpret as itis a quadratic function with all arguments in natural logarithms ([Oum](#page-7-0) [and](#page-7-0) [Waters,](#page-7-0) [1996\).](#page-7-0) As described in [Greene](#page-7-0) [\(2008\),](#page-7-0) one way to derive it is first to write <sup>y</sup> <sup>=</sup> <sup>g</sup>(x1, . . ., xk) of an unknown function form and then, ln <sup>y</sup> <sup>=</sup> ln <sup>g</sup>(x1, . . ., xk) <sup>=</sup> <sup>f</sup>(x1, . . ., xk). Hence, by the trivial transformation xk = exp(ln xk), one interprets the function as a function of the logarithms of <sup>x</sup>'s. Thus, ln <sup>y</sup> <sup>=</sup> <sup>f</sup>(ln <sup>x</sup>1, . . ., ln xk). Now, expand this function in a second-order Taylor series around the point x = [1,1, . . ., 1] so that at the expansion point, the log of each variable is <sup>a</sup> convenient zero, then:
+
+$$\ln y = f(0) + \sum_{k=1}^{K} [\partial f(.)/\partial \ln x_k]_{\ln x = 0} \ln x_k$$
+
+$$+ \frac{1}{2} \sum_{k=1}^{K} \sum_{l=1}^{K} [\partial^2 f(.)/\partial \ln x_k \partial \ln x_l]_{\ln x = 0} \ln x_k \ln x_l$$
+(3)
+
+Because the function and its derivates evaluated at the fixed value 0 are constants, one can interpret them as the parameters and they can be expressed as 1:
+
+$$\ln y = \beta_0 + \sum_{k=1}^K \beta_k \ln x_k + \frac{1}{2} \sum_{k=1}^K \sum_{l=1}^K \gamma_{kl} \ln x_k \ln x_l$$
+ (4)
+
+It is interesting to note that if kl <sup>=</sup> 0, Eq. (4) becomes <sup>a</sup> function of the commonly used log-linear model. The second-order terms allow for possible cross-relationships among the variables and for possible non-linearities in the relationships [\(Oum](#page-7-0) [and](#page-7-0) [Waters,](#page-7-0) [1996\).](#page-7-0)
+
+The explanatory variable elasticity can be found by taking the differential of the function:
+
+$$\frac{\partial \ln y}{\partial \ln x_k} = \beta_k + \sum_{l=1}^K \gamma_{kl} \ln x_l \tag{5}$$
+
+From this, it is clear that, in general, the elasticity varies with the proportions of the explanatory variables and with their individual levels.
+
+The next section describes the methodology used to estimate and compare the NB model with a traditional log-linear function and the NB model with a translog function.
+
+#### **3. Methodology**
+
+Many different functional forms have been proposed to represent the relationship between accident frequency and explanatory variables. Two different types of functional form usually used by transportation safety analysts can be distinguished. One type is models that include several covariates that are related to the functional and geometrical characteristics of road networks [\(Poch](#page-7-0) [and](#page-7-0) [Mannering,](#page-7-0) [1996;](#page-7-0) [Sawalha](#page-7-0) [and](#page-7-0) [Sayed,](#page-7-0) [2001;](#page-7-0) [Greibe,](#page-7-0) [2003\).](#page-7-0) Such models can be used to analyze the factors affecting road safety, their influence and how they are related to the dependent variable. The other type of functional form (often referred to as AADT models) uses only a traffic flow variable. Authors [\(Lord](#page-7-0) et [al.,](#page-7-0) [2008\)](#page-7-0) have mentioned that these types of models are preferable to the former because they can be easily re-calibrated when they are applied in a jurisdiction other than the one in which it was developed.
+
+Because the purpose of the study is not to predict the number of accidents but rather to provide a methodological approach to gain new insights into the ways that explanatory variables influence accident frequency, a functional form was considered with more than the traffic flow variable. In addition to the traffic flow variable, explanatory variables usually used to characterize the segment and that have been reported by researchers to be significantly important in modeling accidents were included ([Fridstrom](#page-7-0) et [al.,](#page-7-0) [1995;](#page-7-0) [Mountain](#page-7-0) [and](#page-7-0) [Fawaz,](#page-7-0) [1996;](#page-7-0) [OCDE,](#page-7-0) [1997;](#page-7-0) [Lord,](#page-7-0) [2006\).](#page-7-0) Therefore, variables describing the number of minor intersections and segment lengths have been included in this segments model. These explanatory variables are easy to determine and consequently can be used at all road safety study stages.
+
+To select the proper relationship between the dependent variable and explanatory variables, a method proposed by [Hauer](#page-7-0) [and](#page-7-0) [Bamfo](#page-7-0) [\(1997\)](#page-7-0) was applied. Basically, the Integrate-Differentiate method consists of drawing an Empirical Integral Function for each explanatory variable and then comparing the shape with the pre-established graphs of well-known functions (power, gamma, exponential or polynomial functions). The function with the most similar shape is selected to represent the relationship between the dependent variable and the explanatory variable being investigated. By applying this method to the explanatory variables being used in this study, it was found that the relationships between accident frequency and both AADT and segment length could be described by the power function. In the case of the minor intersection density variable, the exponential function was found to be more suitable to describe the aforementioned relationship.
+
+A time trend variable has also been included in this study to reflect potential changes in the overall accident level over time. A number of studies have included a time trend variable that allows for changes in terms of risk over time [\(Fridstrom](#page-7-0) et [al.,](#page-7-0) [1995;](#page-7-0) [Mountain](#page-7-0) et [al.,](#page-7-0) [1998\).](#page-7-0) It has been previously demonstrated that this variable has a negative effect on the frequency of accidents, thus leading to overall improvement due to such factors as safety education, enforcement and vehicles.
+
+Thus, the NB model with a traditional log-linear function takes the form:
+
+$$\ln \mu_{it} = \beta_0 + \beta_1 \ln(F_{it}) + \beta_2 \ln(Leng_i) + \beta_3 IntDen_i + \ln(\gamma) TimeT_t$$
+(6)
+
+where it is the mean number of accidents in segment <sup>i</sup> at time period t, Fit is the annual average daily traffic in both directions (segment i; time period t), Lengi represents the length of the segment i, TimeTt is the time trend variable, IntDensi is the minor intersection density (segment <sup>i</sup>) and <sup>ˇ</sup><sup>k</sup> (<sup>k</sup> <sup>=</sup> 0–3) and are the estimated parameters.
+
+The translog functional form is expressed as:
+
+$$\ln \mu_{it} = \beta_0 + \beta_1 \ln(F_{it}) + \beta_2 \ln(Leng_i) + \beta_3 IntDen_i + \ln(\gamma) TimeT_t$$
+
+$$+ \beta_4 [\ln(F_{it})]^2 + \beta_5 [\ln(Leng_i)]^2 + \beta_6 (IntDen_i)^2 + \beta_7$$
+
+$$\times \ln(F_{it}) \ln(Leng_i) + \beta_8 \ln(F_{it}) IntDen_i$$
+
+$$+ \beta_9 \ln(Leng_i) IntDen_i$$
+(7)
+
+where it is the mean number of accidents per year, the explanatory variables are the same as in Eq. (6) and <sup>ˇ</sup><sup>k</sup> (<sup>k</sup> <sup>=</sup> 0–9) and are the estimated parameters. Note that the time trend variable does not take the form of a "cross variable," hence no interaction is expected between this variable and the other explanatory variables on accident frequency.
+
+To compare the two types of model applied in this study, several methods were used to estimate their goodness-of-fit (GOF). Four different GOF statisticaltests –Akaike's Information Criterion (AIC), Freeman–Tuckey <sup>R</sup><sup>2</sup> (R<sup>2</sup> FT), Elvik index (R<sup>2</sup> PE) and McFadden Pseudo R<sup>2</sup> as described in [Bozdogan](#page-7-0) [\(1987\),](#page-7-0) [Fridstrom](#page-7-0) et [al.](#page-7-0) [\(1995\)](#page-7-0) and [Greene](#page-7-0) [\(2008\)](#page-7-0) were employed.
+
+The model with the lowest AIC is considered the model with the best statistical fit. On the other hand, the model with the largest McFadden Pseudo R<sup>2</sup> value indicates the best fitting model. The Elvik index and Freeman–Tuckey R<sup>2</sup> are two measures of GOF that describe how much "variation" in the dependent variable is "explained" by the model estimate as compared to the total variation present in the data set.
+
+A GOF evaluation based on residual analysis was also used. This method is known as the CURE method and it was initially proposed by [Hauer](#page-7-0) [and](#page-7-0) [Bamfo](#page-7-0) [\(1997\).](#page-7-0) It can be used to evaluate the fit of models by examining the cumulative residuals for each explanatory variable separately. The cumulative residuals are plotted in increasing order and the closer the curve oscillates around the
+
+<sup>1</sup> Note that kl <sup>=</sup> lk.
+
+<span id="page-3-0"></span>![](_page_3_Figure_2.jpeg)
+
+**Fig. 1.** Accident number distribution.
+
+**Table 1** Summary statistics for the Porto data (5-year).
+
+| Variablea                                   | Min.   | Max.     | Mean     | S.D.     |
+|---------------------------------------------|--------|----------|----------|----------|
+| Dependent variable (accident number)        | 0      | 27       | 2.85     | 3.90     |
+| AADT                                        | 142.37 | 64067.80 | 15240.38 | 11699.49 |
+| Segment length (in m)                       | 20.71  | 3342.78  | 313.18   | 352.56   |
+| Number of minor intersections per kilometer | 0.00   | 32.04    | 4.57     | 5.18     |
+
+<sup>a</sup> <sup>1980</sup> observations (396 segments <sup>×</sup> <sup>5</sup> years).
+
+zero-residual line, the better the model fits the data (the reader is referred to [Hauer](#page-7-0) [and](#page-7-0) [Bamfo](#page-7-0) [\(1997\)](#page-7-0) for a more detailed description ofthis method). The CURE plot reveals how wellthe functionalform fits the data with respect to each individual explanatory variable.
+
+The next section describes the characteristics of the dataset.
+
+### **4. Data**
+
+To illustrate the application of the translog function to model accidents, data from Porto, Portugal, were used. These data consist of accident data from urban segments classified by local and principal distributor roads collected over a 5-year period (January 1st 2001 to December 31st 2005). The accident data were obtained from the official Portuguese Police Security database covering all police-recorded accidents with local information (injury accidents and property damage only accidents).Allthe accidents were related to a specific locality by applying a Geographic Information System (GIS)tool. The data consist of 5650 police records of accidents, 1183 of which were personal injury accidents and 4467 were property damage only accidents, and they are related to 396 segments resulting from a road network characterization as a series of nodes and segments from a previous work [\(Ferreira,](#page-7-0) [2010\).](#page-7-0) Fig. 1 shows the distribution of these accident numbers.
+
+The daily traffic (defined as the Annual Average Daily Traffic or AADT) was estimated by the Porto "SATURN" traffic model. This model was developed in 2005 for the peak hourly flow (PHF) of the Porto road network and involved all the recommend development stages (specification; coding; error checking; calibration; validation) ([Tavares,](#page-7-0) [2003\).](#page-7-0) The PHF was expanded to AADT every five years by applying zone factors that relate the PHF with the daily traffic flow calculated using data provided by permanent counting stations located throughout the principal city zones belonging to the Urban Traffic Center.
+
+In addition, GIS was used to find geometric characteristics of the segments, namely the number of minor intersections and the lengths. These data were processed in a doctoral study [\(Ferreira,](#page-7-0) [2010\).](#page-7-0) Table 1 presents the summary statistics for the dataset.
+
+#### **5. Estimation results**
+
+Given all the "cross variables" required by the translog function model, the parameters were estimated. However, the results
+
+**Table 2** Model estimation results for the translog function and log-linear function negative binomial models (t-statistics in parentheses).
+
+| Variable                           | Negative binomial parameter estimates |                         |  |
+|------------------------------------|---------------------------------------|-------------------------|--|
+|                                    | Log-linear function model             | Translog function model |  |
+|                                    | 0.7350 (14.141)                       | 0.6766 (11.734)         |  |
+| ˇ0                                 | 0.3701 (13.623)                       | 0.4249 (15.037)         |  |
+| ˇ1                                 | 0.8910 (31.28)                        | 1.0026 (28.109)         |  |
+| ˇ2                                 | 0.0380 (8.738)                        | 0.0233 (3.259)          |  |
+| ˇ3<br>ln()                         | −0.0583 (−3.674)                      | −0.0572 (−3.658)        |  |
+|                                    | –                                     | −0.0690 (−3.311)        |  |
+| ˇ5                                 | –                                     | 0.0018 (2.777)          |  |
+| ˇ6                                 | –                                     | −0.0780 (−2.851)        |  |
+| ˇ7                                 | –                                     | 0.0434 (5.672)          |  |
+| ˇ9<br>˛ (overdispersion parameter) | 0.4849 (15.263)                       | 0.4449 (14.687)         |  |
+| AIC                                | 3.73084                               | 3.70226                 |  |
+| McFadden Pseudo R2                 | 0.1096                                | 0.0984                  |  |
+| R2                                 | 63.7%                                 | 67.9%                   |  |
+| FT<br>R2<br>PE                     | 69.3%                                 | 71.8%                   |  |
+
+![](_page_4_Figure_2.jpeg)
+
+![](_page_4_Figure_3.jpeg)
+
+**Fig. 2.** Cumulative residual plots for the log-linear function and translog function NB models (parameter F).
+
+showed that two "cross variables" were not statistically significant. These variables correspond to [ln(Fit)]2 and ln(Fit)(IntDeni). In fact, the correlation matrix analysis reveals a strong possibility of correlation between [ln(Fit)]2 and ln(Fit) and between ln(Fit)(IntDeni) and (IntDeni). [Table](#page-3-0) 2 presents the estimationresults for both the traditional log-linear function NB model and the translog function NB model excluding the insignificant variables.2,3 As shown in [Table](#page-3-0) 2, excluding the McFadden Pseudo R<sup>2</sup> values, the translog model provides the best fit according to the three different test statistics (i.e., AIC, R<sup>2</sup> FT, R<sup>2</sup> PE), although they are all very similar. The <sup>R</sup><sup>2</sup> FT and <sup>R</sup><sup>2</sup> PE measures indicate that the translog model explains 68% and 72% of the systematic component, respectively, compared with 64% and 69% explained by the traditional NB model. These findings may be an outgrowth of the traditional NB model's restriction that the estimated elasticity is constant.
+
+In fact, the residual analysis stresses these conclusions. Comparing the CURE plotted for the two models (refer to Figs. 2–4), one can conclude that the translog function NB model, in general, fits the data better with respect to each individual explanatory variable than does the log-linear function NB model. The exception
+
+![](_page_4_Figure_9.jpeg)
+
+![](_page_4_Figure_10.jpeg)
+
+**Fig. 3.** Cumulative residual plots for the log-linear function and translog function NB models (parameter Leng).
+
+is Fig. 3b, because the cumulative residual line is slightly larger than the <sup>−</sup>2.0 boundary for segment length values above approximately 1200 m.
+
+An important issue in developing and using regression models is parameter interpretation. To analyze and to compare the influence of each explanatory variable on accident frequency in each of the two models, the elasticity values were analyzed. With regard
+
+![](_page_4_Figure_14.jpeg)
+
+![](_page_4_Figure_15.jpeg)
+
+**Fig. 4.** Cumulative residual plots for the log-linear function and translog function NB models (parameter IntDen).
+
+<sup>2</sup> The explanatory variables of the log-linear function NB model and the firstorder variables of the translog function NB model were previously "normalized" by dividing every variable observation by its respective sample mean to facilitate model comparisons and interpretation of the results.
+
+<sup>3</sup> Despite the panel nature of the data, measures to deal with panel data were not used because information on a range of exogenous variables has been incorporated that characterizes segment effects. These effects are quasi-invariant over time and the use of firm dummy variables was found to produce severe multicollinearity problems. Also, tests for possible temporal correlation and heteroskedasticity problems were conducted using a series of likelihood ratio tests as described by [Poch](#page-7-0) [and](#page-7-0) [Mannering](#page-7-0) [\(1996\),](#page-7-0) revealing that these issues do not significantly affect the resulting estimates.
+
+to the elasticity results from the log-linear function NB model, the values are consistent with the findings of previous research (see for example [Mountain](#page-7-0) [and](#page-7-0) [Fawaz,](#page-7-0) [1996;](#page-7-0) [Mountain](#page-7-0) et [al.,](#page-7-0) [1998;](#page-7-0) [Greibe,](#page-7-0) [2003\).](#page-7-0) Nevertheless,the AADT variable has low elasticity compared with similar studies (accidents increase by about 4% when the traffic volume increases by 10%). This resultindicates reducedinfluence of this variable on accident frequency. Because the segment length parameter is not significantly different from 1, the accident frequency is almost proportional to road length, as was expected. Consistent with expectations, the model also reveals that accident frequency increases when the minor intersection density increases (Eit xik <sup>=</sup> <sup>0</sup>.04(IntDeni)), although the impact on accident frequency is low (ˇ<sup>3</sup> <sup>=</sup> 0.04). Concerning the effects of local and/or national road safety policies and programs on accident frequency, parameter was estimated with statistical significance to be 0.95, implying that for the period studied the accident risk declined annually by an average of 5%, thereby accumulating to a reduction of 23% over the whole period.
+
+Comparing the parameters estimated by the traditional NB model with the translog function NB model (see [Table](#page-3-0) 2), it is clear that the effects of the explanatory variables on accident frequency are similar for both models, although some improvement can be observed in the case of the values estimated by the latter model. Indeed, the elasticities of the AADT and the segment length variables have increased slightly to values more similar to those of past research.
+
+Regardless of the better fit of the translog function NB model, its essential trait is that it adds a new approach to defining the mean function structure of an NB model in terms of the flexibility and interpretability of the explanatory variables' elasticities. In fact, a closer look atthe parameters estimated by the translog function NB model presented in [Table](#page-3-0) 2 reveals that, e.g., with increasing traffic volume, the accident frequency also increases, but when the segment length is higher, the magnitude of this effect is lower ceteris paribus To better illustrate the differences among these models, estimated accident frequencies from the two models are shown in Figs. 5 and 6. Fig. 5 compares the number of accidents estimated by the log-linear function NB model and the translog function NB model for three segment length values and considering a minor intersection density equal to the mean sample value. This figure shows that the estimated values are slightly different, with the translog function NB output being lower than the traditional NB output. The same can be illustrated with the minor intersection density variable interaction with segment length (see [Fig.](#page-6-0) 6) and considering the AADT mean sample value. In this case, the numbers of accidents estimated by the two models are very distinct, especially when IntDen is equal to 10 minor intersections per kilometer, with the translog function NB output being lower than the log-linear function NB output. For IntDen equal to 0, the models' estimated accident frequency outputs are reversed, i.e., the loglinear function NB output is higher than the translog function NB output.
+
+These figures clearly demonstrate that the translog function is particularly distinct from the log-linear function at the boundary values. This fact suggests that data heterogeneity can be considered in the translog function. As such, ignoring this variation can undermine the goodness of any estimate of individual sites as stated by [Miaou](#page-7-0) [and](#page-7-0) [Lord](#page-7-0) [\(2003\).](#page-7-0) Indeed, proper boundary values can be particularly important to modeling data with a large number of zeros (low samplemeanvalues) or withahighernumber of accidents. The latter can be referred to as a case of hotspot identification analysis. Due to the factthatthe residuals analysis ofthe translog function NB model showed lower values when the observations include a high number of accidents, this function is likely to be outperformed in the prediction of accidents at sites with a high probability of many accidents occurring.
+
+![](_page_5_Figure_6.jpeg)
+
+**Fig. 5.** Estimated values for the Porto dataset (with IntDen = 4.57 mean sample value). Log-linear function versus translog function NB models.
+
+Although the study was not motivated by hotspot identification methods, a comparative analysis between these two functions was considered. Using the model estimates from both functions as a criterion for the identification of potential hotspot, the top 10% of the 396 segments (considering a 5 year average) were selected. Then, the potential hotspots were compared with the hotspots identified through observed accident frequencies. As expected, the translog function NB model "correctly" identified more hotspots than the log-linear function NB (8% more sites). Moreover, following similar procedures as those applied in [Geedipally](#page-7-0) [and](#page-7-0) [Lord](#page-7-0) [\(2010\),](#page-7-0) outcome classification was used to compare the performance of the two models, using as a threshold value the mean of all the sites in the Porto data. These comparative results are presented in Table 3. As expected, the translog function NB model "correctly" identified more hotspots than the log-linear function NB. More-
+
+**Table 3** Evaluation of model performance at identifying the "true" hotspot.
+
+| Number of sites                                      | Log | Translog |
+|------------------------------------------------------|-----|----------|
+| Number of false positives (Type I errors)a           | 92  | 89       |
+| Number of false negatives (Type II errors)a          | 66  | 58       |
+| Number of sites correctly classified as non-hotspots | 155 | 158      |
+| Number of sites correctly classified as hotspots     | 83  | 91       |
+
+<sup>a</sup> As defined in [Geedipally](#page-7-0) [and](#page-7-0) [Lord](#page-7-0) [\(2010\).](#page-7-0)
+
+<span id="page-6-0"></span>![](_page_6_Figure_2.jpeg)
+
+![](_page_6_Figure_3.jpeg)
+
+![](_page_6_Figure_4.jpeg)
+
+**Fig. 6.** Estimated values for the Porto dataset (with F = 15240.38 mean sample value). Log-linear function versus translog function NB models.
+
+over, as a measure of the capacity of the method to detect "true" hotspots, the proportion of sites that were correctly detected by the translog function as hotspots was 61%, whereas the log-linear function detected 56%, indicating that the former performs slightly better. Furthermore, the smaller value of the proportion of the total number of errors (Type I and II) to the number of sites under analysis obtained by the translog function (37% compared to 40% for the log-linear function) confirms the previous results.
+
+In order to stress the potential of the translog function form, it wasdecidedto also evaluate itspredictiveperformance considering the methodology described in [Lord](#page-7-0) et [al.](#page-7-0) [\(2008\).](#page-7-0) Thus, two samples consisting of 80% of the original data were randomly extracted to fit the models. Then, the estimated models were applied to the remaining 20%. The mean absolute deviance (MAD) and the mean-squared predictive error (MSPE) were computed to assess the predictive performance and are presented in Table 4 (for a detailed description of this method, the readers are referred to [Lord](#page-7-0) et [al.](#page-7-0) [\(2008\)\).](#page-7-0) As can be seen in Table 4, the results for both models and for the full data model estimation exhibit similar characteristics, although with slight differences in the MAD and MSPE measures suggesting that the translog function NB model performs better.
+
+Finally, to examine the uncertainties associated with the estimated values, an empirical Bayes (EB) method was used in this study as an indirect method of evaluating uncertainty. This
+
+**Table 4** Predictive performance evaluation measures.
+
+| Measurea | Sample 1 |          | Sample 2 |          |  |
+|----------|----------|----------|----------|----------|--|
+|          | Log      | Translog | Log      | Translog |  |
+| MADFit   | 2.0      | 1.9      | 1.9      | 1.8      |  |
+| MSPEFit  | 9.9      | 8.3      | 8.7      | 7.2      |  |
+| MADPred  | 1.6      | 1.5      | 2.0      | 2.0      |  |
+| MSPEPred | 5.8      | 5.7      | 11.1     | 12.1     |  |
+
+<sup>a</sup> For a detailed description of these measures, the readers are referred to [Lord](#page-7-0) et [al.](#page-7-0) [\(2008\).](#page-7-0)
+
+approach is based on the fact that the EB method achieves a better estimate of the expected number of accidents, whereas the present procedure is a result of a combination accident counts with accident estimates. To provide a comparative measure, the EB values were computed and then compared with the estimated model (EM) values for both models analyzed. This comparison is based on the percentage difference calculated as (EM estimate − EB estimate) × 100/EB estimate. The averages ofthis percentage difference for the log-linear function NB model and the translog function NB model were found to be 22% and 19%, respectively.Although this particular formulation provides attractive statistical properties, an extensive investigation is needed using a full Bayesian treatment as a direct method of providing exact measures of uncertainty ([Mitra](#page-7-0) [and](#page-7-0) [Washington,](#page-7-0) [2007\).](#page-7-0)
+
+#### **6. Summary and conclusions**
+
+This paper introduces a novel accident modeling methodology using a flexible function named the translog function that allows future research to adopt a new interpretation of the elasticity of explanatory variables.
+
+This paper demonstrated the potential of the translog function NB model to provide new insights into the ways that explanatory variables influence accident frequency. The translog model is commonly used in econometric studies wherein it provides a flexible function form to model second-order effects, thus allowing the elasticity to vary according to the magnitude of the explanatory variable. In the context of road accident analysis, this innovative methodology can be seen as an extension of the Poisson or NB model in the case of accident modeling.
+
+Using 5 years of road accident data from urban segments (Porto, Portugal), the translog function NB model was compared with the log-linear function NB model commonly used to analyze road accidents. The results of this study show that the translog function NB model, in general, performs better than the log-linear NB model in terms of GOF statistics and residual analysis. Also, the estimation results provide some interesting findings. For instance, the traffic volume elasticity varied (although not substantially) with the segment length, revealing variable influences of these variables on accident frequency, especially for lower segment length values. In addition, it was found that the segment length elasticity changed in conjunction with the minor intersection density, with a higher effect when the number of intersections per segmentlength is high.
+
+These results suggest that the translog function provides proper boundary values and thus contributes a well-defined mean structure that fits the heterogeneous data usually exhibited by accident samples. A simple comparison between the two models was carried out suggesting that the translog function NB model has the potential to provide better estimates of the expected number of accidents at high-risk sites. Nonetheless, further research should be conducted to address data characterized by many zeros and to optimize the identification of hotspots.
+
+In addition, a preliminary study was conducted on the uncertainty associated with the estimates of the model parameters. <span id="page-7-0"></span>Using an EB estimation analysis, the translog function NB model appears to offer positive results. Nonetheless, for the purpose of measuring estimation uncertainty, a full Bayesian modeling framework should be developed for the translog function form in future research.
+
+Although the analysis conducted in this research was conducted for a segment dataset, the potential of flexible function forms to structure the mean function of intersection accident models should be analyzed as an alternative to the function forms usually postulated for the interaction between traffic flows in the minor and major approaches of intersections.
+
+Although this study is exploratory in nature, it suggests that the translog function has considerable potential for modeling accident observations. Finally, it is hoped that the new function represented by the translog model described in this paper may be adopted by other researchers, opening a door to the reliable interpretation and evaluation of the influence of explanatory variables on accident frequency.
+
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+- Lord, D., Park, P.Y.J., 2008.Investigating the effects ofthefixed and varying dispersion parameters of Poisson-gamma models on empirical Bayes estimates. Accident Analysis and Prevention 40, 1441–1457.
+- Lord, D., Persaud, B.N., 2004. Estimating the safety performance of urban road transportation networks. Accident Analysis and Prevention 36, 609–620.
+- Lord, D., Washington, S.P., Ivan, J., 2005. Poisson, Poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory. Accident Analysis and Prevention 37, 35–46.
+- Miaou, S.-P., Lord, D., 2003. Modeling traffic crash-flow relationships for intersections. Transportation Research Record 1840, 31–40.
+- Mitra, S., Washington, S., 2007. On the nature of over-dispersion in motor vehicle crash prediction models. Accident Analysis and Prevention 39, 459–468.
+- Mountain, L., Fawaz, B., 1996. Estimating accidents at junctions using routinelyavailable input data. Traffic Engineering & Control 27 (11), 624–628. Mountain, L., Maher, M., Fawaz, B., 1998. The influence of trend on estimates of
+- accidents at junctions. Accident Analysis and Prevention 30 (5), 641–649. OCDE, 1997. Road Safety Principles and Models: Review of Descriptive, Pre-
+- dictive, Risk and Accident Consequence Models. Organisation for Economic Co-operation and Development, Paris, p. 105.
+- Oum, T.H., Tretheway, M.W., 1989. Hedonic vs. general specifications of the translog cost function. Logistics and Transportation Review 25 (1), 3–21.
+- Oum, T.H., Waters, W.G., 1996. A survey of recent developments in transportation cost function research. Logistics and Transportation Review 32 (4), 423–463.
+- Poch, M, Mannering, F., 1996. Negative binomial analysis of intersection-accident frequencies. Journal of Transportation Engineering 122 (2), 105–113.
+- Rhodes, N., Pivik, K., 2011. Age and gender differences in risky driving: the roles of positive affect and risk perception. Accident Analysis and Prevention 43 (3), 923–931.
+- Satar, N.M., Peoples, J., 2010. An empirical test of modal choice and allocative efficiency: evidence from us coal transportation. Transportation Research Part E 46, 1043–1056.
+- Sawalha, Z., Sayed, T., 2001. Evaluating safety of urban arterial roadways. Journal of Transportation Engineering 127 (2), 151–158.
+- Sze, N.N., Wong, S.C., 2007. Diagnostic analysis of the logistic model for pedestrian injury severity in traffic crashes. Accident Analysis and Prevention 39, 1267–1278.
+- Tavares, J.P., 2003. Aplicabilidade e robustez de modelos de afectac¸ ão de tráfego em redes urbanas. Ph.D. Dissertation. University of Porto.
+- Washington, S., Karlaftis, M., Mannering, F., 2003. Statistical and Econometric Methods for Transportation Data Analysis. Chapman & Hall/CRC, Boca Raton, London, New York, Washington, D.C.
+- Yannis, G., Golias, J., Papadimitriou, E., 2005. Driver age and vehicle engine size effects on fault and severity in young motorcyclists accidents. Accident Analysis and Prevention 37, 327–333.
+
+**António Couto** Assistant Professor; Ph.D., Faculty of Engineering of Porto University, Porto, Portugal, specializes in the economics of transport, focusing particularly on modeling the implications of transport provisions and accessibility for productivity and economic growth.
+
+**Sara Ferreira** Assistant Professor; Ph.D., Faculty of Engineering of Porto University, Porto, Portugal, is mainly engaged in road safety analysis, namely accident modeling, hotspot analysis and mitigating measures.

Zotero/001_artiklid/Road Safety Indicators/dinurandomparametermodelsaccident2011.md

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+---
+category: literaturenote
+citekey: dinurandomparametermodelsaccident2011
+title: Random parameter models for accident prediction on two-lane undivided highways in India
+authors: "Dinu, R.R.; Veeraragavan, A."
+year: 2011
+date: 2011-00-00 2011
+doi: 10.1016/j.jsr.2010.11.007
+publication: Journal of Safety Research
+url: "https://doi.org/10.1016/j.jsr.2010.11.007"
+zotero_key: XUJ6PMQ5
+zotero_storage: 66JCVXKR
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "Dinu, R.R."
+status: converted
+---
+![](_page_0_Picture_1.jpeg)
+
+# Journal of Safety Research
+
+j o u r n a l h om e p a g e : www. e l s ev i e r. c om / l o c a t e / j s r
+
+![](_page_0_Picture_5.jpeg)
+
+# Random parameter models for accident prediction on two-lane undivided highways in India
+
+R.R. Dinu a, ⁎, A. Veeraragavan b,1
+
+- <sup>a</sup> Doctoral Research Student, Department of Civil Engineering, Indian Institute of Technology Madras, Chennai-600036, India
+- <sup>b</sup> Department of Civil Engineering, Indian Institute of Technology Madras, Chennai-600036, India
+
+### article info abstract
+
+Article history: Received 17 January 2010 Received in revised form 5 October 2010 Accepted 29 November 2010 Available online 22 January 2011
+
+Keywords: Road accident modeling Rural highway Mixed traffic Poisson regression Random parameter models
+
+Introduction: Generalized linear modeling (GLM), with the assumption of Poisson or negative binomial error structure, has been widely employed in road accident modeling. A number of explanatory variables related to traffic, road geometry, and environment that contribute to accident occurrence have been identified and accident prediction models have been proposed. The accident prediction models reported in literature largely employ the fixed parameter modeling approach, where the magnitude of influence of an explanatory variable is considered to be fixed for any observation in the population. Similar models have been proposed for Indian highways too, which include additional variables representing traffic composition. The mixed traffic on Indian highways comes with a lot of variability within, ranging from difference in vehicle types to variability in driver behavior. This could result in variability in the effect of explanatory variables on accidents across locations. Random parameter models, which can capture some of such variability, are expected to be more appropriate for the Indian situation. Method: The present study is an attempt to employ random parameter modeling for accident prediction on two-lane undivided rural highways in India. Three years of accident history, from nearly 200 km of highway segments, is used to calibrate and validate the models. Results: The results of the analysis suggest that the model coefficients for traffic volume, proportion of cars, motorized two-wheelers and trucks in traffic, and driveway density and horizontal and vertical curvatures are randomly distributed across locations. Conclusions: The paper is concluded with a discussion on modeling results and the limitations of the present study.
+
+© 2011 National Safety Council and Elsevier Ltd. All rights reserved.
+
+# 1. Introduction
+
+A considerable amount of research effort has gone into understanding factors that contribute to road accidents, and statistical models have been developed to predict accident frequencies under given traffic, road geometric, and environmental factors. The generalized linear modeling (GLM) approach proposed by [Nelder and Wedderburn \(1972\),](#page-3-0) with the assumption of Poisson or negative binomially distributed error, has been the choice in the development of most of these models. Early research in accident modeling [\(Miaou & Lum, 1993; Miaou, 1994; Maher & Summersgill,](#page-3-0) [1996; Poch & Mannering, 1996](#page-3-0)) established the adequacy of this modeling approach and proposed models to estimate expected accident frequencies on highway segments, given the traffic and geometrics of the highway element. The variables such as Average Annual Daily Traffic (AADT), lane and shoulder widths, horizontal curvature, section length, skew angle of intersection, land-use,
+
+<sup>1</sup> Tel.: +91 44 2257 4272.
+
+and so forth were found to be contributing to the variations in accident potential of highway elements [\(Abdel-Aty & Radwan, 2000;](#page-3-0) [Harwood, Council, Hauer, Hughes, & Vogt, 2000; Ivan, Wang, &](#page-3-0) [Bernardo, 2000; Kim, Chung, Song, & Chon, 2005; Ca](#page-3-0)fiso, Graziano, [Silvestro, & Cava, 2009](#page-3-0)).
+
+The models mentioned above come under the category of fixed parameter models, where the model parameters are assumed to be the same for any individual observation in the population. In other words, the magnitude of influence of given explanatory variable on outcome is the same for any individual observation. In the case of accident prediction models, this means that the contribution of given explanatory variable on accidents is the same on any highway segment. Recent research on accident modeling suggests that it would be more appropriate to model accident frequencies with random parameter modeling, which allows the model parameters to vary among individual observations in the population ([Anastasopoulos &](#page-3-0) [Mannering, 2009](#page-3-0)). The argument in favor of this approach is that there could be heterogeneity associated with the process of accident occurrence among highway segments due to variability among vehicle types, driver behavior, and so forth. Hence, the magnitude of influence of explanatory variables on accidents is more likely to be varying across locations than fixed.
+
+<sup>⁎</sup> Corresponding author. Tel.: +91 44 2257 5292.
+
+E-mail addresses: [rrdinu@iitm.ac.in](mailto:rrdinu@iitm.ac.in) (R.R. Dinu), [av@iitm.ac.in](mailto:av@iitm.ac.in) (A. Veeraragavan).
+
+<span id="page-1-0"></span>The aforementioned heterogeneity is more likely on Indian roads where there is large variability within and among vehicle types and driver population. Early research has established the significance of mixed nature of Indian traffic on accident occurrence, with proportions of various types of vehicles contributing to the variability in accident potential of highway elements ([Robert & Veeraragavan,](#page-3-0) [2007; Srinivas, Dinu, & Veeraragavan, 2007\)](#page-3-0). These studies used fixed parameter modeling approach and the appropriateness of random parameter modeling for the mixed traffic situation has not been investigated so far. The present study aims at modeling accident frequencies on Indian two-lane undivided rural highway segments, employing random parameter modeling.
+
+#### 2. Methodology
+
+Number of accidents yi occurring in highway segment i over period of time t follows a Poisson distribution with probability density function;
+
+$$P(y_i) = \frac{(\lambda_i t)^{y_i} e^{-(\lambda_i t)}}{y_i!} \tag{1}$$
+
+where λ<sup>i</sup> is the expected number of accidents in unit time, or in other words, the 'safety' associated with the highway segment. Poisson distributed accident frequencies can be modeled using generalized linear modeling approach, with a logarithmic link function as;
+
+$$\lambda_i = \exp(\beta x_i) \tag{2}$$
+
+where λ<sup>i</sup> is the expected accident frequency on highway segment i over unit period of time, β is the vector of estimable parameters and xi is the vector of explanatory variables. To account for the heterogeneity with random parameters, the estimable parameters can be written as;
+
+$$\beta_i = \beta_i + \nu_i \tag{3}$$
+
+where ν<sup>i</sup> is the randomly distributed term. The random parameter model for Poisson distributed accident frequencies takes the following form;
+
+$$\lambda_i | \nu = \exp(\beta' x_i) \tag{4}$$
+
+where λi|ν is the expected accident frequency on highway segment over unit period of time, conditional on probability distribution of random parameters ν, β' is the vector of estimable random parameters and xi is the vector of explanatory variables. This results in loglikelihood function;
+
+$$LL = \sum_{i} \log \int_{\nu} P(y_i | \nu) g(\nu) \partial \nu$$
+ (5)
+
+where g(ν) is the probability density function of the random term. Maximum likelihood estimation of the above function is computationally cumbersome. Simulation assisted maximum likelihood estimation has been proposed in literature for evaluating likelihood functions that involve such high-dimensional integrals [\(Train, 2009](#page-3-0)). Here the integral, which is the probability of a random process, is approximated from repeated simulation of the random process.
+
+### 3. Data
+
+The data used in the present study were collected from nearly 200 km of highways around the city of Chennai, in the southern Indian state of Tamil Nadu. The highway segments were divided into 33 homogeneous sections, based on traffic volume, carriageway width, and shoulder width. The highway segments were two-lane undivided, with 6.5 m to 7 m wide carriageway and were of length varying from 1 km to 22 km. The accident history for a period of three years, from 2001 to 2003, was collected for these highway segments from the police records. Nearly 3,000 accidents occurred on the selected segments during this period. Traffic surveys carried out along midblock locations and intersections along the segments showed that there is considerable difference in both traffic volume and composition between day (6 a.m.–6 p.m.) and night (6 p.m.– 6 a.m.), with average hourly volume of 1,000 vph during the day and 300 vph during the night. Fig. 1 shows the average composition of day and night traffic. During the day, significant proportions of motorized twowheelers and non-motorized vehicles were present in the traffic, to the tune of an average of 26% and 5% of the traffic, respectively.
+
+The huge differences in traffic volume levels and composition suggested modeling of day-time and night-time accidents separately.
+
+Road geometric and environment data were collected for the selected highway segments through detailed inventory surveys, supplemented with GPS tracking. As the highway segments contained many horizontal (/vertical) curves in it, a weighted averaging procedure was used to arrive at a single representative index for all the horizontal (/vertical) curves within. The index for horizontal curves in a highway segment was calculated as;
+
+$$CI_{H} = \sum_{i} w_{i} DEG_{i} \tag{6}$$
+
+where wi is the weight assigned to i th horizontal curve of curvature DEGi degrees per 100 m. The curvature of horizontal curve was calculated as;
+
+$$DEG_i = \frac{\Delta_i}{l_i} \times 100 \tag{7}$$
+
+where Δ<sup>i</sup> is the central angle in degrees and ll is the length in m of i th horizontal curve. The weight wi was calculated as;
+
+$$w_i = \frac{l_i}{L} \tag{8}$$
+
+![](_page_1_Picture_25.jpeg)
+
+![](_page_1_Figure_26.jpeg)
+
+Fig. 1. (a) Average traffic composition during day (6 AM – 6 PM). (b) Average traffic composition during night (6 PM – 6 AM).
+
+where L is the length of highway segment under consideration. For vertical curves in a segment, the index was computed as;
+
+$$CI_V = \sum_i w_j GRAD_j$$
+ (9)
+
+where wj is the weight for j th vertical curve with gradient GRADj% per 100 m. The gradient of vertical curve was computed as;
+
+$$GRAD_j = \frac{g_j}{l_i} \times 100 \tag{10}$$
+
+where gj is the gradient in % and lj is the length in m of the j th vertical curve. The weight wj is computed similar to that for horizontal curves, which is shown in Eq. [\(8\).](#page-1-0)
+
+## 4. Analysis
+
+The dependent variable modeled was the accident frequency on a given highway segment in a year. Separate models were developed for day time and night time accidents. The traffic variables considered in the modeling were logarithm of average hourly volume and proportion of the different vehicle types in traffic. Length of the highway segment was considered to account for vehicle-kilometers traveled. The road environment variable included in the modeling was driveway density per kilometer, which is the number of access roads joining the main roadway in one kilometer length. Among road geometric variables, the candidate variables were width of shoulder, weighted index for horizontal curvature CIH and weighted index for vertical curvature CIV along the segment.
+
+Simulation assisted maximum likelihood estimation approach was employed for parameter estimation. To account for possible heterogeneity in parameters, each parameter was initially assumed to be normally distributed. After trials with varying number of draws, 500 random draws of each parameter was found to result in stable estimate. The correctness of the assumption of heterogeneity in parameters was tested with the statistical significance of the estimate of standard deviation of parameter distribution. T-test was conducted at 95% level of significance and the parameter was treated as random when the standard deviation of parameter distribution was found significant. The parameters with statistically insignificant variance were treated as fixed parameters.
+
+The goodness-of-fit (GOF) of the model was tested with loglikelihood ratioρ<sup>2</sup> , computed as;
+
+$$\rho^2 = 1 - \frac{LL(\beta)}{LL(0)} \tag{11}$$
+
+where LL(β) is the log-likelihood at convergence of the full model and LL(0) is that of the constant-only model. A ρ<sup>2</sup> value closer to one suggests that the model explains most of the variability in the dependent variable. Out of the three years data, the data pertaining to the first two years is used as the calibration data set and the data for the third year is kept aside as the validation data set. The model parameters were estimated with the calibration data set, employing the simulation based maximum likelihood estimation procedure. The models were then validated by computing the X<sup>2</sup> statistic using the following relationship;
+
+$$X^{2} = -2[LL(\beta)_{c + \nu} - LL(\beta)_{c} - LL(\beta)_{\nu}]$$
+
+$$(12)$$
+
+where LL(β)c, LL(β)<sup>c</sup> and LL(β)c<sup>+</sup> <sup>v</sup> are the log-likelihood values at convergence for the full model, computed over the calibration data set, the validation data set, and both the data sets combined, respectively. The X<sup>2</sup> statistic follows a distribution with degrees of freedom equal to the number of parameters in the model under consideration. The statistic was tested against χ<sup>2</sup> distribution at 95% level of significance. Only those variables that were found significant at 0.05 level in the two-tailed t-test were included in the final models. Table 1 gives the summary of the final models.
+
+## 5. Discussion of results
+
+The results of model parameter estimation show that many of the explanatory variables, especially the ones related to traffic
+
+Table 1 Estimation results for model parameters.
+
+| Variable                                           | Estimate (t-statistic in parenthesis) |                               |
+|----------------------------------------------------|---------------------------------------|-------------------------------|
+| Dependent variable                                 | Day-time accidents per year           | Night-time accidents per year |
+| Constant                                           | -6.47 (-7.43)                         | 1.39 (2.35)                   |
+| Logarithm of hourly traffic volume, vph            | 1.41 (11.10)                          | 0.60 (5.56)                   |
+| Standard deviation of parameter distribution       | 0.02 (5.07)                           | 0.03 (6.17)                   |
+| Length of highway segment, km                      | 0.16 (28.60)                          | 0.13 (23.46)                  |
+| Proportion of buses in traffic, %                  |                                       | 2.75 (2.77)                   |
+| Proportion of cars in traffic, %                   | -8.43 (-13.54)                        | -11.18 (-11.13)               |
+| Standard deviation of parameter distribution       | 1.95 (17.91)                          | 2.85 (17.79)                  |
+| Proportion of motorized two-wheelers in traffic, % | 1.78 (3.97)                           |                               |
+| Standard deviation of parameter distribution       | 1.26 (14.24)                          |                               |
+| Proportion of trucks in traffic, %                 |                                       | -3.96 (-7.56)                 |
+| Standard deviation of parameter distribution       |                                       | 0.28 (4.76)                   |
+| Driveway density, per km                           | 0.05 (9.21)                           | 0.03 (4.64)                   |
+| Standard deviation of parameter distribution       |                                       | 0.04 (10.71)                  |
+| Width of shoulder, m                               | -0.21 (-4.51)                         |                               |
+| Weighted index for horizontal curvature, CIH       | 0.06 (3.16)                           |                               |
+| Standard deviation of parameter distribution       | 0.02 (2.88)                           |                               |
+| Weighted index for vertical curvature, CIV         | 0.19 (2.47)                           | 0.21 (2.36)                   |
+| Model summary                                      |                                       |                               |
+| LL(β)                                              | -219.49                               | -206.97                       |
+| LL(0)                                              | -527.53                               | -434.80                       |
+| ρ2                                                 | 0.58                                  | 0.52                          |
+| Model Validation                                   |                                       |                               |
+| LL(β)c                                             | -219.49                               | -206.97                       |
+| LL(β)v                                             | -104.73                               | -102.33                       |
+| LL(β)c+ v                                          | -326.68                               | -310.45                       |
+| 2<br>χcritical                                     | 18.31                                 | 15.51                         |
+| X2                                                 | 2<br>4.92 (bχcritical<br>)            | 2<br>2.3 (bχcritical<br>)     |
+
+<span id="page-3-0"></span>composition, have standard deviation significantly different from zero, when modeled as random. This suggests that there is heterogeneity associated with the variables, which are not implicitly accounted for in the data. The result of the random parameter modeling is a good reason to believe that the different explanatory variables do not influence accident occurrence by the same amount on all highway segments. As hypothesized earlier, this randomness could be due to the difference among vehicle types in terms of maneuverability, performance, and so forth, as well as the difference in driver behavior and other differences in road condition, weather, and so forth, which are not measured and included in the model.
+
+Hourly traffic volume, length of highway segment, proportion of cars and motorized two-wheelers in traffic, driveway density, width of shoulder, and horizontal and vertical curvatures were found to be significantly influencing day-time accident frequencies. While increase in proportion of cars and width of shoulder were found to decrease the accident frequencies, increase in the other variables resulted in an increase in accidents. In case of night-time accidents, hourly traffic volume, length of highway segment, proportion of buses, cars, and trucks, driveway density, and vertical curvature were found to be significant. Here the proportion of cars and trucks in traffic were found to cause a decrease in accidents, while all other variables had a positive coefficient, showing an increase in accident frequencies.
+
+In the model for day-time accidents, the parameters for logarithm of hourly volume, proportions of cars and motorized two-wheelers, and weighted index for horizontal curvature were found to be randomly distributed with standard deviation significantly different from zero. In the model for night-time accidents, the parameters for logarithm of hourly volume, proportion of cars and trucks, and driveway density were found to be randomly distributed. The randomness associated with the explanatory variables related to traffic volume and composition could be attributed to the variability among and within the different vehicle types in terms of dimensions and dynamics. The randomness of parameters of road geometrics and access could be due to variability in driver behavior. The significance of standard deviations of these variables in the models show that the random parameter modeling approach is promising in Indian context of mixed traffic as well.
+
+As the random parameters were assumed to be normally distributed, their range of influence on accident frequencies can be inferred from the estimates of mean and standard deviation. Thus the parameter for logarithm of hourly volume can be expected to vary between 1.37 and 1.48 in the day-time accidents model and between 0.54 and 0.66 in the night-time accidents model for 95% of the highway segments. The range of variability of other random parameters can also be estimated in a similar manner. This would help safety engineers in evaluating more realistic ranges of safety benefits that can be expected from a corrective measure.
+
+#### 6. Conclusions
+
+This study is an attempt to employ random parameter modeling to develop accident prediction models for Indian two-lane undivided rural highways that operate under mixed traffic conditions. The heterogeneity in the process of accident occurrence across locations due to a number of factors (e.g., variability among vehicle types, variability in driver behavior) is expected to be accounted for in this modeling approach. Accident prediction models were developed for day-time and night-time accidents over a three year accident history of nearly 200 km of two-lane undivided highway segments in India. The explanatory variables considered for modeling included hourly traffic volume, length of highway segment, proportion of buses, cars, motorized two-wheelers and trucks in the traffic, driveway density, shoulder width, and horizontal and vertical curvatures.
+
+The model coefficients were assumed to be normally distributed and a simulation based maximum likelihood method was used for parameter estimation. The results of the analysis showed that the model parameters for hourly volume, proportion of cars, two-wheelers and trucks in traffic, driveway density, and horizontal and vertical curvature had statistically significant standard deviation, suggesting that the parameters are randomly distributed. As the models proposed in the study accommodate for the unaccounted heterogeneity, they are expected to help safety engineers in computing more realistic ranges of safety benefits of remedial measures.
+
+Although this study employs random parameter modeling successfully to model accidents under mixed traffic conditions, it has the following limitations:
+
+- The comparison of random parameter models with fixed parameter counterparts has not been done in the study. Such a comparison would be necessary to assess whether the improvement in modeling with this approach would really result in significant differences when applied to a real world situation, considering the computational complexity involved.
+- The random parameters in the present study were assumed to be normally distributed. It is possible that the variables are indeed random, but the probability distribution is other than normal. Evaluating suitability of different possible probability distributions or having a methodology to identify the distribution is necessary here.
+
+#### References
+
+Abdel-Aty, M. A., & Radwan, A. E. (2000). Modeling traffic accident occurrence and involvement. Accident Analysis and Prevention, 32(5), 633−642.
+
+Anastasopoulos, P. C., & Mannering, F. L. (2009). A note on modeling vehicle accident frequencies with random-parameters count models. Accident Analysis and Prevention, 41(1), 153−159.
+
+Cafiso, S., Graziano, A. D., Silvestro, G. D., & Cava, G. L. (2009). Accident prediction models for evaluation of safety performance on two-lane rural highways. TRB 88th Annual Meeting Compendium of Papers DVD.
+
+Harwood, D. W., Council, F. M., Hauer, E., Hughes, W. E., & Vogt, A. (2000). Prediction of the expected safety performance of rural two-lane highways. Technical Report, FHWA-RD-99-207.
+
+Ivan, J. N., Wang, C., & Bernardo, N. R. (2000). Explaining two-lane highway crash rates using land use and hourly exposure. Accident Analysis and Prevention, 32(6), 787−795.
+
+Kim, S. H., Chung, S. B., Song, K. H., & Chon, K. S. (2005). Development of an Accident Prediction Model using GLIM (Generalized Log-linear Model) and EB method: A case of Seoul. Journal of the Eastern Asia Society for Transportation Studies, 6, 3669−3682.
+
+Maher, M. J., & Summersgill, I. (1996). A comprehensive methodology for the fitting of predictive accident models. Accident Analysis and Prevention, 28(3), 281−296.
+
+Miaou, S. (1994). The relationship between truck accidents and geometric design of road sections: Poisson versus negative binomial regressions. Accident Analysis and Prevention, 26(4), 471−482.
+
+Miaou, S., & Lum, H. (1993). Modeling vehicle accidents and highway geometric design relationships. Accident Analysis and Prevention, 25(6), 689−709.
+
+Nelder, J. A., & Wedderburn, R. W. M. (1972). Generalized linear models. Journal of the Royal Statistical Society, Series A (General), 135(3), 370−384.
+
+Poch, M., & Mannering, F. (1996). Negative Binomial Analysis of Intersection-Accident Frequencies. Journal of Transportation Engineering, 122(2), 105−113.
+
+Robert, V. R., & Veeraragavan, A. (2007). Accident prediction factors for rural highway segments in developing countries. TRB 86th Annual Meeting Compendium of Papers CD-ROM.
+
+Srinivas, C., Dinu, R. R., & Veeraragavan, A. (2007). Application of Poisson and Negative Binomial Regression for Modeling Road Accidents under Mixed Traffic Conditions. TRB 86th Annual Meeting Compendium of Papers CD-ROM.
+
+Train, K. (2009). Discrete Choice Methods with Simulation. Cambridge, UK: Cambridge University Press.
+
+Mr. Dinu holds a Master's Degree in Transportation Engineering from University of Kerala. He is pursuing his doctoral research in the Department of Civil Engineering, Indian Institute of Technology Madras. His research interests include road safety studies under mixed traffic flow and road accident modeling.
+
+Dr. Veeraragavan holds a Master's Degree in Transportation Engineering from Indian Institute of Technology Madras and a Ph.D degree in Civil Engineering from Bangalore University, India. He was employed at Bangalore University, Bangalore, India during 1985-2004, and since 2004 he has been employed as Professor of Civil Engineering at the Indian Institute of Technology Madras, Chennai, India. His research interests include road safety under mixed traffic flow, traffic management, and road asset management.

Zotero/001_artiklid/Road Safety Indicators/ekmekcieffectsroadwidthradii2024.md

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+---
+category: literaturenote
+citekey: ekmekcieffectsroadwidthradii2024
+title: "Effects of road width, radii and speeds on collisions at three-arm priority intersections"
+authors: "Ekmekci, Mustafa; Woods, Lee; Dadashzadeh, Nima"
+year: 2024
+date: 2024-00-00 2024
+doi: 10.1016/j.aap.2024.107522
+publication: "Accident Analysis & Prevention"
+url: "https://doi.org/10.1016/j.aap.2024.107522"
+zotero_key: 4EJRG565
+zotero_storage: BP4JZH48
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "Ekmekci, Mustafa"
+status: converted
+---
+![](_page_0_Picture_1.jpeg)
+
+Contents lists available at [ScienceDirect](www.sciencedirect.com/science/journal/00014575)
+
+# Accident Analysis and Prevention
+
+journal homepage: [www.elsevier.com/locate/aap](https://www.elsevier.com/locate/aap)
+
+![](_page_0_Picture_5.jpeg)
+
+![](_page_0_Picture_6.jpeg)
+
+## Effects of road width, radii and speeds on collisions at three-arm priority intersections
+
+Mustafa Ekmekci a,1,\* , Lee Woods b,2 , Nima Dadashzadeh c,3
+
+- <sup>a</sup> *School of Civil Engineering and Surveying, University of Portsmouth, Portsmouth PO1 3AH, UK*
+- <sup>b</sup> *Faculty of Technology, Portland Building, University of Portsmouth, Portsmouth PO1 3AH, UK*
+- <sup>c</sup> *Future Mobility Centre, Huddersfield Business School, University of Huddersfield, Huddersfield HD1 3DH, UK*
+
+#### ARTICLE INFO
+
+*Keywords:*  Visibility Priority intersection Safety Collisions 20 mph speed limit 30 km/h speed limit piecewise Structural Equation Modelling
+
+#### ABSTRACT
+
+Simulation and observational studies have identified the importance of intersection geometries and vehicle speeds in collisions. However, the causal mechanisms of such collisions in low-speed areas and for different collision types remain unclear. This observational study investigates the complex relationships between geometries, speeds, visibilities, and road traffic collisions in the context of low-speed urban areas. Data were collected from 120 three-arm priority intersections in Portsmouth, UK. In 2007, Portsmouth became the first city in the UK to adopt a 20mph speed limit on all residential streets. The city has also adopted the UK's Manual for Streets (MfS) as the design standard for all new priority intersections in low-speed residential areas. Piecewise structural equation models (pSEM) were developed to represent the causal mechanisms that relate to geometries, speeds, speed limits and collisions. Findings indicate the role of combinations of approach lane width, corner radii, speed limit, and type of collision. The interaction of wider approach lanes on the minor arm and larger radii of turns for left-turning vehicles (left-hand driving perspective) was associated with higher numbers of road traffic collisions for right-turning vehicles. It is posited here that this is due to the orientation of the left-turning vehicle blocking the left visibility of the right-turning vehicle. These results give weight to the introduction of the 20mph speed limit zone in Portsmouth and some of the changes brought about by MfS. However, the combined effect of approach width and radii on collisions is novel and could form the basis of further guidance on reducing specific types of collisions at three-arm priority intersections.
+
+## **1. Introduction**
+
+Globally, there is a growing awareness of the importance of road safety and the high number of road collisions leading to fatalities and severe injuries. According to the World Health Organisation [\(WHO,](#page-9-0)  [2018\)](#page-9-0), 1.35 million people worldwide are killed in road collisions. Among young people aged 15–29, road collisions are the leading cause of death [\(WHO, 2015](#page-9-0)). According to the Federal Highway Administration [\(FHWA, 2018](#page-8-0)), just under 37,000 fatal collisions occurred on the roads of the United States in one year. More than 50 % of the total fatal and injury crashes occur at or near intersections [\(FHWA, 2024](#page-8-0)). Furthermore, 18 % of the fatal collisions happen in unsignalized intersections, with 14 % involving pedestrians and 3 % cyclists.
+
+Intersections, at-grade or grade-separated, are locations of high collision concentration among European countries, 40–60 % of the total (European [Commission, 2024](#page-8-0)). In the UK, 49 % of collisions in urban areas happen at priority control intersections, of which 59 % occurred at T or staggered intersections (statistic calculated from STATS19 ([Department for Transport, 2022\)](#page-8-0) dataset using ArcGIS). These collisions are responsible for many casualties, 66 % of whom were drivers, cyclists or motorbike riders; 19 % passengers; and 15 % pedestrians.
+
+Priority intersection design standards and guidance have evolved in the UK from 1946 (Design & Layout of Roads in Built-Up Areas) ([Cook,](#page-8-0)  [1946\)](#page-8-0) to the most recent guidance published in Manual for Streets and Manual for Street 2 [\(Department for Transport, 2007; CHIT, 2010\)](#page-8-0). MfS has been adopted as the design standard by many highway authorities
+
+<sup>\*</sup> Corresponding author.
+
+*E-mail addresses:* [mustafa.ekmekci@port.ac.uk](mailto:mustafa.ekmekci@port.ac.uk) (M. Ekmekci), [lee.woods@port.ac.uk](mailto:lee.woods@port.ac.uk) (L. Woods), [n.dadashzadeh@hud.ac.uk](mailto:n.dadashzadeh@hud.ac.uk) (N. Dadashzadeh). 1 ORCID: 0000-0003-2636-1739. 2 ORCID: 0000-0002-8336-4939. 3 ORCID: 0000-0001-5425-0572.
+
+when designing new priority intersections, particularly in lower-speed urban areas. There was a recognition in MfS that providing excellent visibilities to drivers through Design Manual for Roads and Bridges (DMRB) ([Highways Agency, 1994\)](#page-8-0) and Design Bulletin 32 (DB32) ([Department of the Environment, 1992\)](#page-8-0) standards had a counterintuitive effect on safety. With excellent visibility, drivers' perceptions of risks reduce, which leads to increased vehicle speeds, less concentration, and greater risk-taking behaviours ([Henson et al., 1992](#page-8-0)). Rather than improving the intersections' safety, it is suggested that excessive visibility reduces the safety of intersections. As such, MfS reduces the minimum visibility requirements at priority intersections alongside guidance on reducing the geometric dimensions of these intersections. MfS also promotes the use of 20mph speed limits in built-up areas. Portsmouth in the UK became the first city where a 20mph city-wide speed limit was introduced across residential areas ([Bunce, 2009\)](#page-8-0).
+
+This study sets out to investigate the traffic safety of low visibility priority intersections at 120 locations in Portsmouth. This paper examines the effect of visibility distance, approach width, radii and speeds on road traffic collisions. Although many studies in the literature look at the effect of geometrical variables on road traffic collisions, these studies did not look at the combined effect of geometrical variables in the context of low-speed/low-speed-limit priority intersections.
+
+The remainder of this paper is structured as follows: Section 2 reviews the existing literature on contributory factors of road traffic collisions (RTC) at priority intersections, human factors of RTC, and visibility issues at priority three-arm intersections. [Section 3](#page-2-0) describes the study area, data collection and analytic methods. Results and discussions are presented in [Section 4,](#page-5-0) followed by the conclusions and suggestions for further work in [Section 5.](#page-7-0)
+
+### **2. Review of literature**
+
+#### *2.1. Contributory factors of road traffic collisions*
+
+A considerable body of literature exists on the causes of road traffic collisions, including several studies related to priority intersections in the UK and globally. It is essential to understand what kind of variables affect intersection safety in order to be able to discern the effects of visibilities, radii and approach width from the effects of all other variables likely to impact the numbers and types of collisions. Table 1 shows general contributory factors of RTCs in the literature.
+
+Many studies show that minor road width is associated with an increase in approach speed and collision frequency both globally (i.e. [Harnen et al., 2003; Vieira Gomes, 2013](#page-8-0)) and in the UK (i.e. [Summersgill](#page-9-0)  [et al., 2001\).](#page-9-0) However, these studies could not explain the wider minor road width, radii and visibility connections.
+
+Vehicle speed is the most commonly recognised contributory factor for collisions. [Ziolkowski \(2016\)](#page-9-0) examined the effect of geometric variables and road features on vehicle speeds in urban areas and found that an increase in road width was associated with an increase in speed. [Salifu \(2004\)](#page-9-0) observed that the major arm's standard deviation of the approach speed was significantly and positively correlated with collision frequency. However, the speed effect may also be contradictory for specific types of collisions, such as right-turning and left-turning movement collisions from minor roads. A microsimulation study of three-arm priority intersections by [Zhang et al. \(2017\)](#page-9-0) found that the number of collisions for turning vehicles from minor roads decreased with increased speed on the major road. The authors thought psychological factors could explain why drivers turning from the minor road may drive cautiously when traffic speed on the major arm is relatively high.
+
+Researchers have paid considerable attention to the relationship between traffic collisions and traffic flow (i.e. [Salifu, 2004; Vieira](#page-9-0)  [Gomes, 2013; Bonneson and McCoy, 1993; Hauer et al., 1988; Kulmala,](#page-9-0)  [1996; Golias, 1991\)](#page-9-0). The common sense of traffic safety concludes that collisions cannot occur with zero traffic flow ([Turner et al., 2003](#page-9-0)) and
+
+**Table 1**  General contributory factors of road traffic collisions at priority intersection.
+
+| Feature                                                      | Reference                                                                                                             |
+|--------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------|
+| The number of arms/approach lanes<br>in junction             | Vieira Gomes (2013), Wang et al. (2015)                                                                               |
+| Channelisation (Ghost Island, Left                           | Summersgill et al. (1996), Abdel-Aty and                                                                              |
+| Turning Line, Right Turning Line)                            | Haleem (2011), Salifu (2004)                                                                                          |
+| The distance to the nearest other<br>intersection            | Haleem and Abdel-Aty (2010)                                                                                           |
+| Visibility                                                   | York et al. (2007), TMS Consultancy (2010),<br>Summersgill et al., (2001), Pickering et al.<br>(1986)                 |
+| Road Width                                                   | Ziolkowski (2016), Greibe (2003), Salifu<br>(2004), Harnen et al. (2003), Vieira Gomes<br>(2013), Ahmed et al. (2014) |
+| Road surface conditions                                      | Akin and Akbas (2010), Wang et al. (2015),<br>Hassan and Al-Faleh (2013)                                              |
+| Speed (Mean, St. deviation, 85th<br>percentage, speed limit) | Charlton (2003), Haleem and Abdel-Aty<br>(2010), Sarkar et al. (2012), Salifu (2004),<br>Wang et al. (2015)           |
+| Day or Night                                                 | Wang et al. (2015), Hassan and Al-Faleh<br>(2013)                                                                     |
+| Road Lighting                                                | Salifu (2004), Hassan and Al-Faleh (2013)                                                                             |
+| Weather Condition                                            | Akin and Akbas (2010), Wang et al. (2015)                                                                             |
+| Traffic Volume                                               | Salifu (2004), Vieira Gomes (2013),                                                                                   |
+|                                                              | Bonneson and McCoy (1993), Hauer et al.                                                                               |
+|                                                              | (1988), Kulmala (1996), Golias (1991),                                                                                |
+|                                                              | Abdel-Aty and Haleem (2011)                                                                                           |
+| Car Parking                                                  | Sarkar et al. (2012)                                                                                                  |
+| Guard, Pedestrian Crossing, Cycle<br>Lane                    | Salifu (2004), Summersgill et al. (1996)                                                                              |
+| Day of the Week, Time of Day                                 | Hassan and Al-Faleh (2013)                                                                                            |
+
+Annual Average Daily Traffic (AADT) flow is a significant predictor of collisions ([Kim et al., 2007\)](#page-8-0).
+
+The study of [Salifu \(2004\)](#page-9-0) at priority T intersections revealed that the absence of street lighting, right turn storage on major arms (left-hand drive perspective), the standard deviation of approach speed on the major arm and wider road width of the minor road were all significantly and positively correlated with the frequency of collisions [\(Salifu, 2004](#page-9-0)).
+
+#### *2.2. Human factors*
+
+The studies in section 2.1 considered factors associated with the intersection. However, research has shown that factors associated with the driver are the most common cause of road traffic collisions, such as speeding, careless driving, distraction due to the use of handheld devices, driving under the influence of alcohol or drugs and other risktaking behaviours. The characteristics of the driver are shown to relate to some of these behaviours, with young men being particularly prone to aggressive driving and higher risk-taking behaviours, which is believed to be the main reason why younger men are more likely to be involved in road traffic collisions than their female counterparts ([Stan](#page-9-0)[ton and Salmon, 2009;](#page-9-0) [Massie et al., 1995; Holland et al., 2010\)](#page-8-0). [Amin](#page-8-0)  [\(2020\)](#page-8-0) examined the effect of contributory factors on male and female older drivers in the West Midlands of the United Kingdom. Complex intersection geometry, extreme weather conditions and time of day were significant factors for older driver collisions.
+
+Human errors have the highest collision contributions depending on research outcomes, between 75 % and 95 % ([Stanton and Salmon, 2009](#page-9-0); [Kostelec, 2020](#page-8-0)).
+
+Whilst it can be seen from these two datasets that road conditions (including here road geometries) feature little in terms of the causes, it is highly plausible that many of the driver behaviours listed as causes are themselves influenced by the geometric design of intersections, particularly the level of care drivers show at an intersection, risk-taking behaviours and speed, which are some of the most critical factors in road traffic collisions.
+
+## <span id="page-2-0"></span>*2.3. Visibility issues at three-arm priority intersections*
+
+Some researchers have used microsimulation studies to explore the causes of road traffic collisions (i.e. [Darzentas et al., 1980; Zhang et al.,](#page-8-0)  [2017\)](#page-8-0). Microsimulation approaches depend on gap acceptance and other driver characteristics specified within the simulation. Hence, they may not be appropriate when investigating such behaviours. Moreover, some microsimulation models also assume junction visibilities [\(Dar](#page-8-0)[zentas et al., 1980](#page-8-0)) rather than investigating their effect.
+
+Most studies in the literature into the causes of collisions are observational rather than based on simulations. [Pickering et al. \(1986\)](#page-8-0)  observed frequencies and characteristics of collisions at priority T intersections in rural areas where the speed limit was 50mph and examined the effect of some features of T intersections, such as ghost islands (major arm to minor arm turning areas demarked with road markings only rather than physical barriers/kerbs) which were found to be associated with a reduction in collisions. The wider road width on the major arm had similar beneficial effects on collisions. The collision rate of turning right movements from the minor road was 40 % lower at intersections without merging and diverging lanes. [Pickering et al. \(1986\)](#page-8-0)  stated that there is no explanation for this but suggested this might be related to visibilities from the minor road. He used the reciprocal and identity forms of visibility variables to test this and found that their inclusion was significant for rear shunt collisions on minor arms only. Longer right-hand visibilities, 9 m back, were associated with higher numbers of minor rear shunt collisions.
+
+[Pickering et al. \(1986\)](#page-8-0) and the Cost Benefit Analysis of collisions (COBA) procedure requires at least a knowledge of traffic inflow to estimate traffic collisions [\(Highways Agency, 2022](#page-8-0)).
+
+[Arndt and Troutbeck \(2001\)](#page-8-0) concluded that the approaching visibilities at minor arms were not associated with collision rates. However, this study did not examine the causality of traffic collisions regarding visibility.
+
+Methodologically similar to Pickering's study (1986), [Summersgill](#page-9-0)  [et al. \(1996\)](#page-9-0) considered the visibility of intersections by measuring these from 2, 4.5 and 9 m back from the give-way line and the association with collisions. However, they did not assess collision types such as rear shunts, right-turn major arm movements. [Layfield et al. \(1996\)](#page-8-0) considered staggered intersections in the UK, highlighting that the inverse of visibility from minor roads can predict collisions instead of using the mean speed of major road vehicles. Another study by [Summersgill et al.](#page-9-0)  [\(2001\)](#page-9-0) compared the operational forms of one-way and two-way priority intersections in urban areas. They found that visibility was associated with speed, so these variables may affect collisions by modifying speed. However, the authors could not demonstrate the mechanism by which this might happen. [York et al. \(2007\)](#page-9-0) and TMS [Consultancy](#page-8-0)  [\(2010\)](#page-8-0) undertook research on visibilities at priority intersections to support the development of the MfS. The results showed that shorter visibility could lower vehicle speeds in line with [Summersgill et al.](#page-9-0)  [\(2001\). York et al. \(2007\)](#page-9-0) concluded that geometries could reduce both the likelihood and severity of collisions. Visibilities of just 40 m can be safe. However, caution was expressed that visibilities less than 20 m may not be safe as speeds may not be reduced sufficiently to offset the shorter visibility. TMS Consultancy concluded that visibility y distance on the major arms could not be seen as a single deterministic factor for road collisions in high-risk urban areas.
+
+The developing body of research into the negative impacts of excessive visibilities at intersections on collisions led to the guidance in the MfS. In contrast with earlier design guidance and standards (Design and Layout of Roads in Built-up Areas, 1946; Design Manual for Roads and Bridges, 1992), MfS promoted shorter visibilities and geometries in order to reduce vehicle speeds and therefore reduce the likelihood and severity of collisions. MfS requires stopping sight distances to the left and right to be provided from only 2.4 m back from the give-way intersection. This 2.4 m x-distance relates to the distance between the front bumper of a large car and the driver's eye position. In doing so, MfS intersections require the driver on the minor arm to stop at the give-way line, as it is only at this point that they have sufficient visibility to determine if there are gaps in the traffic they can turn into. This is a fundamental difference from earlier design standards that allowed drivers to make such judgements from 9 m back, meaning that they did not necessarily need to stop or slow down considerably at the give-way line as two measurements were illustrated in [Fig. 1.](#page-3-0)
+
+TMS [Consultancy \(2010\), York et al. \(2007\)](#page-8-0), and others provide evidence as to the association between visibilities and collisions and an indication that the effect may be through moderation of vehicle speeds, but there remain unanswered questions as to the relationships between geometries, speeds, speed limits and visibilities at intersections in the UK. Their analysis of these associations is problematic. They do not account for the nature of rare collision data, which may not be normally distributed with respect to visibilities. The simple linear regression of a count response variable may not present meaningful results. Generalised Linear Modelling (GLM) approaches taking account of the discrete nature of responses would be more logical. Such approaches have been applied in the UK ([Maher and Summersgill, 1996; Pickering et al., 1986\)](#page-8-0) and overseas (i.e. [Bonneson and McCoy, 1993; Hauer et al., 1988; Kul](#page-8-0)[mala, 1996; Poch and Mannering, 1996; Salifu, 2004; Sawalha and](#page-8-0)  [Sayed, 2006; Sayed and Rodriguez, 1999](#page-8-0)). However, GLM may not be able to represent the complex inter-relationships, and feedback loops between speeds, visibilities, speed limits and collisions posited in this paper. Moreover, the generalizability of previous research to the context of very low-speed limit areas, such as the Portsmouth 20mph city-wide scheme, is questionable. Recent changes to the Highway Code [\(DVSA,](#page-8-0)  [2022\)](#page-8-0), changes brought about by new in-vehicle technologies, driving styles and the change in design standards mean that new empirical research may uncover different associations and relationships to those presented in the current literature.
+
+This study, therefore, seeks to understand the complex interrelationships between visibilities, speeds, speed limits, geometries and different types of road traffic collisions in the context of low-speed (20mph) intersections through an analysis of data from Portsmouth, UK.
+
+## **3. Method and data**
+
+This section describes the study area, sampling strategy, data collection approach, and the analytic methods adopted.
+
+While an experimental approach may be beneficial in determining causality (from a statistical perspective), this has significant ethical issues. Changes in the visibilities at intersections to observe whether collision increases would not pass most ethical tests. Also, collisions are rare events, so the data collection for an experimental design may take several years. Microsimulation, which is beneficial if no collision data exists, can be used, but these require gap acceptance and other driver behaviours to be specified for the model to be run. These behaviours are not interesting to this study; hence, this approach was rejected. The overarching methodological approach deemed most appropriate was observational and quantitative due to the convenience, timescales and ethical considerations. The Department publishes detailed secondary datasets on collisions in the UK (STATS19) for Transport (DfT) which enables such observational studies possible across a large population of intersections (Department for Transport UK, 2022).
+
+#### *3.1. Study area*
+
+The City of Portsmouth was the first city in the UK to adopt a 20mph speed limit on all residential streets in 2007 ([Bunce, 2009\)](#page-8-0). The city is the most densely populated in the UK, with much of the city developed during the industrial Victorian period around the Royal Navy base. Large residential areas are typified by high-density terraced housing with minimal or no setback from the footway and low visibility priority junctions linking these roads to local distributor roads. Mid-century areas adhered to the design standards of the time, which promoted
+
+<span id="page-3-0"></span>![](_page_3_Figure_2.jpeg)
+
+**Fig. 1.** Illustration of how visibility distances can be drawn for different x-distances.
+
+high visibility on minor arms of priority intersections to aid traffic capacity. Most recently, the city has adopted the UK's Manual for Streets as the design standard for all new priority intersections in low-speed residential areas.
+
+#### *3.2. Sampling strategy of low visibility three-arm intersections*
+
+A stratified sampling strategy was used rather than random sampling to efficiently secure the diversity of variables required. Stratification of priority three-arm intersections was based on minor and major road speed limits: 20mph or 30mph, and the visibility of the intersection: low or high, as shown in Table 2.
+
+A standard way of identifying whether intersections had relatively low or high visibility is to compare the visibility of intersections and the corresponding Stopping Sight Distance (SSD). If the visibility of an intersection is more than the SSD of that intersection, it means that the minimum safety requirement related to visibility was met. Equation (1) shows the basic SSD formula. 'v' is speed (m/s), 't' is the reaction time (s) of drivers to recognise a hazardous situation, and 'd' represents deceleration of vehicles (m/s2 ). Stopping sight distances (SSD) were calculated with 1.5 s reaction time and 4.41 m/s2 deceleration coefficients provided by MfS for light vehicles. A spot speed camera measured the speed of vehicles going through the major roads and approaching the intersections. These speeds were used to calculate the SSD rather than speed limits. Intersection visibilities to the right or left, from 4.5 m back that were equal to or less than 1.1\*SSD, were considered low visibility intersections.
+
+$$SSD = v^*t + \frac{v^2}{2^*d}$$
+ (1)
+
+#### *3.3. Data collection*
+
+More than 150 three-arm intersection locations in Portsmouth were reviewed between September 2020 and August 2021 of which 120
+
+**Table 2**  Sample Stratification.
+
+| Speed Limit on<br>Main Road | Speed Limit on<br>Minor Road | Low<br>Visibility | High<br>Visibility | Total |
+|-----------------------------|------------------------------|-------------------|--------------------|-------|
+| 20mph                       | 20mph                        | 20                | 20                 | 40    |
+| 30mph                       | 20mph                        | 20                | 20                 | 40    |
+| 30mph                       | 30mph                        | 20                | 20                 | 40    |
+| Total                       |                              | 60                | 60                 | 120   |
+
+priority three-arm intersections met the criteria set out in section 3.2 to be included in this study [\(Ekmekci et al., 2023](#page-8-0)). Primary data (Speed & Classified Manual Traffic Counts) were collected from these 120 locations in Portsmouth and Gosport, as shown in [Fig. 2](#page-4-0). Speed data for approaching vehicles at 360 intersection arms were measured by using an SL700 spot speed camera. Classified 15-minute traffic counts were undertaken in the am, pm or both peak periods. These were converted to AADT using the standard conversion factors suggested by the Chartered Institution of Highways and Transportation (CIHT, 1997). Secondary response variable data in this study was obtained from the STATS19 database downloaded from "[data.gov.uk](http://data.gov.uk)". The dataset includes separately documented collision, casualty and vehicle files for the base years between 2008 and 2020.
+
+Visibilities to the left and the right were measured in two ways. MfS requires visibilities to the left and the right to be measured to the nearside kerb from 2.4 m back from the give-way line. This is because vehicles approaching from the left may be overtaking vehicles or cars parked and hence be on the "wrong" side of the road. Additionally, in this study, visibilities were measured to the centre line of the major arm, as shown in [Fig. 3](#page-4-0) and also considered obstructions caused by parked vehicles. This study focuses on right-turning vehicles. These involve gaps being accepted to the left and right, hence visibilities to the left and the right. Both sets of visibility measurements were tested in the modelling described later.
+
+## *3.4. Piecewise structural equation modelling (pSEM)*
+
+Piecewise Structural Equations Modelling (pSEM) was developed by Shipley's studies in the 2000 s [\(Shipley, 2009\)](#page-9-0). The relationships between variables in the traditional SEM are simultaneously estimated in a single variance–covariance matrix [\(Stein et al., 2012\)](#page-9-0). However, in piecewise SEM (pSEM), each set of relationships are estimated locally (or, in other words, independently) [\(Shipley, 2009](#page-9-0)). The traditional SEM uses chi-square tests to compare observed and predicted covariance matrices, while the goodness-of-fit of a pSEM is measured as a "test of directed separation" ([Lefcheck, 2016\)](#page-8-0). [Shipley \(2009\)](#page-9-0) highlighted that this test does not depend on asymptotic methods, so it can be used with smaller sample sizes. Secondly, many problems involving non-normality and non-linearity can be overcome. Another aspect of the "test of directed separation" is that it does not conflict with some problems of covariance matrices involving a maximised loss function. Finally, it allows each piece of the local causal model to determine the extent to which it contributes to the lack of fit [\(Shipley, 2009\)](#page-9-0). Therefore, pSEM seems to be a robust technique, and the work presented here is believed
+
+<span id="page-4-0"></span>![](_page_4_Figure_2.jpeg)
+
+**Fig. 2.** Locations for 120 three-arm priority intersections in Portsmouth data collection.
+
+![](_page_4_Figure_4.jpeg)
+
+**Fig. 3.** Used variables in the initial causal path.
+
+to be the first study that models traffic collisions with pSEM.
+
+R Studio was selected as the analytical package, as it is an opensource programming language supported by various academic environments, with three extensions to run SEMs, including "piecewiseSEM" integrated with Generalized Linear Modelling (GLM) techniques [\(RC](#page-9-0)  [Team, 2020; Lefcheck et al., 2023\)](#page-9-0).
+
+As collisions are rare events, the frequencies will not follow normal distributions. One sample Kolmogorov-Smirnov test was used to check whether they followed Poisson distributions. The results show no significant evidence (Asymp. 2-tailed significance is 0.149) to reject the null hypothesis that "H0: The frequency of the sample significantly differs from a Poisson distribution." Therefore, it is assumed that the collisions follow Poisson distributions, and modelling the data with Poisson regression is appropriate.
+
+The associations between speed variables (mean) and other factors
+
+were modelled with pSEM through multiple linear regression, as speeds are dependent variables. Kolmogorov-Smirnov tests were used to check the normal distribution assumptions. As per the results in Table 3, the variables are assumed to be normally distributed.
+
+[Fig. 4](#page-5-0) below shows the path diagram of the pSEM model. Response variables are the mean of minor road speed, major road speeds (from right arms to the left and left arms to the right) and traffic collisions.
+
+**Table 3**  Test of Normality.
+
+|                                         | Kolmogorov-Smirnova |     |        |
+|-----------------------------------------|---------------------|-----|--------|
+|                                         | Statistic           | df  | Sig.   |
+| Mean of Minor Road Speed                | 0.075               | 120 | 0.094  |
+| Mean of Major Road Right to Left Speed  | 0.071               | 120 | 0.200* |
+| Mean of Major Right Left to Right Speed | 0.047               | 120 | 0.200* |
+
+<span id="page-5-0"></span>![](_page_5_Figure_2.jpeg)
+
+**Fig. 4.** Initial pSEM causal path.
+
+(2)
+
+(5)
+
+Predictors are traffic flow, the combination of minor road width and corner radii, visibilities, speed limit and major road width, the mean of minor road speed, and major road speeds (from right arms to the left and left arms to the right).
+
+The hypothesized model's equations can be written as follows:
+
+$$\begin{split} AvrSpeedMinor &= [TF.\beta_1 + Int.\beta_2 + VisR24.\beta_3 + VisR9.\beta_4 + VisL9.\beta_6 + SpeedLimit.\beta_7 + AvrSpeedMajRtoL.\beta_8 \\ &+ AvrSpeedMajLtoR.\beta_9 + \beta_0] \end{split}$$
+
+AvrSpeedMajRtoL = [TF*.*β10 + SpeedLimit*.*β11 + WidthMaj*.*β12 + β13] (3)
+
+$$AvrSpeedMajLtoR = [TF.\beta_{14} + SpeedLimit.\beta_{15} + WidthMaj.\beta_{16} + \beta_{17}]$$
+ (4)
+
+$$\begin{split} E &= Exp(TF.\beta_{18} + Int.\beta_{19} + VisR24.\beta_{20} + VisR9.\beta_{21} + VisL24.\beta_{22} + VisL9.\beta_{23} \\ &+ SpeedLimit.\beta_{24} + AvrSpeedMinor.\mu_1 + AvrSpeedMajRtoL.\mu_2 \\ &+ AvrSpeedMajLtoR.\mu_3 + \beta_{25}) \end{split}$$
+
+Where,
+
+βi and μi : Estimated coefficients*.*
+
+TF: Traffic Flow (vehicle/hour). Int: Interaction of minor road width and corner radii (metres<sup>2</sup> ). VisR24: Right-hand visibility at 2.4 m back from give-way lines projected to the near side kerb of the major road (metres). VisR9: Right-hand visibility at 9 m back from give-way lines projected to the near side kerb of the major road (metres). VisL24: Left-hand visibility at 2.4 m back from give-way lines projected to the centre line of the major road (metres). VisL9: Left-hand visibility at 9 m back from give-way lines projected to the centre line of the major road (metres). SpeedLimit: Speed limit (variable is 1 if 20mph is applied; 0 if not). WidthMinor: Minor road width measured at 9 m back from give-way lines (metres). WidthMaj: Major road width (metres). AvrSpeedMinor: Average speed of vehicles approaching on the minor arms (mph). Avr-SpeedMajRtoL: Average speed of vehicles traveling from the major road's right arm to its left arm (mph). AvrSpeedMajLtoR: Average speed of vehicles traveling from the major road's left arm to its right arm (mph). E: Expected frequency of collisions predicted by the model (collision/year). Exp (): Exponential function of the natural number (e).
+
+## **4. Results and discussions**
+
+The connections in the initial model shown in Fig. 4 were step by step removed from the model using a backward elimination method. The final form of the pSEM path diagram is shown in [Fig. 5](#page-6-0). Traffic flow, minor road width, visibility to the right (R 2.4 m), and visibility to the left (L 2.4 m) have a statistically significant impact on the number of the turn right from minor motorised veh-veh collisions at the 95 % confidence level (P-value of 0.05).
+
+The parameters estimated and P-values for the latest form of the pSEM model are summarised in [Table 4,](#page-6-0) and estimates of model fit are shown in [Table 5](#page-6-0). The variables included in the final model were able to predict circa 60 % of the variation in the numbers of right-turn motorised veh-veh collisions. This compares to 37 % for the flow-based model and 50 % for the geometry-flow-based model by Salifu et al. (2004), and two models (multivariate adaptive regression splines (MARS) and negative binomial (NB)) produced by [Abdel-Aty and Haleem \(2011\)](#page-8-0)  with 39 % and 19 %, respectively.
+
+These results reinforce the findings in the literature that vehicle flows relate to the number of collisions at priority intersections [\(Hauer](#page-8-0)  [et al., 1988; Golias, 1991; Kulmala, 1996; Bonneson and McCoy, 1993;](#page-8-0)  [Salifu, 2004](#page-8-0); [Bonneson and McCoy, 1993; Hauer et al., 1988; Kulmala,](#page-8-0)  [1996; Golias, 1991; Salifu, 2004;](#page-8-0) [Vieira Gomes, 2013](#page-9-0)). This study has also confirmed that these findings remain true in the context of lowspeed limit (20mph) areas.
+
+Speed limit and a combination of approach width and corner radii on the left (geometries) affect approach speed. In low-speed limit areas, the effect of speed limits and geometries on vehicle speeds negates any apparent effects of visibilities on speeds on the minor approach. The lower visibilities are not slowing vehicles down further than the speed limits, and geometry has already slowed vehicles. This may suggest that there is a role for lower speed limits, even at intersections where visibilities are already low. However, visibilities do appear to have a direct relationship with the number of collisions rather than an indirect one through vehicle speeds. Visibility distances at 2.4 m back from the giveway line were directly associated with the number of collisions for rightturning vehicles. All else being equal, the greater the left-hand visibility at 2.4 m back, the better the safety, while greater right-hand visibility had a counter effect on safety. This is contrary to the literature ([York](#page-9-0)  [et al., 2007](#page-9-0); TMS [Consultancy, 2010;](#page-8-0) [Summersgill et al., 2001](#page-9-0)) and to the design standards ([Department for Transport, 2007; CHIT, 2010](#page-8-0);
+
+<span id="page-6-0"></span>![](_page_6_Figure_2.jpeg)
+
+**Fig. 5.** The latest form of pSEM after implementing the backward elimination method.
+
+**Table 4**  Results of pSEM Parameters estimate and P-value for the final pSEM model.
+
+| Response                                    | Predictor                         | Estimate | P.<br>Value |
+|---------------------------------------------|-----------------------------------|----------|-------------|
+| Mean of Major Road Right to<br>Left Speed   | Traffic Flow                      | 0.0005   | 0.0000      |
+| Mean of Major Road Right to<br>Left Speed   | Speed Limit                       | 3.9902   | 0.0000      |
+| Mean of Major Road Left to<br>Right Speed   | Traffic Flow                      | 0.0005   | 0.0000      |
+| Mean of Major Road Left to<br>Right Speed   | Speed Limit                       | 3.1690   | 0.0000      |
+| Mean of Minor Road Speed                    | Speed Limit                       | 2.3575   | 0.0000      |
+| Mean of Minor Road Speed                    | Corner Radii: Minor<br>Road Width | 0.0221   | 0.0028      |
+| Right Turn from Minor Veh<br>Veh Collisions | Vis. Right 2.4                    | 0.0026   | 0.0364      |
+| Right Turn from Minor Veh<br>Veh Collisions | Vis. Left 2.4                     | − 0.0035 | 0.0293      |
+| Right Turn from Minor Veh<br>Veh Collisions | Traffic Flow                      | 0.0002   | 0.0000      |
+| Right Turn from Minor Veh<br>Veh Collisions | Corner Radii: Minor<br>Road Width | 0.0113   | 0.0003      |
+
+**Table 5**  R-square values of response variables.
+
+| Response                                 | R-squared of pSEM |
+|------------------------------------------|-------------------|
+| Mean of Major Road Right to Left Speed   | 0.34              |
+| Mean of Major Road Left to Right Speed   | 0.34              |
+| Mean of Minor Road Speed (MMRS)          | 0.26              |
+| Right Turn from Minor Veh-Veh collisions | 0.60              |
+
+[Highways Agency, 1994\)](#page-8-0) that do not distinguish between left-hand and right-hand visibilities. The reasons behind this counterintuitive finding are not yet known. It may be the case that for right-turning vehicles, drivers first look for a gap to the right before looking for a gap to the left. When visibility to the right is good, this may encourage drivers to pull out into the intersection when a clear gap to the left is not yet apparent. Further work to investigate this phenomenon is required.
+
+Major road mean speeds are not significant predictors of turning
+
+movement collisions from the minor road. This result is not surprising. A microsimulation study of three-arm priority intersections by [Zhang et al.](#page-9-0)  [\(2017\)](#page-9-0) found that the number of conflicts for turning vehicles from minor roads decreased with increased speed on the major road. The authors thought that psychological factors could explain this situation that drivers turning from the minor road may drive cautiously when traffic speed on the major arm is relatively high.
+
+The results confirm the effects of speed limits and vehicle flows on the approach speeds as expected. On the other hand, Table 6. shows the effect of a + 1 standard deviation change in input variables on traffic collision frequency. The direct effect of traffic flow seems to be more potent than others. + 1 standard deviation change in the visibility (105.4 m) to the left, from the minor arm, was associated with a 31 % reduction of collisions over the observed period. To the contrary, the + 1 standard deviation change in the visibility (91.1 m) to the right was associated with an increase in the number of collisions by 27 %. Additionally, wider approaches and larger radii are associated with higher approach speeds on minor arms. + 1 standard deviation change in this combination caused by 45 % increase in the collision frequency. From a statistical perspective, [Fig. 6](#page-7-0) provides insight into why the interaction effect of corner radii and minor road width is significant. It is suggested here that this might be due to the fact that at wider minor arms, two cars can be at the give-way line together. Where the corner radii for the leftturning vehicle is small [\(Fig. 6](#page-7-0)A), the left-turning vehicle is likely to be
+
+**Table 6**  The effects of 1 SD change in independent variables on collision frequency.
+
+| Variable                              | Mean   | Standard<br>Deviation (SD) | Coefficient | Effect on<br>Collision (%)            |
+|---------------------------------------|--------|----------------------------|-------------|---------------------------------------|
+| Vis. Right 2.4                        | 80.5   | 91.1                       | 0.0026      | EXP (91.1x<br>0.0026) − 1 =<br>+27    |
+| Vis. Left 2.4                         | 104.8  | 105.4                      | − 0.0035    | EXP (105.4x<br>− 0.0035) − 1 =<br>-31 |
+| Traffic Flow                          | 3790.5 | 3295.6                     | 0.0002      | EXP (3295.6x<br>0.0002) − 1 =<br>+93  |
+| Corner Radii *<br>Minor Road<br>Width | 33.5   | 32.7                       | 0.0113      | EXP (32.7x<br>0.0113) − 1 =<br>+45    |
+
+<span id="page-7-0"></span>![](_page_7_Picture_2.jpeg)
+
+**Fig. 6.** The effect of the interaction of minor road width and turning radii.
+
+relatively perpendicular to the give-way line. In such an orientation, the driver of the right-turning vehicle sat at the same give-way line is clear as it passes over the bonnet of the left-turning vehicle. Where the corner radii for the left-turning vehicle is wider (Fig. 6B); due to the orientation of the left-turning vehicle, the vision of the right-turning vehicle is obstructed by the cabin space of the left-turning vehicle. See the diagram below.
+
+#### **5. Conclusion and future studies**
+
+The purpose of this study was to explain the complex interplay between approach width, radii, speed and visibility in the context of lowspeed limit priority intersections. This paper has provided a deeper insight and given novel evidence into visibility and traffic collision interactions. A novel pSEM approach was adopted to explore these complex interactions. The initial model's connections were refined using a backward elimination procedure to develop the final model. Results of the final pSEM model show that:
+
+- As expected, flows were found to be important, even in the context of low-speed limit areas.
+- Approach speed is affected by the speed limit and the combination of approach width and left corner radii.
+- On the minor approach, the effect of speed limits and geometry on vehicle speeds negates any apparent benefits of visibilities on speeds in low-speed limit locations. The lower visibility does not slow vehicles any more than the speed limits and geometry already do. This could imply that lower speed limits have a role to play, especially at intersections where visibility is already low. On the other hand,
+
+- visibilities appear to have a direct relationship with collision frequency rather than an indirect one via vehicle speeds.
+- Major road mean speeds are not significant predictors of the minor road turning movement collisions.
+- Visibilities did not moderate the effect of approaching vehicles' speed at low-speed intersections, while minor road width and turning radii are significant predictors of minor road speed.
+- The direct effect of traffic flow appears to be stronger than others.
+- Collisions are also related to the width and radius of the nearside kerb on minor arms at three-arm priority junctions.
+- Furthermore, wider minor road width and larger radii are related to faster minor arm approach speeds.
+- It is highly plausible that wider road width and corner radii allow a second vehicle wishing to turn left to be at the give-way line blocking the left-hand visibility.
+
+MfS promotes single-lane minor arm intersections and smaller turning radii (MfS section 9.4). However, this study found that the combination of these two factors appears to be significant rather than either factor on its own.
+
+The number of collisions for right-turning vehicles was directly related to visibility distances at 2.4 m back from the give-way line. All else being equal, higher left-hand visibility at 2.4 m increased safety, while greater right-hand visibility decreased safety. This contradicts the literature [\(York et al., 2007;](#page-9-0) TMS [Consultancy, 2010;](#page-8-0) [Summersgill et al.,](#page-9-0)  [2001\)](#page-9-0) and design standards [\(Department for Transport, 2007; CHIT,](#page-8-0)  [2010;](#page-8-0) [Highways Agency, 1994](#page-8-0)) that do not differentiate between leftand right-hand visibilities. The causes for this unexpected discovery are unknown. Drivers of right-turning vehicles may check for a gap to the
+
+<span id="page-8-0"></span>right before looking for a gap to the left. When visibility to the right is good, drivers may be tempted to pull out from the intersection due to a clear gap to the left is not yet visible. More research into this phenomenon is needed.
+
+Major and minor road speeds cannot be seen as a determining factor of right-turning from minor with major road motor vehicle collisions, even if it is a crucial aspect for another type of collision not included in this paper.
+
+As explanatory variables, visibilities at 9 m to the left and right did not significantly affect the type of collision presented in this paper. However, other types of collisions, such as motor vehicle-bicycle, should be analysed to understand the effect of visibilities at 9 m.
+
+While the study primarily focuses on driving behaviours in the United Kingdom where vehicles are driven on the left side of the road, it is essential to acknowledge the potential applicability of the findings to other high-income countries with right-hand driving practices such as United States. Despite the natural differences in traffic regulations and cultural norms between left and right-hand driving nations, there may be similarities in certain driving behaviours and decision-making processes. However, it is crucial to recognize that direct transferability may be limited due to contextual variations, such as infrastructure differences, road design, and socio-economic factors. Future research should explore how the findings can be estimated for diverse driving environments, thereby contributing to a more comprehensive understanding of global road safety dynamics.
+
+#### **CRediT authorship contribution statement**
+
+**Mustafa Ekmekci:** Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Validation, Visualization, Writing – original draft, Writing – review & editing. **Lee Woods:** Conceptualization, Investigation, Methodology, Project administration, Supervision, Writing – review & editing. **Nima Dadashzadeh:** Conceptualization, Methodology, Supervision, Writing – review & editing.
+
+### **Declaration of competing interest**
+
+The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
+
+#### **Data availability**
+
+The data that has been used is confidential.
+
+#### **Acknowledgements**
+
+This work is a part of first author's PhD thesis which is fully funded by the Republic of Turkey Ministry of National Education, Çanakkale Onsekiz Mart University: Study Abroad Program.
+
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Zotero/001_artiklid/Road Safety Indicators/ekslermeasuringunderstandingroadsafety2010.md

@@ -0,0 +1,217 @@
+---
+category: literaturenote
+citekey: ekslermeasuringunderstandingroadsafety2010
+title: Measuring and understanding road safety performance at local territorial level
+authors: "Eksler, Vojtech"
+year: 2010
+date: 2010-00-00 2010
+doi: 10.1016/j.ssci.2009.12.010
+publication: Safety Science
+url: "https://doi.org/10.1016/j.ssci.2009.12.010"
+zotero_key: T7F962GA
+zotero_storage: 3A2M2QKK
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "Eksler, Vojtech"
+status: converted
+---
+![](_page_0_Picture_1.jpeg)
+
+Contents lists available at [ScienceDirect](http://www.sciencedirect.com/science/journal/09257535)
+
+# Safety Science
+
+![](_page_0_Picture_4.jpeg)
+
+![](_page_0_Picture_5.jpeg)
+
+# Measuring and understanding road safety performance at local territorial level Vojtech Eksler \*
+
+European Transport Safety Council (ETSC), 20 Avenue des Celtes, 1040 Bruxelles, Belgium
+
+#### article info
+
+Article history: Received 12 August 2009 Received in revised form 18 November 2009 Accepted 12 December 2009
+
+Keywords: Local territorial level Bayes risk Serious injuries Safety performance
+
+#### abstract
+
+Road safety performance has traditionally been measured at national level, because the national authorities have assumed main responsibility for managing road safety of citizens. With the rise of EU governance, the role of national government has slightly decreased while the role of local authorities has been reinforced in many countries, creating a new playfield for policy actions. Assessing road safety performance at local territorial level may provide new inputs needed to trigger further improvements in road safety, as it brings about a higher accountability of policy makers and brings relevant issues closer to citizens. The measures and methods for such evaluation have now become broadly available and their application may bring a difference in current pace of road safety improvements. An example of the application of full Bayes spatio-temporal model on local road risk data is provided, illustrating the potential of local areal analysis for a better road safety management.
+
+> -2009 Elsevier Ltd. All rights reserved.
+
+# 1. Introduction
+
+Historically, cities and regions have played an essential role in the formation of national-states and national societies. Their inhabitants gave the sense to the notion of national identity, cultural norms and habits. The sense of social identity, citizen responsibility and respect of authorities which are acquired through active community life have then a great impact on the way how people obey the law. Since behaviour and compliance with traffic rules are the key determinants for the occurrence of road crashes, it is straightforward to seek how to improve compliance with law at local level, at which many behaviour-shaping mechanisms operate.
+
+The European integration has contributed to a certain relaxation of the 'constraints of state' and cities and regions have emerged as one possible level for regulation of interests, groups and institutions. Several European countries have recently seen their governance systems decentralized. Decentralized governance systems tend to have stronger accountability mechanisms and lower corruption ([Nas et al., 1986; Rose-Ackerman, 1999](#page-4-0)), which are the factors presumably related to compliance with road traffic law. [Lederman et al. \(2005\)](#page-4-0) argue that decentralization leads to a higher accountability, since easier monitoring means less severe informational problems at local level. In countries with decentralized administrative power, employment of the least amount of special legal powers of the state compatible with the task to be performed, are sought [\(Hood and Schuppert, 1988](#page-4-0)) to bring power as close to people as possible. Moreover, local governments are directly responsive to their citizens needs but may be subject to capture by elites [\(Bardhan and Mookherjee, 2006](#page-4-0)).
+
+A common feature of policy making in all so called SUN countries (Sweden, United Kingdom and the Netherlands, three countries with the best road safety record in the world) is a vital participation of civil society organized in associations and interest groups [\(Koornstra et al., 2002](#page-4-0)) and the proximity of policy making to citizens. These have a huge implication contributing to a higher accountability and responsiveness. It is indeed a common feature of road safety improvement strategies in countries with best road safety records not to rely on traditional topdown governance, in which actions at local level are governed exclusively from the national level to which they are subordinated. Specific arrangements and responsibility distributions could be tracked in SUN countries. While in the UK, the key areas of application were infrastructure improvements and traffic law enforcement including contracts between local police forces and local authorities on the number of checks of specific offences, in the Netherlands, the accountability was enhanced through the local transport plans, being regularly put under scrutiny by the central government. In Sweden, the local initiatives by civil society, companies and authorities were likely contributing to the improvements leading to its exceptional road safety record.
+
+Alongside with the natural interest in local territories as areas of policy actions in road safety, there are several other motifs to put local territorial level at the centre of attention of contemporary road safety research. First, it can be claimed that European and national authorities have already used a great part of the potential for interventions. The EU has already passed legislation on driver licensing, properties of vehicles, and safety of infrastructure.
+
+<sup>\*</sup> Tel.: +32 (0) 22 30 41 06. E-mail address: [vojtech.eksler@etsc.eu](mailto:vojtech.eksler@etsc.eu)
+
+National authorities have brought extensive legislation regarding road user behaviour, including tools for enhancing compliance with law, such as penalty point system. Fields of actions targeting citizens at local level have, at the same time, been left unexploited until now.
+
+Beside, territories have recently become the trial fields of numerous advances in road safety research, such as intelligent transport system applications (e.g. intelligent speed adaptation, alcohol interlocks, or the shared-space urban road design concept).
+
+To allow assessment to be made on the impact of these innovative concepts on road safety, there is a need for evaluation tools and techniques, which are reliable and robust, but at the same time simple and understandable. This contradiction is most likely the reason why assessment of road safety level is so rarely done at local level. However, exceptions exist and several observation and evidence based studies could be identified in the literature. Their authors realized that at specific cases, it is indeed more feasible to somewhat restrain the geographical area for running statistical analysis. For example [Servadei et al. \(2003\)](#page-4-0) assessed the effect of Italy's motorcycle helmet law on brain injuries performed at Romagna region and [Farchi et al. \(2007\)](#page-4-0) assessed the effectiveness of the new penalty point system in Italy in Lazio region. Similarly, there are studies showing the evidence of differences in road users' behaviour at sub-national level. For example, there are significant intra-national differences in terms of the usage rate of restraint systems between Italian ([Taggi](#page-5-0) [et al., 2006\)](#page-5-0) or Swiss regions ([Siegrist et al., 2006\)](#page-4-0). Similarly, the prevalence of driving while intoxicated varies between regions of France, Italy or Spain.
+
+To summarize, there is a growing interest in local territorial level as the area of various policy actions. There is also a great potential for road safety improvements through local policy actions, which should not be ignored. The thorough understanding of mechanisms and the availability of tools for the statistical analysis are the main prerequisites for allowing road safety practitioners to evaluate the effects of various policy measures applied at local level and give appropriate feedback to policy makers on the effectiveness of their actions.
+
+# 2. Framework for the analysis
+
+There are numerous consideration issues when it comes to assessing road safety performance at local territorial level. They include among else the choice of spatial unit, time frame, indicators and relevant statistical method, but all of these are driven by the general framework for the analysis.
+
+The assessment of road safety at local territorial level is of a particular interest where the main areas of policy actions are likely corresponding. The administrative areas of a country are to be considered first, as the areas of general actions, spending powers and targeted policy actions. As second, the administrative area of police forces is to be considered, as police enforcement is one of the most efficient road safety interventions. Last but not least, the invisible borders of cultural and normative background should be taken into account [\(Wegman et al., 2008\)](#page-5-0).
+
+Ideally, these would correspond, allowing a non-distorted picture about the effectiveness of policies to be made on the background of road safety outcomes analysis. Recently, benchmarking as an evaluation tool has gained popularity also in road safety. The benchmarking as an integrated part of a continuous improvement plan should be viewed as a set of activities designed to bring gradual, but continual improvement to a process through constant review. It can be understood as an implementation tool of the Shewhart's cycle consisting of plan, do, check, act (PDCA), which is perhaps the best known theoretical framework for improvements [\(Shewhart, 1939\)](#page-4-0). Thus the analysis is the core of the improvement process.
+
+The quantitative analysis of crash outcomes as the measure of road safety performance is thus the prerequisite for managerial approach in road safety. As lord Kelvin put it: ''I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be" ([Stellman, 1998\)](#page-5-0).
+
+The evaluation of road safety performance could be accomplished by analyzing the level and trend in road crash outcomes standardized per exposure. Crash outcomes traditionally considered by road safety practitioners are road fatalities. Road injuries are often missing, as the statistics suffer from incompleteness, due to underreporting and data handling deficiencies. The use of health system based data combined with police reports may overcome this weakness. While at national level, health care systems could provide data necessary for the estimation of indicators regarding injury; in some countries the emergency department is the most common source especially for slight injuries, while in others, there are general practitioners or primary care centres ([Gio](#page-4-0)[rgi Rossi et al., 2005](#page-4-0) or [MacKay, 2003\)](#page-4-0). While in case of fatal and serious injuries, the local registrations are forwarded to central registry, this is not always the case for other types of injury data. But road injury data are available at registry of all emergency medical care centres operating under given jurisdiction in a given territory. To that end, it can be argued that at local level, road injury data are easier to collect and link with road crashes. This is also the main reason why studies on underreporting of road crash injuries are usually carried out at local territorial level, such as regions ([Amoros et al., 2003](#page-4-0)). Thus ideally, the use will be made of both fatal and serious injury counts at local level. As regards exposure indicator, vehicular travel is preferred over a static use of population of vehicle registry data.
+
+It is a common practice to benchmark road safety performance of countries, despite obvious difficulties with the interpretation of differences identified. While a substantial part of the gap between any two countries can be explained by differences attributable to the application of different road safety policies, there is always a part of the gap caused by structural differences, such as road network composition, climate, urbanization, climate, culture and many others. Similarly, differences in the development of risk indicators at national level can be partly attributable to changes in mobility patterns, traffic performance and modal split.
+
+At local territorial level, many of these factors do not have to be taken anymore in consideration when searching for the explanation of various road safety performances ([Wegman et al., 2008\)](#page-5-0). Factors such as climate, culture or norms could be often considered the same for sub-national entities. At the same time, however, some physical structural factors could come to play a more important role, but they can be easily accounted for by a simple standardization. For example, [Eksler and Lassarre \(2008\)](#page-4-0) identified the population density and urbanization as the single most important synthetic factor suitable for standardizing risk rates at sub-national level, when a comparison of road safety levels is made. The trend in road safety indicators is likely less sensitive to certain structural factors, despite some evidence on the effect of urbanization on amenability to road safety intervention. Benchmark on the trend of the risk thus has a higher explanatory value compared to the benchmark made at national level, where the availability of effective interventions can make a crucial difference in the performance over the time.
+
+# 3. Analytical methods
+
+Injuries from road crashes had originally been understood as a part of public health problem. But due to their relatively limited weight on health system at beginning of 20th century, they were often marginalized and eventually became forgotten part of public health research and initiatives ([Porter, 1999\)](#page-4-0). As a consequence, modern statistical techniques developed in epidemiology were rarely applied in road safety research. More particularly, the methods for statistical analysis in epidemiology have developed considerably during the past century, including changes in basic concepts, methods of data analysis, and methods of exposure measurement [\(Pearce, 1996](#page-4-0)). For example, since early 1990s, we have been witnessing a broad application of Bayesian analysis in descriptive epidemiology contributing to major advances in ecological research.
+
+Such a gradual development in analytical methods has not always been a case in road safety research, where the basic concepts and methods have undergone a rather limited development. The use of modern statistical methods such as the use of Bayesian statistical techniques have been limited to the analysis of road crash data on road stretches rather than to general data on territorial level (see e.g. [Heydecker and Wu, 2001](#page-4-0) or [Qin et al., 2005\)](#page-4-0).
+
+When analyzing various road safety outcomes in terms of counts or rates, different statistical approaches must be considered for different spatial levels of analysis. More particularly, when analyzing scare events at local level, the rough rates are not more appropriate as the counts suffer from the randomness. For the difference in road deaths counts to be statistically significant, a large difference is needed. For example, if there were 20 deaths in one year, there must be maximum 12 deaths in another for the observed reduction to be statistically significant. This only demonstrates an obvious difficulty in working with crash outcomes of lower frequency such as road fatalities and trying to figure out the differences in their occurrence in time and space. This is particularly true for the analysis at sub-national level. Several spatial levels are usually considered in road safety analysis, from continent to the tiny communities. While the numbers analysed at the local level can be too small and subjected to random variations to produce reliable rates, the numbers at aggregated spatial level are usually enough stable and representative to be analysed directly as crude rates. Analysis of road risk rates at different levels of spatial aggregation may therefore require different statistical approaches and methods.
+
+While at the level of EU and its member states the use of crude rates appears satisfactory, at the level of small areal units, the use of relative rates estimated via Bayesian methods reveals to be utterly indispensable. Similarly, where the traditional methods encompassing crude rates are appropriate for the analysis done at continental and country level, the analysis performed at regional or community level necessitates special statistical methods to be applied.
+
+Similarly, different road safety outcomes should be considered at local territorial level, to overcome the problem with the scarcity of crashes and their outcomes. Counts of serious injuries on roads are the obvious additional measures beside traditionally used counts of road deaths (see Table 1).
+
+Table 1 Type of rates and outcomes for the assessment of road safety at local level.
+
+| Level          | Rates | Outcomes     |
+|----------------|-------|--------------|
+| EU             | Crude | Deaths (KSI) |
+| Countries      | Crude | Deaths (KSI) |
+| Regions        | Bayes | KSI          |
+| Municipalities | Bayes | KSI          |
+
+Applying absolute figures of fatalities or other road safety outcomes and dividing them by a chosen exposure is the simplest and most commonly used method for comparing road safety performance of countries. Epidemiologists often insist in the necessity to account for the demography by applying Standardized Mortality Ratio (SMR), but this approach is rarely used in road safety analysis. Epidemiologists insists that standardization is necessary when comparing several populations that differ with respect to age (and/ or gender), because age and gender have such a powerful influence on health risk. Despite the recent evidence of some epidemiological studies that such indirect standardization is inappropriate for small area comparisons (not necessarily in terms of area, or population size), since SMRs for different geographic areas have different denominators ([Julious et al., 2001](#page-4-0)), this is not a major obstacle for an analysis that includes regions, because fairly similar geographic units are usually subject to assessment.
+
+The risk faced by people in road traffic is not equal for men and women, and the degree of risk also varies significantly with age ([Massie et al., 1994; Evans, 2001](#page-4-0)). Given the demographical differences between sub-national units, it is straightforward to apply the sex–age standardization to road injury rates. The following formula is then used to calculate the SMR of a particular geographical unit (country, region):
+
+$$SMR_i = \frac{Y_i}{Y_i^*}$$
+
+where Yi is the observed number of road injuries in the unit i; Y<sup>i</sup> is the expected number of road injuries in the same unit i.
+
+$$Y_i^* = \sum_{jk} \tau_{jk} \cdot N_{ijk}$$
+
+where sjk, is the standardized injury rate of the age–sex group j, k; Nijk is the population count of this group in the geographical unit i.
+
+Comprehensive set of analyses unveiled that the demography accounts for up to 10% of the variance in road mortality registered within regions of some EU countries. The effect of population structure is usually insignificant and seems to be more relevant in larger countries such as Germany or Spain [\(Eksler, 2007](#page-4-0)).
+
+The concept of standardized ratios could be applied for all types of injury and indeed combined with different measures of exposure. However it has some limitations as the events under consideration are scarce and subjected to randomness. Given that the variance in rates is proportional to the square root of the mean, there will be high sampling variability for the small area units. To overcome this variability one can carry out smoothing of the raw rates via hierarchical modelling. This approach can be justified in a likelihood random effects context, or via a minimum mean squared error argument and it is now exclusively applied from a fully Bayesian perspective. The approach is more flexible in adapting to each unique situation, more efficient in using all available evidence and more useful in providing relevant quantitative arguments, than traditional methods [\(Spiegelhalter et al., 2004](#page-5-0)).
+
+Crash injuries, where the crash injury count is denoted Yi, expected number of injuries k<sup>i</sup> and the exposure (number of inhabitants or traffic volume in MVKMs) Ei are modelled assuming the data to be Poisson distributed:
+
+$$Y_i \sim Poisson(\lambda_i)$$
+
+This model can be rewritten in terms of rates rather than counts as:
+
+$$Y_i \sim Poisson(\theta_i E_i)$$
+
+where h<sup>i</sup> is the crash injury rate in area i and Ei is the exposure in the area i, here either the number of registered population of area i, or the estimated number of kilometers travelled by motorized vehicles within the area i. The k<sup>i</sup> = hiEi and the log(Ei) are treated as known offset terms. The maximum likelihood estimates h<sup>i</sup> = Yi/Ei of this classical model assumed in many disease mapping studies correspond to standardized ratios. These ratios would be highly unstable due to the use of sparse character of the counts modelled. In the generalized linear model the h<sup>i</sup> for each area is a function of covariates and parameters indicating the association between the covariates and the rate. This model can be extended to form a generalized mixed linear model incorporating a random effect within hi. The modelling is implemented for counts (Yi), assuming that the response Yi's given a vector m of random effects are conditionally independent.
+
+$$\lambda_i | v \sim \text{Poisson}(\theta_i^v E_i)$$
+
+hm <sup>i</sup> represents the expected rate of Yi/Ei given all the random effects. The log risk is modelled as:
+
+$$\log(\theta_i^{\nu}) = \alpha + \boldsymbol{X}_i \boldsymbol{\beta} + \nu_i$$
+
+where a is a fixed effect, X<sup>i</sup> represents a vector of explanatory variables (if considering an ecological model), b a vector of fixed effect parameters, m<sup>i</sup> is the unstructured heterogeneity (error) known also as random effects, therefore, this kind of model is commonly known as a mixture model where fixed and random effects are combined (mixed) together. The exp(mi)'s represent local area crash (injury) ratios adjusted for the explanatory variables. If m<sup>i</sup> is drawn from the zero mean normal distribution m = N(0, r<sup>2</sup> ), where r<sup>2</sup> is the variance parameter, the model takes on a pretty standard mixed form, with only r having to be estimated during the model fitting procedure. A prior gamma distribution Gamma (0.5, 0.0005) is assumed for the precision equal to the inverse variance.
+
+The application of the full Bayes modelling can be demonstrated by the example of a Bayesian analysis of road fatality risk at municipality level in Belgium over the period 2001–2006 [\(Eksler and](#page-4-0) [Lassarre, 2008\)](#page-4-0). Fatalities per vehicular travel in terms of motor vehicle kilometres were used here as the measure of road safety performance. The full Bayes spatio-temporal model has been run, allowing to account for the structure in underlying crash mechanisms distribution, resulting in a smoothed representation of fatal road injury risk distribution across the country. The model had a following form:
+
+$$\log(\theta_{ij}^{v}) = \alpha + \beta \cdot X_{ij} + v_i + (\varphi + \delta_i)t_j$$
+
+where Yij is the observed number of road fatalities for the ith area, (i = 1, ..., N), and the jth year, (j = 1, ..., T), a the constant term, xij the covariate for the ith area, in the jth year, b the regression coefficient, m<sup>i</sup> the total heterogeneity of the intercept (consisting of Vi the unstructured heterogeneity and Ui the spatially structured heterogeneity), u the mean linear time trend over all areas, tj the year j, and d<sup>i</sup> spatial structured heterogeneity of the time trend.
+
+It is possible to map the Bayes relative risk as the exponential of various random effects. The temporal trend estimate expressed as the 1 exp(di) could be mapped to provide an idea about the distribution of the trend in fatality risk across the country. The area specific time effect consists here again of the unstructured and structured component. In Fig. 1, the structured component is mapped only, as to highlight the underlying structure in road risk trend. When using the estimated vehicular travel as the exposure of risk, the effect of safe agglomeration when measured by road mortality disappears and the single spots are no more visible on the map. The nests of municipalities with similar trends appear, in most cases following the border of hierarchically superior regions. The latter allow a judgement to be made about the effectiveness of regional road safety policies in the country. The gradient appearing in the map of the trend in fatality risk points to the
+
+![](_page_3_Figure_12.jpeg)
+
+Fig. 1. Structured part of Bayes Relative Risks (BRR) and of the relative temporal trend estimates for Belgian municipalities (2000–2005).
+
+<span id="page-4-0"></span>north–south division of country in terms of reduction, which was in general very high in the Northern part of the country (Flanders) and much smaller in the Southern part of the country (Wallonia). This may point to different effectiveness of road safety policies in the two regions.
+
+When aiming at the comparison of risk levels, or providing full understanding on the distribution of risk and its trends, a direct standardization of risk rates could be useful. It is possible to standardize by a large number of variables depending on the exposure considered and explanation sought. For example, when analyzing mortality rates, population density could be used as suggested by numerous authors (e.g. Orselli, 2003; Baker et al., 1987 and Chapelon 2002). These authors identified an almost log linear relationship between the road mortality and population density at the level of countries and regions. The direct standardization by population density reduces the variance of mortality rates significantly. Eksler (2009) estimated that for different EU countries, on average 60% of the variance of road mortality comes from the sub-national differences in population density. The remaining difficulty is to correctly interpret rates standardized by explanatory factors such as population density and provide relevant recommendations for policy making, since some factors remains abstract and not directly linked with measures at the scope of policy makers.
+
+# 4. Discussion and conclusions
+
+There are two basic reasons for comparing safety performance of sub-national jurisdictions. In the first place, a ranking of relative performance of each are very useful for comparison within countries. To ensure a meaningful benchmarking process, factors that could enable safety practitioners to achieve similar safety improvements need to be included within the ranking process. This might be done by developing a model of safety outcomes that includes these factors. The second reason is to provide better understanding of the factors affecting safety improvement, so that safety practitioners can design more effective programmes. This requires greater focus on understanding how the effects of programmes are modified by the nature of the safety problems faced by each area. Lessons can not only be learned from comparison between areas within countries, but also from comparison between similar areas in different countries. This can probably be more effectively achieved by case studies comparing small groups of areas, than by attempting to model a wide range of areas. Evaluation of road safety performance at local territorial level requires an application of good measures of safety performance and of appropriate analytical tools. Most notably, the analysis should be based on fatal and serious injury figures and the application of robust statistical techniques shall be assured.
+
+The methods described in this paper are purely descriptive and cannot fully explain distribution of risk and of its trend at local territorial level. A direct standardization by explanatory factors may be necessary, but the choice of appropriate factors remains a difficult task. Analyses making use of highly sophisticated statistical techniques could bring new impetus to the work of road safety practitioners and policymakers, but their impact could be limited by the fact that the results of statistical modelling could be difficult to communicate to general public.
+
+The analysis of local area road safety data should be viewed as a complementary approach to local road crash data analysis. Recent advances and increased popularity of modern geographic information system applications made it possible to regularly analyse crash data in respect to road network leading to the identification of high risk sections. Such analysis is a common part of network safety management and a crucial tool for road administrators. Its benefits are concentrated around infrastructure improvements, while the benefits of local area analysis could potentially point to other target areas for safety improvements.
+
+When benchmarking the performance of local entities, the trend is preferred above the level, which is likely more sensitive to various structural factors attributable to local territories. The benchmark of the trend (progress in improving road safety) is also more appropriate measure in respect to policymakers' accountability. Benchmarking road safety performance at local territorial level has a great potential for road safety improvements. The methods and tools for such benchmarking have now become available and road safety authorities shall be encouraged to apply them alongside with traditional approaches.
+
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+- Wegman, F., Commandeur, J., Doveh, E., Eksler, V., Gitelman, V., Hakker, S., Lynam, D., Oppe, S., 2008. SUNflowerNext: towards a Composite Road Safety Performance Index. SWOV Institute for Road Safety Research, Leidschendam, the Netherlands.

Zotero/001_artiklid/Road Safety Indicators/elbasyounyapplicationgeneralizedlinkfunctions2010.md

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+---
+category: literaturenote
+citekey: elbasyounyapplicationgeneralizedlinkfunctions2010
+title: Application of generalized link functions in developing accident prediction models
+authors: "El-Basyouny, Karim; Sayed, Tarek"
+year: 2010
+date: 2010-00-00 2010
+doi: 10.1016/j.ssci.2009.09.007
+publication: Safety Science
+url: "https://doi.org/10.1016/j.ssci.2009.09.007"
+zotero_key: FDHG26KS
+zotero_storage: 5EWGTQW7
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "El-Basyouny, Karim"
+status: converted
+---
+![](_page_0_Picture_1.jpeg)
+
+Contents lists available at [ScienceDirect](http://www.sciencedirect.com/science/journal/09257535)
+
+# Safety Science
+
+![](_page_0_Picture_4.jpeg)
+
+![](_page_0_Picture_5.jpeg)
+
+# Application of generalized link functions in developing accident prediction models
+
+Karim El-Basyouny \*, Tarek Sayed <sup>1</sup>
+
+Dept. of Civil Engineering, University of British Columbia, Vancouver, BC, Canada V6T 1Z4
+
+#### article info
+
+Article history: Received 29 September 2008 Received in revised form 8 September 2009 Accepted 16 September 2009
+
+Keywords: Canonical link Full Bayes estimation Generalized link Markov Chain Monte Carlo Poisson–gamma hierarchy
+
+#### abstract
+
+The Bayesian Poisson–Gamma hierarchy, leading to the negative binomial distribution, has been the standard practice in developing accident prediction models. To linearize the relationship connecting the mean of the negative binomial distribution to relevant covariates, a canonical log link has traditionally been used. Typically, little information is available regarding the choice of a particular link. To avoid link misspecification, it is proposed to nest the canonical log link model within a generalized link family and subsequently use the full Bayes method for parameter estimation, performance evaluation and inference. The proposed approach was applied to a sample of accident and traffic volume data corresponding to 99 intersections in the city of Edmonton, Alberta. The results showed that both the generalized link model and the traditional canonical link model provided adequate fit to the data. However, the Bayes factor provided a clear statistical support for the use of the generalized link approach. A procedure for link validation is also described. It allows the users (e.g., road authorities) to consider the changes in predicted accidents that will result if a generalized link is used instead of a canonical link. If a certain maximal change is tolerated, the canonical link can be used to analyze the data; otherwise the generalized link is worth the extra efforts and should be adopted. When compared with the traditional approach, the generalized link model was found to predict a lower number of accidents whenever there is a heavy traffic at the major approach, especially if combined with light flow on the minor approach. The paper concludes by identifying out areas for further research.
+
+> Crown Copyright -2009 Published by Elsevier Ltd. All rights reserved.
+
+#### 1. Introduction
+
+The application of accident prediction models (APMs) in assessing the safety of a road entity (intersection, road segment, etc.) has become a standard practice among safety researchers and practitioners. An APM is a mathematical model that relates the expected accident frequency at a road entity to the various traffic and geometric characteristics of that entity. Accident prediction models have several road safety applications such as: evaluating the safety of various road facilities, identifying and ranking accident prone locations and evaluating the effectiveness of road safety improvement measures ([Sawalha and Sayed, 2006](#page-6-0)).
+
+Current practice utilizes the negative binomial (NB) model, which results from a Poisson–Gamma hierarchy, to develop APMs. The log function (canonical link) is usually used to connect the random (accidents) and systematic (traffic and geometric characteristics) components of the NB model to produce a linear predictor. Nevertheless, there is often no or little information available concerning the appropriate link to use in a given application. An improper choice of link may result in a link misspecification leading to substantial bias in the model coefficients and the mean response estimates [\(Czado and Munk, 2000; Czado and Raftery,](#page-6-0) [2006;](#page-6-0) and the references therein). To avoid this problem, link families have been considered by [Pregibon \(1980\)](#page-6-0) and [Czado \(1992\).](#page-6-0) Such families generalize the canonical link through the use of an extra parameter h > 0 characterizing the generalized link. The basic idea has been to embed the canonical log link of the NB model, which corresponds to the choice h = 1, in a wide parametric class of links and allow for a data selected choice of the link function.
+
+This paper proposes that generalized links are considered while developing APMs. If the canonical link is validated against the generalized link, then it can be used, otherwise the generalized link is to be adopted. The proposed approach is applied to a sample of accident and traffic volume data corresponding to 99 intersections in the city of Edmonton, Alberta. The objective is to compare the generalized and canonical link functions with respect to accident prediction. The statistical software WinBUGS [\(Lunn et al., 2000\)](#page-6-0), which provides MCMC sampling for a variety of Bayes models, was used in the analysis.
+
+The rest of the paper is organized as follows: Section [2](#page-1-0) describes previous work. A family of generalized links is introduced in Section [3,](#page-1-0) where the issues of link misspecification and validation are discussed. Section [4](#page-2-0) describes the methodology used for
+
+<sup>\*</sup> Corresponding author. Tel.: +1 604 716 4470.
+
+E-mail addresses: [basyouny@civil.ubc.ca](mailto:basyouny@civil.ubc.ca) (K. El-Basyouny), [tsayed@civil.ubc.ca](mailto:tsayed@civil.ubc.ca) (T. Sayed).
+
+<sup>1</sup> Tel.: +1 604 822 4379.
+
+<span id="page-1-0"></span>estimating the models as well as goodness of fit measures. The data set and the model used in the analysis are described in Section [5.](#page-3-0) The results are presented in Section [6](#page-4-0) and are discussed in Section [7](#page-5-0). Section [8](#page-5-0) presents a summary and conclusions.
+
+#### 2. Previous work
+
+Some of the most commonly applied statistical models to accident data include: binomial, Poisson, Poisson–gamma (negative binomial), Zero-Inflated Poisson (ZIP), Zero-Inflated Negative Binomial (ZINB), and multinomial probability models [\(Lord et al., 2005\)](#page-6-0). They showed that the Poisson and NB models serve as statistical approximations to the accident process, but since over-dispersion is exhibited in most accident data the APM models based on NB are usually preferred over Poisson regression models.
+
+Let Y be the random variable that represents the accident frequency at a given location during a specific time period, and let y be a certain realization of Y. The mean of Y, denoted by K, is itself a random variable. For K = k, Y is Poisson distributed with parameter k. It is the usual practice to assume that the distribution of K can be described by a gamma probability density function with shape parameter j and scale parameter j/l. Then, the distribution of Y is negative binomial with a mean l and variance l + l<sup>2</sup> /j.
+
+Several other distributions were proposed for developing APMs. For instance, assuming a normal distribution for K leads to the Poisson-lognormal model. Since the lognormal tails are asymptotically heavier than those of the Gamma distribution [\(Kim et al.,](#page-6-0) [2002](#page-6-0)), the Poisson–lognormal is a good candidate for modeling accident rates in the presence of outliers. [Lord et al. \(2008\)](#page-6-0) used the Conway–Maxwell–Poisson distribution to develop APMs. Such a distribution is a generalization of the Poisson that can cope with both over- and under-dispersion. They found that the generalized linear models based on the Conway–Maxwell–Poisson distribution perform as well as NB models in terms of goodness of fit and predictive performance.
+
+Recently, researchers have tried to address a problem arising from the ''excess" zeroes in accident data, by applying zero-inflated probability models such as ZIP and ZINB. The models assume that a dual-state process ''safe" and ''unsafe" is responsible for generating the accident data. The general consensus indicated an improved fit to data compared to the regular Poisson and NB models. [Lord et al.](#page-6-0) [\(2005\)](#page-6-0) criticized the dual-state approach and argued that ''excess" zeroes arise from a combination of low exposure, high heterogeneity and sites categorized as high risk; inappropriate selection of time/space scales; under-reporting; and/or omitting important covariates. They recommended that a careful selection of the time/space scales for analysis, including an improved set of explanatory variables and/or unobserved heterogeneity effects in count regression models, or applying small area statistical methods (for data characterized by low exposure) represent the most defensible modeling approaches for datasets with a preponderance of zeros.
+
+Developing APMs using data characterized by a low sample mean is problematic, especially if combined with a small sample size due to the expensive costs of collecting accident data and other relevant variables. The low mean problem has been studied in the traffic safety literature, see [Maher and Summersgill \(1996\),](#page-6-0) who showed how such a problem affects the goodness of fit of APMs, [Wood \(2002\),](#page-6-0) who proposed a method to test the fit of APMs developed using data exhibiting a low mean, and [Lord \(2006\)](#page-6-0), who confirmed that a low sample mean combined with a small sample size can seriously affect the estimation of the dispersion parameter and undermine common analyses performed in highway safety.
+
+The majority of APMs were developed using a NB model with a fixed dispersion parameter. Such an assumption was challenged and various dispersion parameter relationships were examined ([El-Basyouny and Sayed, 2006](#page-6-0)). In particular, [Mitra and Washing](#page-6-0)[ton \(2007\)](#page-6-0) indicated that the modeling of the dispersion parameter depends on how the mean structure is modeled. It appears that extra-variation is a function of covariates when the mean structure is poorly specified and suffers from omitted variables. In contrast, when sufficient explanatory variables are used to model the mean extra-Poisson variation is not significantly related to these variables.
+
+Let Xj, j = 1, ... , p, represent the independent variables (e.g., traffic flow and other site characteristics). The log function, which is the canonical link for the NB distribution, is then used to relate the mean l to the covariates
+
+$$ln(\mu) = \beta_0 + \beta_1 X_1 + \dots + \beta_p X_p. \tag{1}$$
+
+The functional form in Eq. (1) has been extensively reviewed [\(Miaou](#page-6-0) [and Lord, 2003](#page-6-0)). The most common functional form used for developing APMs for road intersections is
+
+$$ln(\mu) = ln(\alpha_0) + \alpha_1 \, ln(V_{\it mj}) + \alpha_2 \, ln(V_{\it mi}) + \sum_{j=1}^{\it m} \gamma_j X_j, \eqno(2)$$
+
+where Vmj is the annual average daily traffic (AADT) on the major approach, Vmi is the AADT on the minor approach, the Xj are covariates representing certain traffic and geometric characteristics, and a0, a1, a2, c1, ... , c<sup>p</sup> are model parameters. The corresponding form used for developing APMs for road segments is
+
+$$\ln(\mu) = \ln(\alpha_0) + \alpha_1 \ln(L) + \alpha_2 \ln(V) + \sum_{i=1}^{m} \gamma_i X_i, \tag{3}$$
+
+where L is segment length and V is the annual average daily traffic (AADT). [Miaou and Lord \(2003\)](#page-6-0) examined the mathematical limitations of the various functional forms, particularly their properties at the boundaries. The authors demonstrated that, for a given data set, a large number of plausible functional forms with almost the same overall statistical goodness of fit are possible. Furthermore, they introduced an alternative class of logical formulations that may enable a richer interpretation of the data.
+
+Other methods for developing APMs that were recently researched include: the application of the multivariate Poisson-lognormal (MVPLN) to model accident count data at different levels of severity ([El-Basyouny and Sayed, 2009a](#page-6-0)), the use of a two-state Markov Switching model [\(Malyshkina et al., 2009\)](#page-6-0) to analyze collision frequencies, and the use of models with random parameters ([El-Basyouny and Sayed, 2009b\)](#page-6-0).
+
+#### 3. Generalized links
+
+As we have seen above, previous work in the traffic safety literature has investigated many aspects of APMs, except the link function. Canonical links in generalized linear models, such as the log link in NB regression, are used to linearize the relationship between the predicted value and the predictors. They are popular among practitioners as they provide maximum information and simple interpretation of the regression parameters ([McCullagh](#page-6-0) [and Nelder, 1989\)](#page-6-0). Yet, a canonical link may not furnish the best fit available for a given data set.
+
+It has been shown in the statistical literature that the use of an inappropriate link results in a link misspecification, which might lead to a substantial bias in the model estimates ([Czado and Munk,](#page-6-0) [2000; Czado and Raftery, 2006](#page-6-0); and the references therein). Noting that the choice of the link function is often made arbitrarily, recent research has: (i) permitted the data to estimate the link function by incorporating it as an unknown in the model [\(Mallick and Gelfand,](#page-6-0) [1994\)](#page-6-0), (ii) described full Bayesian inference for generalized linear models where uncertainty exists about the structure of the linear <span id="page-2-0"></span>predictor, the linear parameters and the link function [\(Ntzoufras](#page-6-0) [et al., 2003\)](#page-6-0), and (iii) used a non-parametric approach to estimate a generalized additive model with unknown link function ([Horowitz and Mammen, 2007](#page-6-0)).
+
+To guard against link misspecification, the canonical link is usually embedded into a wide class of links. One such useful family of link functions is given by [Czado \(1997\), Czado and Raftery \(2006\)](#page-6-0)
+
+$$\mu(\eta, \theta) = \exp\{[(1 + \eta)^{\theta} - 1]/\theta\}; \quad \eta \geqslant 0, \theta > 0,$$
+ (4)
+
+where g = Xb, X = (1, X1, ... , Xp) and b ¼ ðb0; b1; - ; bpÞ 0 . In the generalized linear models terminology, Eq. (4) is actually an inverse link function corresponding to the following (forward) link function
+
+$$g(\mu, \theta) = (\theta \ln(\mu) + 1)^{1/\theta} - 1; \quad \mu \ge 0, \theta > 0.$$
+ (5)
+
+Regarding notation, the simplified notation lh will be used instead of l(g, h) unless it is needed to stress the dependence of l on g. Note also that as h increases away from 1, lh increases away from l<sup>1</sup> on one hand, while the scale of the regression parameters b<sup>i</sup> is reduced on the other hand as a tradeoff in order to adequately fit the data. A similar tradeoff (albeit reversed) occurs as h decreases away from 1. Thereby, the notation bh will be used occasionally to highlight the fact that the regression parameters are on different scales for different link functions. Also, the notation g(b) will be used sometimes to emphasize the dependence of the linear predictor g on b.
+
+Let M<sup>h</sup> denote the NB APM based on g(l, h) and note that the canonical log link is the special case h = 1, corresponding to M1. Note also that M<sup>h</sup> is a generalized linear model when h is known, while this is no longer true if h, b and j are jointly estimated by the data.
+
+Eq. (4) defines a family of power transformations to impose linearity, i.e., to make the linear model more appropriate to the data in the sense that the transformation is approximately linear over the range of observations. To illustrate, let us consider the consequences of fitting a model with the canonical link g(l, 1) (=ln (l)) when the correct but unknown link function is indeed g(l, h ). Using a first order Taylor series expansion about the canonical link, we have the approximate equation
+
+$$g(\mu, \theta^*) \cong \ln(\mu) + (\theta^* - 1)[\ln(\mu) - \ln(\ln(\mu) + 1)(\ln(\mu) + 1)].$$
+ (6)
+
+The correct link function g(l, h ) = g = Xb may thus be approximated by
+
+$$ln(\mu) = X\beta + Z\delta,$$
+ (7)
+
+with an obvious definition for Z and d = (h 1). The term Zd, which describes the local differences between the two link functions, represents the misspecification of the model using the wrong link function.
+
+We propose to test M<sup>1</sup> against M<sup>h</sup> so that the traditional model M<sup>1</sup> is used only if supported by the data, i.e., if the hypothesis h = 1 is plausible. Otherwise M<sup>h</sup> should be adopted. Such a testing problem is discussed in the following subsection.
+
+## 3.1. Link validation
+
+The usual practice of treating model selection (M<sup>1</sup> vs. Mh) as a testing problem of a point null hypothesis h = 1 was criticized by many researchers [\(Czado and Munk, 2000](#page-6-0)). Alternatively, they proposed a hypothesis of the form
+
+$$H_0: \theta \notin [1 - \theta_l, 1 + \theta_u]$$
+ vs.  $H_1: \theta \in [1 - \theta_l, 1 + \theta_u],$  (8)
+
+where (1 hl, 1+ hu) is a neighborhood of h within which the canonical link is validated. Eq. (8) represents the validation problem and its converse (H<sup>1</sup> vs. H0) represents the discrimination problem. The following p-value was then derived
+
+$$p(\hat{\theta}, s, \theta_l, \theta_u) = \Phi\{(\hat{\theta} - 1 - \theta_u)/s\} - \Phi\{-(\hat{\theta} - 1 + \theta_l)/s\}, \tag{9}$$
+
+where ^h and s denote the maximum likelihood estimate of h and its standard deviation. (For a full Bayes estimator, Eq. (9) can still be used to approximate the p-value due to the asymptotic normality of the posterior distribution.)
+
+The bounds 1 h<sup>l</sup> and 1 + h<sup>u</sup> depend on the APM and the interests of the practitioner. To fix ideas, assume that data are available on yi and xi = (xi1, ... , xip) for a sample of n locations (i = 1, ... , n). In the NB APM context, an appropriate discrepancy measure between the two links g(l, h) and g(l, 1) can be defined as the maximal change in the predicted accidents when switching from the canonical link to the generalized link
+
+$$\Delta(\theta) = \max_{i=1,\dots,n} |\mu(\eta_i(\beta_\theta), \theta) - \mu(\eta_i(\beta_1), 1)|. \tag{10}$$
+
+The next step is to determine a tolerance bound D<sup>0</sup> such that testing
+
+$$H_0: \Delta(\theta) > \Delta_0$$
+ vs.  $H_1: \Delta(\theta) \leq \Delta_0$ , (11)
+
+is equivalent to (8). Since the criterion D(h) is convex with a minimum at h = 1, the bounds 1 h<sup>l</sup> and 1 + h<sup>u</sup> are uniquely determined by solving h = D<sup>1</sup> (D0).
+
+For a given data set, [Czado and Munk \(2000\)](#page-6-0) indicated that the two-dimensional surface p(...,hl, hu) is reduced to the one-dimensional curve p(h.,., D0), where the level sets a = p give the asymptotic minimal bound D<sup>0</sup> for which H<sup>0</sup> can be rejected at level a as well as the maximal bound for which H<sup>1</sup> can be rejected by the discrimination test at level 1 a.
+
+The performance of M<sup>1</sup> vs. M<sup>h</sup> can be also assessed by way of simulation. Such an assessment will have to be based on criteria similar to (10), e.g., mean absolute deviation (difference) or mean squared deviation, since the regression parameters b<sup>1</sup> and bh are on different scales and cannot be directly compared.
+
+#### 4. Methodology
+
+The joint maximum likelihood estimation of the parameters h, b and j of the NB APM based on the generalized link g(l, h) is outlined in [Czado and Munk \(2000\)](#page-6-0). The Empirical Bayes (EB) estimates may then be used in subsequent applications of APMs. Alternatively, the full Bayes estimates can be obtained using the MCMC method. For a discussion of ''EB versus full Bayes", the reader is referred to ([Miaou and Lord, 2003; Mitra and Washington,](#page-6-0) [2007\)](#page-6-0).
+
+Subsection 4.1 describes the full Bayes approach that was used for model specification, parameter estimation and performance evaluation in this paper, whereas Subsection [4.2](#page-3-0) is devoted to goodness of fit measures.
+
+#### 4.1. Full Bayes estimation
+
+The posterior distributions needed in the full Bayes approach were obtained using MCMC sampling of the NB APM in Eq. [\(1\)](#page-1-0) by means of the statistical software WinBUGS.
+
+MCMC methods were used to repeatedly sample from the joint posterior distribution of the parameters h, b and j. These techniques generate sequences (chains) of random points (h(t) , b(t) , j(t) t = 1, ... , T (iterations), whose distributions converge to the target posterior distributions. A sub sample (h(t) , b(t) , j(t) ), t = 1, ... , T<sup>0</sup> < T, was used to monitor convergence and was then excluded as a burn-in sample. The remaining iterations (t = T<sup>0</sup> + 1, ... , T) were used for parameter estimation, performance evaluation and inference.
+
+Monitoring convergence is important because it ensures that the posterior distribution has been ''found" and thereby indicates when sampling of parameters should begin. A common methodology to check convergence is by tracking two or more parallel <span id="page-3-0"></span>chains with diverse starting values to ensure full coverage of the sample space of the parameters. Convergence of multiple chains was assessed using the Gelman–Rubin convergence statistic as modified by [Brooks and Gelman \(1998\).](#page-6-0) For a given parameter monitored over J chains, the Brooks–Gelman–Rubin (BGR) statistic is
+
+$$BGR = I_P/I_U, (12)$$
+
+where IP is the length of the 100(1 a)% interval for the parameter based on the pooled TJ samples and IU is the mean of the J withinchain interval lengths. A value under 1.2 of the BGR statistic indicates convergence. The BGR diagnostics are available in WinBUGS.
+
+To obtain the full Bayes estimates the user is required to specify prior distributions for the parameters. In the absence of sufficient prior knowledge of the distributions for individual parameters on the risk factors, uninformative proper prior distributions are usually specified ([Miaou and Lord, 2003; Mitra and Washington,](#page-6-0) [2007](#page-6-0)).
+
+Under M1, it is usually assumed that j gamma (0.001, 0.001) and b<sup>j</sup> N(0, 1002 ), j = 0, 1, ... , p. Such priors represent proper distributions that are flat; hence the term uninformative (also called diffused) proper priors.
+
+Under Mh, the same uninformative prior was used for j. A truncated normal distribution is then used as a proper prior for h, namely, h N(1, r<sup>2</sup> <sup>h</sup> ), 0 < h < 1, as it seems natural to have the prior distribution of the link parameter centered at (or symmetric about) the canonical log link ([Czado and Raftery, 2006](#page-6-0)). It can be verified that, the symmetry of these prior choices requires small standard deviations (rh 0.3, or smaller). The authors considered rh = 1, 2, 4 and noted that link values (h) larger than 1 are favored when these parameter values are used. Alternatively, Pareto priors with high density at small values of h and monotonically decreasing tails were also considered, as the generalized link function in Eq. [\(4\)](#page-2-0) changes most rapidly for small values of h.
+
+The following development is along the lines of [Czado and Raf](#page-6-0)[tery \(2006\),](#page-6-0) who advocated a reference proper prior distribution for bh. These priors vary with h and assume little prior information. Let zh<sup>i</sup> = ln(lhi) + (yi lhi)/lh<sup>i</sup> denote the adjusted dependent variable, xh<sup>i</sup> = j lhi/(j + lhi) denote its weight and define the weighted summary statistics:
+
+$$\bar{z}_{\theta} = \sum_{i=1}^{n} \omega_{\theta i} z_{\theta i} / \sum_{i=1}^{n} \omega_{\theta i}, 
+s_{\theta 0}^{2} = \sum_{i=1}^{n} \omega_{\theta i} (z_{\theta i} - \bar{z}_{\theta})^{2} / \sum_{i=1}^{n} \omega_{\theta i}, \quad \bar{x}_{\theta j} = \sum_{i=1}^{n} \omega_{\theta i} x_{i j} / \sum_{i=1}^{n} \omega_{\theta i}, 
+s_{\theta j}^{2} = \sum_{i=1}^{n} \omega_{\theta i} (x_{i j} - \bar{x}_{\theta j})^{2} / \sum_{i=1}^{n} \omega_{\theta i}, \quad j = 1, \dots, p.$$
+(13)
+
+For the (p + 1)-dimensional regression coefficient vector, including an intercept, it is assumed that bh Np+1(th, Rh), where the mean vector is given by th ¼ ðzh; 0; - ; 0Þ <sup>0</sup> and the covariance matrix is given by
+
+$$\Sigma_{\theta} = s_{\theta 0}^{2} \begin{pmatrix} 1 + \sum_{j=1}^{p} \bar{\chi}_{\theta j}^{2} / s_{\theta j}^{2} & -\bar{\chi}_{\theta 1} / s_{\theta 1}^{2} & \cdots & -\bar{\chi}_{\theta p} / s_{\theta p}^{2} \\ -\bar{\chi}_{\theta 1} / s_{\theta 1}^{2} & 1 / s_{\theta 1}^{2} & \cdots & 0 \\ \cdots & \cdots & \cdots & \cdots \\ -\bar{\chi}_{\theta p} / s_{\theta p}^{2} & 0 & \cdots & 1 / s_{\theta p}^{2} \end{pmatrix}.$$
+(14)
+
+# 4.2. Goodness of fit measures
+
+Let D denote the un-standardized deviance of the negative binomial model. [Spiegelhalter et al. \(2002\)](#page-6-0) proposed the deviance information criteria (DIC) as a measure of model complexity and fit
+
+$$DIC = \bar{D} + p_D; \quad p_D = \bar{D} - \hat{D}, \tag{15}$$
+
+where D is the posterior mean of D, D^ is the point estimate obtained by substituting the posterior means of (li, j) in D and pD is a measure of model complexity estimating the effective number of parameters. As a goodness of fit measure, DIC is a Bayesian generalization of Akaike's information criteria (AIC) that is penalizing larger parameter models. According to the WinBUGS' DIC guide ([Spiegelhalter et al., 2005](#page-6-0)), it is difficult to determine what would constitute an important difference in DIC. Very roughly, differences of more than 10 might definitely rule out the model with the higher DIC. Differences between 5 and 10 are substantial. If the difference in DIC is less than 5, and the models make very different inferences, then it could be misleading just to report the model with the lowest DIC.
+
+The Bayes factor Bh<sup>1</sup> was also employed to assess the improvement in fit over a NB APM with a canonical link (M1) when a generalized link (Mh) is used. Following [Czado and Raftery \(2006\),](#page-6-0) Bh<sup>1</sup> is approximated by
+
+$$2 \ln(B_{\theta 1}) \approx D(M_1) - D(M_{\theta}) + (E_{\theta} - E_1),$$
+ (16)
+
+where D(M1) and D(Mh) are obtained by substituting the corresponding posterior means of (li, j) in D. The computation of E<sup>h</sup> in Eq. (16) requires the maximum likelihood estimates of the parameters and their covariance matrix in addition to the prior means and covariance matrices specified for j and bh. E<sup>1</sup> is the corresponding function under the canonical link. The details are given in [\(Cza](#page-6-0)[do and Raftery, 2006\)](#page-6-0). According to [Raftery \(1996\)](#page-6-0), M<sup>1</sup> is supported if 2 ln(Bh1) is less than 0, otherwise M<sup>h</sup> is supported; with the range 0–2.2 indicating weak support, 2.2–6 representing positive evidence, 6–10 demonstrating strong evidence and higher values signifying very strong evidence.
+
+Other measures such as the model deviance G<sup>2</sup> and R<sup>2</sup> have been suggested ([Mitra and Washington, 2007\)](#page-6-0). Yet, the G<sup>2</sup> and R<sup>2</sup> measures proposed in their Eqs. (14) and (15) use a Poisson-distributed error structure where the mean is equal to the variance and hence need to be modified to account for the extra-variation ([Wood, 2002\)](#page-6-0). This was not pursued for the following reasons. According to the WinBUGS' DIC guide ([Spiegelhalter et al., 2005\)](#page-6-0), the posterior mean of the deviance (Dbar = G<sup>2</sup> ) should perhaps not really be considered as a measure of fit. The fit might better be measured by deviance evaluated at the parameter of interest (Dhat). As emphasized by [Linde \(2005\)](#page-6-0), the posterior mean of the deviance (Dbar) is more a measure of model 'adequacy'. This is evident since the addition of a covariate might in certain cases increase the Dbar value. On the other hand, the R<sup>2</sup> measure of fit has been criticized in the literature and it has been shown to provide misleading results [\(Miaou et al., 1996](#page-6-0)).
+
+#### 5. Data and model description
+
+A total of 99 signalized intersections in the city of Edmonton were investigated for the purpose of developing accident prediction models relating the safety of urban 4-leg intersections to their traffic flows. This data set was used as a reference group for the evaluation of the City of Edmonton Intersection Safety Camera ([Sayed and de Leur, 2007\)](#page-6-0). The data on accident frequencies and traffic volumes within the intersections were obtained from the city of Edmonton and covered the period from 1997 to 2003.
+
+Average values for the traffic volumes (over the 7 years period) are used to build APMs for predicting the total (aggregate) number of accidents using
+
+$$\eta = \ln(\alpha_0) + \alpha_1 \ln(V_{mj}) + \alpha_2 \ln(V_{mi}).$$
+ (17)
+
+The aggregation is justified on several grounds. For instance, an aggregate APM was found to perform well compared with APMs <span id="page-4-0"></span>developed to handle temporal correlation [\(Lord and Persaud, 2000\)](#page-6-0). Also, the aggregation of accidents over a period of reasonable length helps to avoid confounding effects and such a phenomenon like regression-to-the-mean [\(Cheng and Washington, 2005\)](#page-6-0). A statistical summary of the data is shown in Table 1.
+
+The AADT functional form [\(17\)](#page-3-0) is popular among practitioners and is often preferred over models that include several covariates because it can be easily re-calibrated (Lord et al., 2008; and the references therein). Further, it will be adopted for estimating safety
+
+Table 1 Statistical summary of data set (99 intersections).
+
+|                                 | Minimum | Maximum | Mean   | Standard<br>deviation |  |
+|---------------------------------|---------|---------|--------|-----------------------|--|
+| AADT on minor<br>approach (Vmi) | 2809    | 29,128  | 16,043 | 6564                  |  |
+| AADT on major<br>approach (Vmj) | 5642    | 61,744  | 28,010 | 9705                  |  |
+| Total number of<br>accidents    | 0       | 193     | 70     | 39                    |  |
+
+Table 2 Model statistics.
+
+| Canonical link        | Estimate | Standard<br>deviation |                | 95% Credible intervals |  |  |  |
+|-----------------------|----------|-----------------------|----------------|------------------------|--|--|--|
+| (M1)                  |          |                       | Lower<br>limit | Upper<br>limit         |  |  |  |
+| Intercept             | 8.96     | 1.20                  | 11.28          | 6.64                   |  |  |  |
+| AADT major            | 0.88     | 0.13                  | 0.64           | 1.12                   |  |  |  |
+| AADT minor            | 0.44     | 0.09                  | 0.25           | 0.63                   |  |  |  |
+| j                     | 7.02     | 1.18                  | 4.95           | 9.58                   |  |  |  |
+| DIC                   | 924.87   |                       |                |                        |  |  |  |
+| Generalized link (Mh) |          |                       |                |                        |  |  |  |
+| Intercept             | 3.35     | 0.60                  | 4.41           | 2.25                   |  |  |  |
+| AADT major            | 0.34     | 0.06                  | 0.22           | 0.46                   |  |  |  |
+| AADT minor            | 0.29     | 0.04                  | 0.18           | 0.34                   |  |  |  |
+| j                     | 6.76     | 1.16                  | 4.78           | 9.28                   |  |  |  |
+| h                     | 1.48     | 0.14                  | 1.25           | 1.81                   |  |  |  |
+| DIC                   | 926.96   |                       |                |                        |  |  |  |
+|                       |          |                       |                |                        |  |  |  |
+| Bayes factor (Bh1)    |          |                       |                |                        |  |  |  |
+| 2ln (Bh1)             | 15.11    |                       |                |                        |  |  |  |
+
+performance in the forthcoming highway safety manual (HSM) ([Hughes et al., 2005\)](#page-6-0). It should be noted that AADT models may suffer from omitted variables bias since many non-flow related factors are known to affect accident frequency. Nevertheless, such models are well recognized in the traffic safety literature.
+
+#### 6. Results
+
+This section compares the results of the canonical log link and those of the generalized link function. The results were evaluated in terms of model prediction and goodness of fit.
+
+The posterior summaries in Table 2 were obtained using J = 2 chains, T = 10,000 iterations, T<sup>0</sup> = 5000 burn-in sample in Win-BUGS. The BGR statistics in Eq. [\(12\)](#page-3-0), for the parameters h, b and j were less than 1.2, indicating convergence.
+
+Table 2 summarizes the model parameter estimates and their associated statistics using the canonical and generalized links, respectively. The table shows that the parameter estimates are significant as the 95% credible intervals are bounded away from zero. The coefficients of the major and minor flows are all positive, indicating an increase in the mean accident frequency with traffic flow. The shape parameter j of the negative binomial model is significant, demonstrating the presence of over-dispersion in the data. The credible interval for the parameter h does not straddle 1, signifying the need for a generalized link function.
+
+The DIC statistics (Eq. [\(15\)](#page-3-0)) were 924.87 and 926.96 under M<sup>1</sup> and Mh, respectively, giving a slight advantage to M<sup>1</sup> over Mh. In contrast, the Bayes factor calculation (Eq. [\(16\)](#page-3-0)) produced
+
+$$2\ln(B_{\theta 1}) = 920.7 - 923.7 + (-39.64 + 57.75) = 15.11,$$
+
+providing very strong support for Mh.
+
+In order to validate the canonical model M<sup>1</sup> against Mh, the maximal change discrepancy measure in Eq. [\(10\)](#page-2-0) is adopted. PROC GENMOD in SAS was used, with the inverse and forward link functions in Eqs. [\(4\) and \(5\),](#page-2-0) to compute D(h), h 2 [0.5, 2.5]. The maximal change and p-value curves are portrayed in Figs. 1 and 2, respectively.
+
+The p-curve in [Fig. 2](#page-5-0) shows that using a generalized link will result in a maximal absolute difference of 2.4 in predicted accidents at a = 0.1 compared to a canonical link. A canonical link can be validated at a = 0.1, if one is willing to tolerate a change of 6.3 predicted accidents.
+
+![](_page_4_Figure_18.jpeg)
+
+Fig. 1. Maximal change in predicted accidents when switching from M<sup>1</sup> to Mh.
+
+<span id="page-5-0"></span>![](_page_5_Figure_2.jpeg)
+
+Fig. 2. p-value curve for assessing the maximal change in predicted accidents.
+
+# 7. Discussion
+
+For the current data set, convergence was indicated with 10,000 iterations, of which 5000 were discarded as a burn-in sample. For larger data sets and/or the addition of covariates, a larger number of iterations might be needed to achieve convergence. The user might also consider alternative priors, e.g., gamma (0.1, 0.1) for j, N(0, 102 ), for bj, a truncated normal with mean 1 and larger standard deviation or a Pareto prior for h.
+
+The two models M<sup>h</sup> and M1, may predict very different values depending on the traffic flow data as depicted in Fig. 3, which displays the difference between the two means lh and l<sup>1</sup> at various combinations of traffic flows (10,000–60,000 for the major approach and 5000–30,000 for the minor approach). The response
+
+![](_page_5_Figure_7.jpeg)
+
+Fig. 3. Response surface of differences in predicted accidents (canonical – generalized link functions) by major and minor flows.
+
+surface in Fig. 3 indicates that the difference l<sup>1</sup> lh increases considerably with the major flow. In contrast, it decreases as the minor flow rises (with few exceptions in the right upper corner of the graph). Consequently, the difference l<sup>1</sup> lh is positive and large whenever there is a heavy traffic at the major approach, especially if combined with light traffic at the minor approach. On the other hand, the difference l<sup>1</sup> lh is negative and smallest whenever the opposite holds true.
+
+For the current data set, the results of goodness of fit as measured by DIC seem to be similar under M<sup>h</sup> and M1. However, as pointed out by [O'Hara \(2007\),](#page-6-0) comparisons of DIC from different models may lead to similar results unless DIC is focused on the right part of the model, which is not a straightforward task. Alternatively, the Bayes factor can be used to assess the improvement in fit over M<sup>1</sup> when M<sup>h</sup> is used. In this case the Bayes factor lends strong support to the generalized link model Mh.
+
+On the other hand, link validation has indicated that an absolute difference of 2 predicted accidents is sufficient to discriminate between the two models, but the canonical link can be validated only if an absolute difference of 7 predicted accidents is tolerated. Whether or not a change of 7 predicted accidents is acceptable is entirely up to the practitioner (e.g., road authority). If a change of this magnitude is allowed, the canonical link can be used; otherwise the generalized link should be adopted.
+
+#### 8. Summary and conclusions
+
+The generalized link was employed in association with the traditional negative binomial model to predict the number of accidents at 99 intersections using traffic flows at the major and minor approaches as covariates.
+
+Using DIC as a goodness of fit measure, the NB APM adopting the generalized link was found to fit the data as well as the corresponding model based on the usual canonical log link. In contrast, the Bayes factor provided strong support to the generalized link over the canonical link.
+
+A procedure for link validation was also described. It allows the practitioners (road authorities) to consider the changes in predicted accidents that will result if a generalized link is used instead of a canonical link. If a certain maximal change is tolerated, the <span id="page-6-0"></span>canonical link can be used to analyze the data; otherwise the generalized link is worth the extra efforts and should be adopted.
+
+The two models differ in terms of prediction. Compared with the NB APM based on the canonical log link, the model associated with the generalized link seems to produce lower predictions whenever the major flow is heavy, especially if combined with light flow on the minor approach. It also seems to predict a higher number of accidents when the opposite holds true. The canonical and generalized links may also lead to large differences in the identification and ranking of accident prone locations.
+
+It should be emphasized that erroneous selection of one model over the other can lead to serious consequences. Thereby, it is crucial to assess the goodness of fit of the two models and to validate the generalized link as outlined above. Also, while fitting the generalized link may take longer (in terms of convergence), it is not markedly complicated (in terms of WinBUGS coding) than the canonical link. Finally, whether a specific accident difference (e.g., 7 or more or less) is worth the extra effort is completely up to the user.
+
+It should be noted that these findings maybe be valid to this data set only. In order to generalize the comparison of the two models, it is perhaps necessary to involve other datasets and to carry on a large simulation study considering different data scenarios (different roadway elements, sample sizes, period of time, etc.) for locations with known safety status.
+
+This study can be extended in many directions. For example, a log-normal prior could be used instead of the gamma prior leading to generalized links associated with Poisson log-normal models. Also, a generalized link could be developed to connect the dispersion parameter j to relevant covariates. Other extensions include applying the generalized link approach to other data sets, in order to evaluate its performance over a wide class of traffic environments, and conducting a simulation study as suggested above.
+
+## References
+
+- Brooks, S.P., Gelman, A., 1998. Alternative methods for monitoring convergence of iterative simulations. Journal of Computational and Graphical Statistics 7, 434– 455.
+- Cheng, W., Washington, S.P., 2005. Experimental evaluation of hotspot identification methods. Accident Analysis and Prevention 37, 870–881.
+- Czado, C., Munk, A., 2000. Noncanonical links in generalized linear models when is the effort justified? Journal of Statistical Planning and Inference 87, 317–345.
+- Czado, C., Raftery, A.E., 2006. Choosing the link function and accounting for link uncertainty in generalized linear models using Bayes factors. Statistical Papers 47, 419–442.
+- Czado, C., 1992. On link selection in generalized linear models. In: Fahrmein, L., Francis, B., Gilchrist, R., Tutz, G. (Eds.), Advances in GLIM and Statistical Modeling, Lecture Notes in Statistics, vol. 78. Springer, New York, pp. 60–65.
+- Czado, C., 1997. On selecting parametric link transformation families in generalized linear models. Journal of Statistical Planning and Inference 61, 125–139.
+- El-Basyouny, K., Sayed, T., 2006. Comparison of two negative binomial regression techniques in developing accident prediction models. TRR: Journal of the TRB. 1950, 9–16.
+- El-Basyouny, K., Sayed, T., 2009a. Collision prediction models using multivariate Poisson–lognormal regression. Accidents Analysis and Prevention 41 (4), 820– 828.
+
+- El-Basyouny, K., Sayed, T., 2009b. Accident prediction models with random corridor parameters. Accidents Analysis and Prevention 41 (5), 1118–1123.
+- Horowitz, J.L., Mammen, E., 2007. Rate-optimal estimation for a general class of nonparametric regression models with unknown link functions. Annals of Statistics 35 (6), 2589–2619.
+- Hughes, W., Eccles, K., Harwood, D., Potts, I., Hauer, E., 2005. Development of a highway safety manual. Appendix C: highway safety manual prototype chapter: two-lane highways. NCHRP Web Document 62 (Project 17–18(4)). Washington, DC. [<http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp\\_w62.pdf>](http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_w62.pdf).
+- Kim, H., Sun, D., Tsutakawa, R.K., 2002. Lognormal vs. gamma: extra variations. Biometrical Journal 44 (3), 305–323.
+- Linde, A., 2005. DIC in variable selection. Statistica Neerlandica 59 (1), 45–56.
+- Lord, D., Persaud, B., 2000. Accident prediction models with and without trend: application of the generalized estimating equation. Transportation Research Record 1717, 102–108.
+- Lord, D., 2006. Modeling motor vehicle crashes using Poisson–gamma models: examining the effects of low sample mean values and small sample size on the estimation of the fixed dispersion parameter. Accident Analysis and Prevention 38 (4), 751–766.
+- Lord, D., Guikema, S.D., Geedipally, S.R., 2008. Application of the Conway–Maxwell– Poisson generalized linear model for analyzing motor vehicle crashes. Accident Analysis and Prevention 40, 1123–1134.
+- Lord, D., Washington, S.P., Ivan, J.N., 2005. Poisson, Poisson–gamma and zero inflated regression models of motor vehicle crashes: balancing statistical fit and theory. Accident Analysis and Prevention 37 (1), 35–46.
+- Lunn, D.J., Thomas, A., Best, N., Spiegelhalter, D., 2000. WinBUGS a Bayesian modelling framework: concepts, structure, and extensibility. Statistics and Computing 10, 325–337.
+- Maher, M.J., Summersgill, I., 1996. A comprehensive methodology for the fitting of predictive accident models. Accident Analysis and Prevention 28 (3), 281–296.
+- Mallick, B., Gelfand, A.E., 1994. Generalized linear models with unknown link functions. Biometrika 81 (2), 237–245. Malyshkina, N.V., Mannering, F.L., Tarko, A.P., 2009. Markov switching negative
+- binomial models: an application to vehicle accident frequencies. Accident Analysis and Prevention 41 (2), 217–226.
+- McCullagh, P., Nelder, J.A., 1989. Generalized Linear Models, second ed. Chapman & Hall, London.
+- Miaou, S.P., Lord, D., 2003. Modeling traffic crash-flow relationships for intersections: dispersion parameter, functional form, and Bayes versus empirical Bayes. Transportation Research Record 1840, 31–40.
+- Miaou, S.P., Lu, A., Lum, H.S., 1996. Pitfalls of using R-squared to evaluate goodness of fit of accident prediction models. Transportation Research Record 1542, 6–
+- Mitra, S., Washington, S., 2007. On the nature of over-dispersion in motor vehicle crash prediction models. Accident Analysis and Prevention 39, 459–468.
+- Ntzoufras, I., Dellaportas, P., Forster, J., 2003. Bayesian variable and link determination for generalised linear models. Journal of Statistical Planning and Inference 111, 165–180.
+- O'Hara, B., 2007. Focus on DIC. [<http://www.deepthoughtsandsilliness.blogspot.](http://www.deepthoughtsandsilliness.blogspot.com/2007/12/focus-on-dic.html) [com/2007/12/focus-on-dic.html>,](http://www.deepthoughtsandsilliness.blogspot.com/2007/12/focus-on-dic.html) (accessed May 2008).
+- Pregibon, D., 1980. Goodness of link tests for generalized models. Journal of the Royal Statistical Society C 29, 5–24.
+- Raftery, A.E., 1996. Approximate Bayes factors and accounting for model uncertainty in generalized linear models. Biometrika 83, 251–266.
+- Sawalha, Z., Sayed, T., 2006. Traffic accidents modeling: some statistical issues. Canadian Journal of Civil Engineering 33 (9), 1115–1124.
+- Sayed, T., de Leur, P., 2007. Evaluation of Edmonton's intersections safety camera programs. In: Proceedings of the 2007 Annual meeting of the Transportation Research Board, Washington, DC.
+- Spiegelhalter, D., Thomas, A., Best, N., Lunn, D., 2005. WinBUGS user manual. MRC Biostatistics Unit, Cambridge. [<http://www.mrc-cam.ac.uk/bugs>](http://www.mrc-cam.ac.uk/bugs).
+- Spiegelhalter, D.J., Best, N.G., Carlin, B.P., Van der Linde, A., 2002. Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society B 64, 1–34.
+- Wood, G.R., 2002. Generalised linear accident models and goodness of fit testing. Accident Analysis and Prevention 34 (4), 417–427.

Zotero/001_artiklid/Road Safety Indicators/elbasyounycollisionpredictionmodelsusing2009.md

@@ -0,0 +1,475 @@
+---
+category: literaturenote
+citekey: elbasyounycollisionpredictionmodelsusing2009
+title: Collision prediction models using multivariate Poisson-lognormal regression
+authors: "El-Basyouny, Karim; Sayed, Tarek"
+year: 2009
+date: 2009-00-00 2009
+doi: 10.1016/j.aap.2009.04.005
+publication: "Accident Analysis & Prevention"
+url: "https://doi.org/10.1016/j.aap.2009.04.005"
+zotero_key: 3UW6E3BC
+zotero_storage: Q3W57QTW
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "El-Basyouny, Karim"
+status: converted
+---
+![](_page_0_Picture_1.jpeg)
+
+Contents lists available at [ScienceDirect](http://www.sciencedirect.com/science/journal/00014575)
+
+# Accident Analysis and Prevention
+
+journal homepage: [www.elsevier.com/locate/aap](http://www.elsevier.com/locate/aap)
+
+![](_page_0_Picture_5.jpeg)
+
+# Collision prediction models using multivariate Poisson-lognormal regression
+
+Karim El-Basyouny<sup>∗</sup>, Tarek Sayed<sup>1</sup>
+
+*Dept. of Civil Engineering, University of British Columbia, 2002-6250 Applied Science Lane, Vancouver, BC, Canada V6T 1Z4*
+
+# article info
+
+*Article history:* Received 24 December 2008 Received in revised form 20 March 2009 Accepted 2 April 2009
+
+*Keywords:* Collision prediction models Full Bayes estimation Markov Chain Monte Carlo Multivariate lognormal distribution Multivariate identification of hot spots
+
+# abstract
+
+This paper advocates the use of multivariate Poisson-lognormal (MVPLN) regression to develop models for collision count data. The MVPLN approach presents an opportunity to incorporate the correlations across collision severity levels and their influence on safety analyses. The paper introduces a new multivariate hazardous location identification technique, which generalizes the univariate posterior probability of excess that has been commonly proposed and applied in the literature. In addition, the paper presents an alternative approach for quantifying the effect of the multivariate structure on the precision of expected collision frequency. The MVPLN approach is compared with the independent (separate) univariate Poisson-lognormal (PLN) models with respect to model inference, goodness-of-fit, identification of hot spots and precision of expected collision frequency. The MVPLN is modeled using the WinBUGS platform which facilitates computation of posterior distributions as well as providing a goodness-of-fit measure for model comparisons. The results indicate that the estimates of the extra Poisson variation parameters were considerably smaller under MVPLN leading to higher precision. The improvement in precision is due mainly to the fact that MVPLN accounts for the correlation between the latent variables representing property damage only (*PDO*) and injuries plus fatalities (*I* + *F*). This correlation was estimated at 0.758, which is highly significant, suggesting that higher *PDO* rates are associated with higher *I* + *F* rates, as the collision likelihood for both types is likely to rise due to similar deficiencies in roadway design and/or other unobserved factors. In terms of goodness-of-fit, the MVPLN model provided a superior fit than the independent univariate models. The multivariate hazardous location identification results demonstrated that some hazardous locations could be overlooked if the analysis was restricted to the univariate models.
+
+Crown Copyright © 2009 Published by Elsevier Ltd. All rights reserved.
+
+## **1. Introduction**
+
+The application of collision prediction models (CPMs) in assessing the safety of a road entity (intersection, road segment, etc.) has become a standard practice among safety researchers and practitioners [\(Hauer et al., 1988; Persaud and Dzbik, 1993; Lord, 2000;](#page-8-0) [Miaou and Lord, 2003; Sawalha and Sayed, 2006a,b\).](#page-8-0)
+
+Data on the number of collisions at a particular site are usually available where the collisions are classified by severity (e.g., fatal, minor injury, major injury or property damage only), by the number of vehicles involved (e.g., single or multiple), and/or by the type of collision (e.g., angle, head-on, rear-end, sideswipe or pedestrianinvolved), etc. In such cases, it is necessary to account for the likely correlations among collision counts at different levels of classification. These correlations may be caused by omitted variables, which can influence collision occurrence at all levels of classification, or
+
+In contrast to the above two-stage approach of using a model to predict total collisions and a conditional model to predict severity, recent models for unconditional accident severity analysis have been proposed in the safety literature [\(Tunaru, 2002; Ma and](#page-8-0) [Kockelman, 2006; Brijs et al., 2007; Park and Lord, 2007; Ma et](#page-8-0) [al., 2008; Ye et al., 2009; Aguero-Valverde and Jovanis, 2009\).](#page-8-0) These multivariate extensions are based on either multivariate Poisson (MVP) models ([Tsionas, 2001; Karlis, 2003; Karlis and](#page-8-0) [Meligkotsidou, 2005\)](#page-8-0) or multivariate Poisson-lognormal (MVPLN) models [\(Chib and Winkelmann, 2001\).](#page-7-0) The MVPLN regression is
+
+[tsayed@civil.ubc.ca](mailto:tsayed@civil.ubc.ca) (T. Sayed). <sup>1</sup> Tel.: +1 604 822 4379.
+
+from ignoring shared information in unobserved error terms. Several researchers such as [Hydén \(1987\)](#page-8-0) and [Sayed and Zein \(1999\)](#page-8-0) showed that severe conflicts and various collision severity levels did in fact share the same severity distribution. However, most studies have avoided the issue of correlations by using a frequency model to predict the total number of collisions and then conditional on collision occurring, severity can be predicted using techniques such as multinomial logit models, nested logit models, ordered probit models, sequential binary probit models, heteroskedastic multivariate generalized extreme value models and mixed logit models (e.g., see [Yamamoto et al., 2008; Kim et al., 2008; Milton et al., 2008; a](#page-8-0)nd the references therein).
+
+<sup>∗</sup> Corresponding author. Tel.: +1 604 716 4470. *E-mail addresses:* [basyouny@civil.ubc.ca](mailto:basyouny@civil.ubc.ca) (K. El-Basyouny),
+
+preferred to the MVP approach for the analysis of multivariate collision count data because (i) it accounts for over-dispersion (extra Poisson variation), which is often observed in collision data; and (ii) it allows for a full general correlation structure. Since the classical estimation of the parameters of the MVP and MVPLN regression models is not straightforward, the Markov chain Monte Carlo (MCMC) simulation method ([Gilks et al., 1996\)](#page-8-0) is typically used in the applications.
+
+This paper advocates the use of MVPLN for modeling collision count data. The MVPLN regression model presents an opportunity to corroborate the findings reported in the literature regarding the nature of the correlations across collision severity levels and their influence on safety analyses. The paper introduces a new multivariate hazardous location identification technique, which generalizes the univariate posterior probability of excess that has been commonly proposed and applied in the literature. In addition, the paper presents an alternative approach for quantifying the effect of the multivariate structure on the precision of expected collision frequency. The MVPLN approach is compared with the independent (separate) univariate PLN models with respect to model inference, goodness-of-fit, identification of hot spots and precision of expected collision frequency.
+
+The development of the MVPLN model is undertaken using WinBUGS [\(Lunn et al., 2000\)](#page-8-0) which is an open-source statistical software. WinBUGS is a flexible platform for the Bayesian analysis of complex statistical models using MCMC methods. The proposed implementation of the MVPLN regression model is relatively simpler than other MVPLN approaches using special codes written for the MATLAB and R computing environments [\(Park and Lord, 2007;](#page-8-0) [Ma et al., 2008\).](#page-8-0) WinBUGS has the additional advantage of providing the user with a goodness-of-fit measure (the deviance information criteria) that can be used for model comparisons.
+
+# **2. Previous work**
+
+To distinguish between the collision prediction models that use multivariate explanatory variables to predict a univariate dependent variable (e.g., the total number of collisions) and those which involve multivariate dependent as well as independent variables, the former will be termed univariate CPMs, while the latter will be termed multivariate CPMs. It should be noted that both univariate and multivariate CPMs use multivariate independent variables (covariates). In view of this terminology, the popular univariate approach for developing CPMs uses the Poisson-gamma hierarchy, which leads to the negative binomial regression model (e.g., [Poch](#page-8-0) [and Mannering, 1996; Hauer, 1997; Hinde and Demetrio, 1998;](#page-8-0) [Lord, 2000; Miaou and Lord, 2003\).](#page-8-0) The PLN regression represents a viable alternative for modeling the extra-Poisson variation ([Kim](#page-8-0) [et al., 2002; Miranda-Moreno, 2006\).](#page-8-0)
+
+The majority of CPMs were developed using models with a fixed dispersion parameter. Such an assumption was challenged and various dispersion parameter relationships were examined [\(Heydecker](#page-8-0) [and Wu, 2001; Miaou and Lord, 2003; Miranda-Moreno et al., 2005;](#page-8-0) [El-Basyouny and Sayed, 2006; Mitra and Washington, 2007; Lord](#page-8-0) [and Park, 2008\).](#page-8-0)
+
+There is extensive research addressing the problem of observing excessive zeroes in collision data (e.g., [Shankar et al., 2004; Lee and](#page-8-0) [Mannering, 2002; Kumara and Chin, 2006; Qin et al., 2004; Warton,](#page-8-0) [2005; Lord et al., 2005, 2007\).](#page-8-0) Another problem of considerable interest is the development of CPMs using data characterized by a low sample mean, especially if combined with a small sample size, (e.g., [Maycock and Hall, 1984; Fridstrøm et al., 1995; Wood, 2002;](#page-8-0) [Lord, 2006\).](#page-8-0) Other modeling techniques have also been proposed in the literature advocating the use of random parameter negative binomial regression model ([Anastasopoulos and Mannering, 2009\)](#page-7-0) or a two-state Markov Switching model [\(Malyshkina et al., 2008\)](#page-8-0) to analyze collision frequencies.
+
+Multivariate extensions of the simple Poisson distribution to account for the correlations among different count processes (such as counts of different crash severities) have been proposed in the literature. For instance, a model that assumes the same nonnegative covariance term for all pairs has been considered by [Tsionas](#page-8-0) [\(2001\)](#page-8-0) and [Karlis \(2003\).](#page-8-0) [Ma and Kockelman \(2006\)](#page-8-0) adapted a multivariate Poisson (MVP) regression approach to assess the effects of different covariates on collision counts at different severity levels. The assumption of equal covariance terms has been relaxed by [Karlis and Meligkotsidou \(2005\), b](#page-8-0)ut the restriction to nonnegative covariance terms was still maintained. [Brijs et al. \(2007\)](#page-7-0) used a similar non-regression model for ranking hazardous sites in Belgium.
+
+Multivariate zero-inflated Poisson (MVZIP) models were also considered ([Li et al., 1999\).](#page-8-0) Since the MVP regression models do not allow for over-dispersion, a multivariate negative binomial (MVNB) model was used to investigate the simultaneity of fatality and injury collision outcomes [\(Ladron de Guevara and Washington, 2004\).](#page-8-0) A major drawback of the MVNB models is its inability to tolerate negative correlations.
+
+To address the shortcomings of MVP and MVNB, [Chib and](#page-7-0) [Winkelmann \(2001\)](#page-7-0) developed the MVPLN regression approach. The MVPLN model does not only account for over-dispersion, but also it has a fairly general correlation structure allowing for (i) different covariance terms; and (ii) the possibility of negative correlations, which cannot be ruled out unquestionably for all classifications.
+
+Recently, applications of the MVPLN to model collision count data at different levels of severity were undertaken. [Tunaru \(2002\)](#page-8-0) used an MVPLN non-regression model implemented via WinBUGS for analyzing multiple response count data (classified by severity and the number of vehicles involved) taking into account complex correlation structures.
+
+[Park and Lord \(2007\)](#page-8-0) used MATLAB codes [MATLAB \(2006\), t](#page-8-0)ailored according to the MCMC algorithm of [Chib and Winkelmann](#page-7-0) [\(2001\), f](#page-7-0)or jointly modeling collision frequency by severity using data from 451 three-leg un-signalized intersections in California obtained through the Highway Safety Information System (HSIS). Their results showed promise toward obtaining more accurate estimates by accounting for correlations in the multivariate collision counts and over-dispersion.
+
+[Ma et al. \(2008\)](#page-8-0) coded a Gibbs sampler and two Metropolis–Hastings algorithms ([Gilks et al., 1996\)](#page-8-0) in the R language for the prediction of collision counts by severity using data collected from Washington State through the HSIS on 7773 rural two-lane roadways in the Puget Sound region. Their results indicated that the MVPLN approach offered better predictions than those from univariate Poisson and negative binomial models. The results indicated that there were statistically significant correlations between (as well as over-dispersion in) collision counts at different levels of injury severity. Several recommendations for highway safety treatments and design policies were suggested, e.g., they concluded that wide lanes and shoulders are key for reducing collision frequencies, as are longer vertical curves.
+
+[Ye et al. \(2009\)](#page-8-0) developed a simultaneous equations model of collision frequencies by collision type for a sample of 165 rural intersections in 38 counties of Georgia. The model was formulated using multivariate Poisson regression with multivariate normal heterogeneity. A simulation-based maximum likelihood approach was used to estimate the parameters. The model estimation results support the notion of the presence of significant common unobserved factors across collision types, although the impact of these factors on parameter estimates was found to be rather modest.
+
+[Aguero-Valverde and Jovanis \(2009\)](#page-7-0) used Full Bayes MVPLN models implemented via WinBUGS to estimate the expected col<span id="page-2-0"></span>lision frequency for different collision severity levels using data on 6353 rural two-lane segments in central Pennsylvania. They found high correlations among collision severities, with highest values between contiguous severity levels. In terms of goodness-of-fit, the multivariate model outperformed the independent univariate PLN models and provided improved precision for collision frequency estimates. The multivariate estimates were combined with cost data from PennDOT to rank sites for safety improvements via expected collision cost and excess expected cost per segment. The results showed that the multivariate-based top ranked segments have consistently higher costs and excess costs than the univariate estimates as a result of higher multivariate estimates of fatalities and major injuries. These higher estimates resulted in different rankings for the multivariate and independent models.
+
+### **3. Methodology**
+
+# *3.1. The multivariate Poisson-lognormal model*
+
+For a set of data on road collisions at *n* locations, where the collisions at each location are classified into *K* categories, define the vector *yi* = (*yi*<sup>1</sup> *yi*2...*yiK*) , where *yik* denote the number of collisions at the *i*th location in category *k*. It is assumed that the *yi* are independently distributed and that the Poisson distribution of *yik*, given *ik*, is
+
+$$f(y_{ik}|\lambda_{ik}) = \lambda_{ik}^{y_{ik}} \frac{e^{-y_{ik}}}{y_{ik}!}, \quad i = 1, 2, \dots, n, \quad k = 1, 2, \dots, K.$$
+ (1)
+
+To model extra variation, assume further that ln(*ik*) = ln(*ik*) + ε*ik*, where
+
+$$\ln(\mu_{ik}) = \beta_{k0} + \beta_{k1}X_{i1} + \dots + \beta_{kj}X_{ij}, \qquad (2)$$
+
+the *Xij* denote relevant traffic and road characteristics and the ε*ik* denote multivariate normal errors distributed as ε*<sup>i</sup>* ∼ *Nk*(0, ˙), where
+
+$$\varepsilon_i = \begin{pmatrix} \varepsilon_{i1} \\ \varepsilon_{i2} \\ \vdots \\ \varepsilon_{iK} \end{pmatrix}, \quad \Sigma = \begin{pmatrix} \sigma_{11} & \sigma_{12} & \dots & \sigma_{1K} \\ \sigma_{21} & \sigma_{22} & \dots & \sigma_{2K} \\ \vdots & \vdots & \ddots & \vdots \\ \sigma_{K1} & \sigma_{K2} & \dots & \sigma_{KK} \end{pmatrix}.$$
+
+Let *X* and ˇ*<sup>k</sup>* denote the matrix of covariates and the vector of regression coefficients, respectively, and let ˇ denote the set {ˇ1, ˇ2,..., ˇ*K*}. Thus, given (*X*, ˇ, ˙), the *<sup>i</sup>* are independently distributed as
+
+$$f(\lambda_i|X,\beta,\Sigma) = \frac{\exp\{-0.5(\lambda_i^* - \mu_i^*)'\Sigma^{-1}(\lambda_i^* - \mu_i^*)\}}{(2\pi)^{K/2} \left(\prod_{k=1}^K \lambda_{ik}\right) |\Sigma|^{1/2}},$$
+(3)
+
+which is a *K*-dimensional log-normal distribution, where
+
+$$\begin{array}{lll} \lambda_i = (\lambda_{i1} & \lambda_{i2} \cdots \lambda_{iK})', & \lambda_i^* = (\ln(\lambda_{i1}) & \ln(\lambda_{i2}) \cdots \ln(\lambda_{iK}))', \\ \mu_i = (\mu_{i1} & \mu_{i2} \cdots \mu_{iK})', & \mu_i^* = (\ln(\mu_{i1}) & \ln(\mu_{i2}) \cdots \ln(\mu_{iK}))'. \end{array}$$
+
+It should be noted that the univariate PLN models are obtained as the special case where ˙ is a diagonal matrix.
+
+#### *3.2. Prior distributions*
+
+Let denote the set {-1, -2,..., *<sup>n</sup>*}. To obtain the full Bayes estimates of (-, ˇ, ˙), it is required to specify prior distributions for the hyper parameters (ˇ, ˙). Prior distributions are meant to reflect to some extent prior knowledge about the parameters of interest. If such prior information is available, it should be used to formulate the so-called informative priors. The specification of informative priors for generalized linear models was dealt with by [Bedrick et](#page-7-0) [al. \(1996\), w](#page-7-0)ho considered conditional means priors as well as data augmentation priors of the same form as the likelihood and showed that such priors result in tractable posteriors. A good discussion on the elicitation of priors in collision data analysis can be found in [Schluter et al. \(1997\).](#page-8-0)
+
+In the absence of sufficient prior knowledge of the distributions for individual parameters, uninformative (vague) proper prior distributions are usually specified. The most commonly used priors are diffused normal distributions (with zero mean and large variance) for the regression parameters and a Wishart (*P*, *r*) prior for ˙<sup>−</sup>1, where *P* and *r* ≥ *K* represent the prior guess at the order of magnitude of the precision matrix ˙−<sup>1</sup> and the degrees of freedom, respectively. The parameterization of the Wishart probability density function is
+
+$$f(\Sigma^{-1}|P, r) = |P|^{K/2}|\Sigma^{-1}|^{(r-K-1)/2} \exp\{-0.5Tr(P\Sigma^{-1})\}.$$
+
+Choosing *r* = *K* as the degrees of freedom corresponds to vague prior knowledge [\(Spiegelhalter et al., 1996; Tunaru, 2002\).](#page-8-0)
+
+# *3.3. Posterior distributions*
+
+Let*f*(ˇ) *k*,*<sup>j</sup> N*(0,10,000) and *f*(˙<sup>−</sup>1) Wishart (*P*, *K*) denote the hyper-prior distributions for the regression parameters and the precision matrix, respectively, Further, let *y* denote the set {*y*1, *y*2,..., *yn*}. Given *X*, the joint distribution of (*y*, -, ˇ, ˙) is
+
+$$f(y,\lambda,\beta,\Sigma|X) = \frac{f(\beta)f(\Sigma^{-1})}{(2\pi)^{nK/2}|\Sigma|^{n/2}\left(\prod_{i=1}^{n}\prod_{k=1}^{K}y_{ik}!\right)}g(y,\lambda,X,\beta,\Sigma),$$
+
+where
+
+$$\begin{split} g(y,\lambda,X,\beta,\Sigma) &= \exp\left\{-0.5\sum_{i=1}^{n} \left((\lambda_i^* - \mu_i^*)'\Sigma^{-1}(\lambda_i^* - \mu_i^*) + \sum_{k=1}^{K} [(y_{ik} - 1)\ln(\lambda_{ik}) - \lambda_{ik}]\right)\right\}. \end{split}$$
+
+The posterior distributions are given by
+
+$$f(\lambda_{i}|y,X,\beta,\Sigma) = \frac{g_{i}(y_{i},\lambda_{i},X,\beta,\Sigma)}{\int_{0}^{\infty} \int_{0}^{\infty} \dots \int_{0}^{\infty} g_{i}(y_{i},\lambda_{i},X,\beta,\Sigma) d\lambda_{i1} d\lambda_{i2} \dots d\lambda_{iK}},$$
+(4)
+
+where
+
+$$\begin{split} g_i(y_i, \lambda_i, X, \beta, \Sigma) &= \exp\left\{-0.5\lambda_i^* - \mu_i^*)'\Sigma^{-1}(\lambda_i^* - \mu_i^*) \\ &+ \sum\nolimits_{k=1}^K [(y_{ik} - 1)\ln(\lambda_{ik}) - \lambda_{ik}]\right\}, \end{split}$$
+
+$$f(\beta|y,\lambda,X,\Sigma)$$
+
+$$= \frac{g(y, \lambda, X, \beta, \Sigma)f(\beta)}{\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \dots \int_{-\infty}^{\infty} g(y, \lambda, X, \beta, \Sigma)f(\beta)d\beta_{10}d\beta_{11} \dots d\beta_{KJ}},$$
+ (5)
+
+and
+
+$$f(\Sigma^{-1}|\mathbf{y},\lambda,X,\beta) \equiv Wishart\left(P + \sum_{i=1}^{n} (\lambda_i^* - \mu_i^*)(\lambda_i^* - \mu_i^*)', K + n\right). \tag{6}$$
+
+# *3.4. Full Bayes estimation*
+
+The posterior distributions needed in the full Bayes approach can be obtained using MCMC sampling. The Wishart distribution in (6) can be sampled using a Gibbs sampler. In contrast, the posterior distributions in (4) and (5) are not standard and require the <span id="page-3-0"></span>Metropolis–Hastings algorithm [\(Park and Lord, 2007; Ma et al.,](#page-8-0) [2008\).](#page-8-0)
+
+In this paper, the posterior distributions are sampled using the MCMC techniques available in WinBUGS 2.2.0; the windows interface of OpenBUGS. The techniques generate sequences (chains) of random points, whose distributions converge to the target posterior distributions. A sub-sample is used to monitor convergence and then excluded as a burn-in sample. The remaining iterations are used for parameter estimation, performance evaluation and inference.
+
+Monitoring convergence is important because it ensures that the posterior distribution has been "found". Thereby indicating when parameters sampling should begin. To check convergence, two or more parallel chains with diverse starting values are tracked to ensure full coverage of the sample space. Convergence of multiple chains is assessed using the Brooks–Gelman–Rubin (BGR) statistic ([Brooks and Gelman, 1998\).](#page-7-0) A value under 1.2 of the BGR statistic indicates convergence. Convergence is also assessed by visual inspection of the MCMC trace plots for the model parameters as well as by monitoring the ratios of the Monte Carlo errors relative to the respective standard deviations of the estimates; as a rule of thumb these ratios should be less than 0.05.
+
+# *3.5. Model comparisons*
+
+The Deviance Information Criteria (DIC) is used for model comparisons ([Spiegelhalter et al., 2002\).](#page-8-0) As a goodness of fit measure, DIC is a Bayesian generalization of Akaike's Information Criteria (AIC) that penalizes larger parameter models. According to [Spiegelhalter et al. \(2005\), i](#page-8-0)t is difficult to determine what would constitute an important difference in DIC. Very roughly, differences of more than 10 might definitely rule out the model with the higher DIC. Differences between 5 and 10 are considered substantial. If the difference in DIC is less than 5, and the models make very different inferences, then it could be misleading just to report the model with the lowest DIC.
+
+To show that DIC is additive under independent models and priors, let *f*(*y*|) and *f*(*y*) denote the conditional and marginal distributions of *y*, where denote the vector of parameters associated with *y*. Then, DIC = D¯ + p, where p = D¯ − D( ¯), ¯ = E[|y] and D¯ = E[D()|y] are the posterior means of and the Bayesian deviance
+
+$$D(\theta) = -2 \ln\{f(y|\theta)\} + 2\ln\{f(y)\}. \tag{7}$$
+
+For *K* collision categories, let *y* and be partitioned as (*y*1,..., *yk*) and (1,..., *k*). Define DICk <sup>=</sup> <sup>D</sup>¯ <sup>k</sup> <sup>+</sup> pk, pk <sup>=</sup> <sup>D</sup>¯ <sup>k</sup> <sup>−</sup> Dk(¯ <sup>k</sup>), D¯ <sup>k</sup> = <sup>E</sup>[Dk(k)|yk], ¯ <sup>k</sup> = E[k|yk] and Dk(k) = −2 ln{f(yk|k)} + 2 ln{f(yk)}. Under independent models and priors, we have that f(y|) = <sup>K</sup> <sup>k</sup>=1f(yk|k) and <sup>f</sup>(y) <sup>=</sup> <sup>K</sup> k=1f(yk). These multiplicative conditional and marginal distributions of *y* translate additively in the Bayesian deviance (7) leading to DIC <sup>=</sup> <sup>K</sup> <sup>k</sup>=1DICk.
+
+#### **4. Multivariate identification**
+
+The treatment in this section is not meant to account for the extensive literature on the selection of hazardous locations, but rather to illustrate the generalization to the multivariate setting of some of the techniques that were developed for univariate analysis.
+
+Several hazardous location identification techniques exist in the literature. These include the probability of worst site, posterior distribution of the ranks of the collisions costs or expected number of collisions, or through expected collision cost and excess expected cost [\(Tunaru, 2002; Brijs et al., 2007; Aguero-Valverde and Jovanis,](#page-8-0) [2009\).](#page-8-0)
+
+However, assigning costs to different types of injury can be controversial for a variety of reasons [\(Brijs et al., 2007\).](#page-7-0) These reasons include ethical arguments (e.g., can we assign a cost to a human life?) and economic arguments (what are the quantities that must be measured to estimate the cost of a seriously injured person?). To avoid such difficulties, an alternative approach of selecting hot spots is adopted which is based on the posterior probability of excess [\(Higle and Witkowski, 1988; Sayed and Abdelwahab, 1997;](#page-8-0) [Heydecker and Wu, 2001\).](#page-8-0) The Bayesian posterior probability that a site has an excessive mean collision frequency provides an indication of sites at which the future collision record is expected to be worse than usual. In the univariate analysis, this probability is expressed as:
+
+$$\int_{\mu_0}^{\infty} f(\lambda_i | y, X, \beta, \sigma^2) d\lambda_i > 1 - \delta, \quad i = 1, 2, \dots, n,$$
+(8)
+
+where 2, <sup>0</sup> and ı denote the extra-Poisson variation, an upper limit of the "acceptable" mean number of collisions and a threshold value between 0 and 1, respectively. In practice, <sup>0</sup> is typically specified as either the median or mean of the prior distribution, whereas ı has been arbitrarily assumed to equal 0.05 ([Higle and](#page-8-0) [Witkowski, 1988; Sayed and Abdelwahab, 1997\).](#page-8-0)
+
+Under the multivariate Poisson-lognormal model, the criterion (8) generalizes to
+
+$$\int_{\mu_{10}}^{\infty} \int_{\mu_{20}}^{\infty} \dots \int_{\mu_{K0}}^{\infty} f(\lambda_i | y, X, \beta, \Sigma) d\lambda_{i1} d\lambda_{i2} \dots d\lambda_{iK} > 1 - \delta,$$
+
+$$i = 1, 2, \dots, n,$$
+(9)
+
+where *f*(*<sup>i</sup>*|*y*, *X*, ˇ, ˙) is given by [\(4\)](#page-2-0) and *k*<sup>0</sup> denotes an upper limit of the "acceptable" mean number of collisions in category *k*. It should be noted that the univariate Eq. (8) is the special case *K* = 1. The evaluation of the multiple integral in (9) is rather complicated. Thereby, the following approximation, due to [Clayton and Kaldor](#page-7-0) [\(1987\), i](#page-7-0)s proposed to simplify the computation of (9),
+
+$$f(\lambda_i^*|y, X, \beta, \Sigma) \approx N_K(mi, Si)$$
+ (10)
+
+where
+
+$$m_{i} = S_{i} \left( \Sigma^{-1} \mu_{i}^{*} + \begin{pmatrix} (y_{i1} + 0.5) \ln(y_{i1} + 0.5) - 0.5 \\ (y_{i2} + 0.5) \ln(y_{i2} + 0.5) - 0.5 \\ \dots \\ (y_{iK} + 0.5) \ln(y_{iK} + 0.5) - 0.5 \end{pmatrix} \right),$$
+(11)
+
+and
+
+$$S_{i} = \begin{pmatrix} \Sigma^{-1} + \begin{pmatrix} y_{i1} + 0.5 & 0 & \dots & 0 \\ 0 & y_{i2} + 0.5 & \dots & 0 \\ \dots & \dots & \dots & \dots \\ 0 & 0 & \dots & y_{iK} + 0.5 \end{pmatrix} \end{pmatrix}^{-1}. \quad (12)$$
+
+The approximation (10) can be used in the Bayesian probability of excess criterion (9) to compare the univariate and multivariate approaches of selecting hot spots.
+
+For univariate PLN models (*K* = 1) let <sup>∗</sup> <sup>0</sup> denote the natural logarithm of the average of the prior means. Then, the *i*th intersection would be selected as a hazardous location whenever
+
+$$\Phi(\mu_{i0}^*) < \delta, \tag{13}$$
+
+where ˚ denotes the univariate standard normal distribution function and
+
+$$\mu_{i0}^* = \frac{\mu_0^* - m_i}{\sqrt{S_i}}$$
+
+The standardized multivariate normal distribution function can be used in a similar procedure to select hot spots under MVPLN. Thus, using a similar notation, the *i*th intersection would be selected as a hazardous location whenever
+
+$$\Phi_{K}(\mu_{i10}^{*}, \mu_{i20}^{*}, \dots, \mu_{iK0}^{*}, \hat{R}) < \delta,$$
+ (14)
+
+where ˚*<sup>k</sup>* denotes the multivariate standard normal distribution function,
+
+$$\mu_{ik0}^* = \frac{\mu_{k0}^* - m_{ik}}{\sqrt{S_{ikk}}}, \quad k = 1, 2, \dots, K,$$
+
+and Rˆ denotes the correlation matrix corresponding to ˙ˆ , the Bayesian estimate of the covariance matrix ˙.
+
+# **5. Data and model description**
+
+A total of *n* = 99 signalized intersections in the city of Edmonton were investigated for the purpose of developing collision prediction models relating the safety of urban 4-leg intersections to their traffic flows. This data set was used as a reference group for the evaluation of the City of Edmonton's Intersection Safety Camera program ([Sayed and de Leur, 2007\).](#page-8-0)
+
+The data on collision frequencies and traffic volumes within the intersections were obtained from the city of Edmonton. The traffic and collision data were provided for a 3-year period before the implementation of the program and were selected to ensure that no changes in either the intersection layout or traffic volumes occurred over the course of the 3 years. The term "collision" as defined by Edmonton's Transportation Department, refers to reportable onstreet collisions that do not occur on private property, include at least one motor vehicle, and result in injury, at least \$1,000 in property damage, or both. The database does not include non-vehicular collisions (e.g., cyclist hitting a pedestrian) and includes collisions that are forwarded to the department by the police service within a specified period. The term "intersection collisions" include collisions that occur inside and 10 m past the legally defined limits of the outer crosswalk lines of intersecting roads and include rightturn cut-offs. The collisions were classified into *K* = 2 categories: property damage only (*PDO*), *k* = 1, and injuries and fatalities (*I* + *F*), *k* = 2.
+
+Average values for the traffic volumes (over the 3 years period) are used to build CPMs for predicting aggregate number of collisions
+
+$$\ln(\mu_{ik}) = \beta_{k0} + \beta_{k1} X_{i1} + \beta_{k2} X_{i2}, \tag{15}$$
+
+where *Xi*<sup>1</sup> = ln(*Vi*1), *Vi*<sup>1</sup> = AADT at the major approach, and *Xi*<sup>2</sup> = ln(*Vi*2), *Vi*<sup>2</sup> = AADT at the minor approach. The aggregation is justified on several grounds. For instance, an aggregate CPM was found to perform well compared with CPMs developed to handle temporal correlation [\(Lord and Persaud, 2000\).](#page-8-0) Also, the aggregation of collisions over a period of reasonable length helps to avoid confounding effects and such a phenomenon like regression-tothe-mean [\(Cheng and Washington, 2005\).](#page-7-0) A statistical summary of the data is shown in [Table 1.](#page-5-0)
+
+To explore the potential relationships between *PDO*/*I* + *F* and major and minor traffic volumes, [Fig. 1](#page-5-0) displays the threedimensional relationships via wireframe plots.
+
+[Fig. 1](#page-5-0) lends support to the AADT functional form (15), as the relationship between each of *PDO* and *I* + *F* and major and minor traffic volumes, is effectively linear on the logarithmic scale, except for a very few cases where there were no collisions. The AADT functional form (15) is popular among practitioners and is often preferred over models that include several covariates because it can be easily re-calibrated ([Lord et al., 2008\).](#page-8-0) Further, it will be adopted for estimating safety performance in the forthcoming highway safety manual [\(Hughes et al., 2005\).](#page-8-0) It should be noted that AADT models may suffer from omitted variables bias since many non-flow related factors are known to affect collision frequency. Nevertheless, such models are well recognized in the traffic safety literature.
+
+# **6. Results and discussion**
+
+## *6.1. Model results*
+
+[Tables 2 and 3](#page-5-0) summarize the parameter estimates and their associated statistics using the univariate and multivariate Poissonlognormal models. In contrast to the univariate PLN which has multivariate explanatory variables, the MVPLN involves multivariate dependent as well as independent variables. It should also be noted that while MVPLN can handle more than two collision categories, the current application involves only two severity levels leading to a bivariate PLN.
+
+The posterior summaries in [Tables 2 and 3](#page-5-0) were obtained via two chains with 20,000 iterations 10,000 of which were excluded as a burn-in sample using WinBUGS. A Wishart prior with an identity scale matrix and two degrees of freedom was adopted [\(Chib](#page-7-0) [and Winkelmann, 2001; Congdon, 2006\).](#page-7-0) Examination of the BGR statistics, ratios of the Monte Carlo errors relative to the standard deviations of the estimates and trace plots for all model parameters indicated convergence.
+
+The results of [Tables 2 and 3](#page-5-0) show that: (i) the parameter estimates are significant, as the 95% credible intervals are bounded away from zero; (ii) the regression coefficients are positive, indicating an increase in the mean collision frequency with traffic volumes; (iii) the impact of traffic volumes at the major approach is larger than that at the minor approach; and (iv) traffic volumes have a larger effect on *PDO* collisions than on *I* + *F* collisions.
+
+Also, [Tables 2 and 3](#page-5-0) reveal small differences in the estimates of the regression parameters between the univariate and multivariate models. However, the estimates of the extra Poisson variation parameters (<sup>11</sup> and 22) were considerably smaller under MVPLN. In fact, the MVPLN 95% credible intervals were entirely shifted to the left of those obtained under the univariate PLN models, for both *PDO* and *I* + *F*.
+
+For *i* = 1, 2,..., *n* and *k* = 1, 2,..., *K*, the mean and variance of *Yik* are given by
+
+$$E(Y_{ik}) = \mu_{ik} \exp(0.5\sigma_{kk}), \tag{16}$$
+
+and
+
+$$Var(Y_{ik}) = E(Y_{ik}) + [E(Y_{ik})]^{2}(\exp(\sigma_{kk}) - 1).$$
+(17)
+
+Since the second term in Eq. (17) dominates the first, we have that
+
+$$Var(Y_{ik}) \cong [E(Y_{ik})]^2 (\exp(\sigma_{kk}) - 1),$$
+
+leading to the ratio
+
+$$\frac{Var(Y_{ik}|MVPLN)}{Var(Y_{ik}|PLN)} \cong \frac{(\exp(\hat{\sigma}_{kk}) - 1)}{(\exp(\hat{\sigma}_{kk}) - 1)},$$
+(18)
+
+where ˆkk and ˜kk are the posterior estimates of *kk* under MVPLN and PLN, respectively. As precision is inversely proportional to the variance of expected collision frequency, it is estimated that MVPLN is more than twice as precise as the independent univariate PLN models; the actual precision ratios were computed via Eq. (18) as 2.5 and 2.1 for *PDO* and *I* + *F*, respectively. The precision of the expected collision frequencies can be estimated also using the standard deviations via Eq.(17). [Fig. 2](#page-6-0) displays these standard deviations by severity and model.
+
+[Fig. 2](#page-6-0) reveals that (i) the standard deviations of *I* + *F* are smaller than those of *PDO*, (ii) the standard deviations of the multivariate model are uniformly smaller than those of the PLN models, (iii) the relationship between the two sets of standard deviations appears to be linear for the two severity levels, and (iv) the standard deviations of the multivariate model were decreased 41% and 36% for *PDO* and *I* + *F*, respectively. With a larger data set for rural two-lane segments in central Pennsylvania, [Aguero-Valverde and](#page-7-0)
+
+<span id="page-5-0"></span>**Table 1** Statistical summary of data set (99 intersections).
+
+|                                                      | Minimum | Maximum | Mean   | Standard deviation |
+|------------------------------------------------------|---------|---------|--------|--------------------|
+| AADT on major approach                               | 5,642   | 61,744  | 28,010 | 9,705              |
+| AADT on minor approach                               | 2,809   | 29,128  | 16,043 | 6,564              |
+| Number of property damage only (PDO) collisions      | 0       | 126     | 43.13  | 24.96              |
+| Number of injuries and fatalities (I + F) collisions | 0       | 78      | 26.99  | 15.59              |
+
+![](_page_5_Figure_4.jpeg)
+
+**Fig. 1.** Left: wireframe plot of ln(*PDO*) vs. ln(*V*1) and ln(*V*2). Right: wireframe plot of ln(*I* + *F*) vs. ln(*V*1) and ln(*V*2). *PDO*: property damage only, *I* + *F*: injuries and fatalities.
+
+**Table 2** Univariate models' statistics.
+
+| Univariate Poisson-lognormal    | Estimate | Standard deviation | 95% credible intervals |             |
+|---------------------------------|----------|--------------------|------------------------|-------------|
+|                                 |          |                    | Lower limit            | Upper limit |
+| Property damage only (PDO)      |          |                    |                        |             |
+| Intercept                       | −10.590  | 1.282              | −13.090                | −7.950      |
+| Ln(V1) (major AADT)             | 0.927    | 0.131              | 0.667                  | 1.188       |
+| Ln(V2) (minor AADT)             | 0.496    | 0.097              | 0.307                  | 0.686       |
+| 11                              | 0.361    | 0.036              | 0.297                  | 0.437       |
+| DIC                             | 730.3    |                    |                        |             |
+| Injuries and fatalities (I + F) |          |                    |                        |             |
+| Intercept                       | −9.267   | 1.447              | −12.180                | −6.440      |
+| Ln(V1) (major AADT)             | 0.754    | 0.148              | 0.480                  | 1.042       |
+| Ln(V2) (minor AADT)             | 0.493    | 0.105              | 0.292                  | 0.706       |
+| 22                              | 0.415    | 0.043              | 0.339                  | 0.507       |
+| DIC                             | 684.3    |                    |                        |             |
+
+[Jovanis \(2009\)](#page-7-0) obtained reductions in the standard deviations of 20.5% (*PDO*), 10.5% (minor injuries), 21.5% (moderate injuries), 48.1% (major injuries) and 40.7% (fatalities).
+
+The improvement in precision is due mainly to the fact that MVPLN accounts for the correlation between the latent variables *<sup>i</sup>*<sup>1</sup> (*PDO*) and *<sup>i</sup>*<sup>2</sup> (*I* + *F*). This correlation ( ) was estimated at 0.758, which is highly significant. In essence, higher *PDO* rates are associated with higher *I* + *F* rates, as the collision likelihood for both types is likely to rise due to the same deficiencies in roadway design and/or other unobserved factors.
+
+As noted in previously, AADT-only models may suffer from omitted variables bias since the unobserved heterogeneity from other factors known to influence collision frequency (such as number of lanes, signal-control timing, speed limits, etc.) ends up in the
+
+**Table 3** Multivariate models' statistics.
+
+| Multivariate Poisson-lognormal  | Estimate | Standard deviation | 95% credible intervals |             |
+|---------------------------------|----------|--------------------|------------------------|-------------|
+|                                 |          |                    | Lower limit            | Upper limit |
+| Property damage only (PDO)      |          |                    |                        |             |
+| Intercept                       | −10.680  | 1.347              | −13.420                | −8.250      |
+| Ln(V1) (major AADT)             | 0.902    | 0.138              | 0.643                  | 1.179       |
+| Ln(V2) (minor AADT)             | 0.531    | 0.104              | 0.320                  | 0.723       |
+| 11                              | 0.163    | 0.030              | 0.113                  | 0.230       |
+| Injuries and fatalities (I + F) |          |                    |                        |             |
+| Intercept                       | −9.346   | 1.565              | −12.410                | −6.240      |
+| Ln(V1) (major AADT)             | 0.742    | 0.159              | 0.435                  | 1.059       |
+| Ln(V2) (minor AADT)             | 0.513    | 0.121              | 0.276                  | 0.761       |
+| 22                              | 0.217    | 0.042              | 0.145                  | 0.312       |
+| Covariance                      |          |                    |                        |             |
+| 12                              | 0.143    | 0.029              | 0.092                  | 0.208       |
+| Correlation                     |          |                    |                        |             |
+| √1122<br>= 12/                  | 0.758    | 0.056              | 0.634                  | 0.852       |
+| DIC                             | 1373     |                    |                        |             |
+
+<span id="page-6-0"></span>![](_page_6_Figure_2.jpeg)
+
+**Fig. 2.** Standard deviations (S.D.) of expected collision frequencies by severity and model. *PDO*: property damage only, *I* + *F*: injuries and fatalities.
+
+correlation structure, thus affecting the estimated correlation. To study the magnitude of this effect on the correlation, the literature was consulted where several independent variables were used to develop multivariate CPMs.
+
+[Park and Lord \(2007\)](#page-8-0) reported a number of correlations between *PDO* and four severity levels. Upon combining these 4 severity levels in one category (*I* + *F*) and using the covariance matrix, the correlation between *PDO* and *I* + *F* was estimated at 0.8608. A similar calculation using the results of [Aguero-Valverde and Jovanis \(2009\)](#page-7-0) produced a correlation estimate of 0.58. [Ma et al. \(2008\)](#page-8-0) did not report the variances associated with the various severity levels. However, assuming comparable precisions, their results produced a rough correlation estimate of 0.44.
+
+These results indicate that the current estimate of 0.758 is in the upper range of the estimates reported in the literature. Although the inclusion of additional relevant covariates is expected to reduce the correlation, it is conjectured to remain significant with crucial inferential impact.
+
+The DIC statistics were 730.3, 684.3 and 1373 under the *PDO* PLN, *I* + *F* PLN and MVPLN, respectively. Thus, the MVPLN model provides a superior fit over the two univariate models as its (multivariate) DIC is much less than the sum of their (univariate) DICs; a very significant drop off of 41.6.
+
+### *6.2. Multivariate identification of hazardous locations*
+
+Hazardous locations were identified via Eqs. [\(13\) and \(14\)](#page-3-0) using ı = 0.10, 0.05 and 0.01. For *K* = 2, the standardized bivariate normal distribution function PROBBNRM ([SAS, 2002\)](#page-8-0) was used in the implementation of Eq. [\(14\). T](#page-3-0)he PROBBNRM function required three input arguments (<sup>∗</sup> <sup>10</sup> − mi1)/ Si11,(<sup>∗</sup> <sup>20</sup> − mi2)/ Si22, and ˆ = 0.758. The outcomes appear in [Table 4, w](#page-7-0)here the results of the univariate Total PLN model were obtained through direct simulation of the sum *PDO* + *I* + *F*.
+
+According to [Table 4, t](#page-7-0)he numbers of intersections identified as hot spots were 31, 29, 35 and 41 under *PDO* PLN, *I* + *F* PLN, Total PLN and MVPLN, respectively, for ı = 0.10. The corresponding numbers were 30, 28, 32 and 37, for ı = 0.05, and 22, 20, 28 and 30 for ı = 0.01. As expected the numbers of hot spots was reduced as the threshold value decreased. However, several locations identified as hazardous by the MVPLN model were missed by the univariate models regardless of the choice of threshold value. It should also be noted that none of the intersections that were not identified as hazardous by MVPLN were identified by any of the univariate models except for one location under the *PDO* PLN model for ı = 0.10 and 0.05.
+
+The results of [Table 4](#page-7-0) demonstrate that some hazardous locations can be overlooked if the analysis was restricted to the univariate models. These results are consistent with those of the cost ranking approach of [Aguero-Valverde and Jovanis \(2009\)](#page-7-0) in that the MVPLN and independent PLN models yield different identification/ranking of hot spots.
+
+The advantage of MVPLN over separate univariate analyses is illustrated in Fig. 3, where posterior information is also contrasted to prior knowledge. The figure displays two credible ellipses and a credible rectangle for (ln(-*PDO*),ln(-*I+F*)), with 95% confidence. Fig. 3 was prepared using the data for Site 56, which was identified as hazardous by MVPLN and *I* + *F* PLN but neither by *PDO* PLN nor by Total PLN. Similar patterns were observed for other identified sites.
+
+![](_page_6_Figure_14.jpeg)
+
+**Fig. 3.** 95% credible ellipses and rectangle for (ln(-*PDO*),ln(-*I+F*)), using the data for Site 56. *PDO*: property damage only, *I* + *F*: injuries and fatalities.
+
+<span id="page-7-0"></span>**Table 4** Number of hot spots selected under different PLN models.
+
+|                                 | Hazardous? | Multivariate PLN |     |          |     |          |     |
+|---------------------------------|------------|------------------|-----|----------|-----|----------|-----|
+|                                 |            | ı = 0.10         |     | ı = 0.05 |     | ı = 0.01 |     |
+|                                 |            | No               | Yes | No       | Yes | No       | Yes |
+| Univariate PLN                  |            |                  |     |          |     |          |     |
+| Property damage only (PDO)      | No         | 57               | 11  | 61       | 8   | 69       | 8   |
+|                                 | Yes        | 1                | 30  | 1        | 29  | 0        | 22  |
+| Injuries and fatalities (I + F) | No         | 58               | 12  | 62       | 9   | 69       | 10  |
+|                                 | Yes        | 0                | 29  | 0        | 28  | 0        | 20  |
+| Total                           | No         | 58               | 6   | 62       | 5   | 69       | 2   |
+|                                 | Yes        | 0                | 35  | 0        | 32  | 0        | 28  |
+
+The larger ellipse corresponds to the prior distribution in Eq. [\(3\). T](#page-2-0)he area inside that ellipse corresponds to 95% probable values for (ln(-*PDO*),ln(-*I+F*)) before the sample data were collected. The smaller ellipse corresponds to the posterior distribution in Eq. [\(10\). T](#page-3-0)he area inside that ellipse corresponds to 95% probable values for (ln(-*PDO*),ln(-*I+F*)) after incorporating the sample data into the analysis. It is clear that the sample information has enhanced prior knowledge and resulted in a more focused "posterior" ellipse that is a (small) subset of the "prior" ellipse.
+
+The rectangle was constructed via the Bonferroni method using the two credible intervals obtained from the separate univariate models, *PDO* PLN and *I* + *F* PLN. The shaded area inside that rectangle corresponds to 95% probable values for (ln(-*PDO*),ln(-*I+F*)) obtained by combining the two separate univariate posterior intervals. The posterior ellipse is nearly contained in the rectangle indicating that some values that are improbable under the MVPLN posterior analysis would be probable under the separate univariate analyses and vice versa. Also, some of the probable values under the rectangle seem to contradict prior knowledge as they lie outside the prior ellipse.
+
+# **7. Conclusions and future research**
+
+A MVPLN regression was used to jointly analyze a sample of collision counts classified by two severity levels (*PDO* and *I* + *F*) at 99 urban intersections. To illustrate the importance of the multivariate technique, it was compared with the independent univariate PLN models with respect to model inference, goodness-of-fit, identification of hazardous locations and precision of expected collision frequency.
+
+The development of the MVPLN model is undertaken using the WinBUGS platform which facilitates computation of posterior distributions as well as providing a measure for model comparisons.
+
+The estimates of the extra Poisson variation parameters were considerably smaller under MVPLN. As precision is inversely proportional to the variance of expected collision frequency, it is estimated that the MVPLN model is more than twice as precise as the univariate PLN models. The improvement in precision is due mainly to the fact that MVPLN accounts for the correlation between the latent variables (*PDO*) and (*I* + *F*). This correlation ( ) was estimated at 0.758, which is highly significant. The results indicate that higher *PDO* rates are associated with higher *I* + *F* rates, as the collision likelihood for both types is likely to rise due to similar deficiencies in roadway design and/or other unobserved factors. This correlation was identified by other researchers in the literature.
+
+In terms of the goodness-of-fit, the MVPLN provided a superior fit over the two univariate models as its (multivariate) DIC is much less than the sum of their (univariate) DICs. The differences between the DICs show a significant drop off of 41.6.
+
+In term of model application, the paper introduces a new multivariate technique for the identification of hazardous locations. The new technique generalizes the univariate posterior probability of excess that has been commonly proposed and applied in the literature to fit the multivariate relationship between latent variables. The results showed that all the hazardous locations identified by the univariate models were identified by multivariate model (except one location under *PDO* PLN). The results also demonstrated that some hazardous locations could be overlooked if the analysis was restricted to the univariate models.
+
+The results presented in this paper are based on a single dataset. Even though these results conform to those in the literature, further research with different datasets and infrastructures is required to confirm the paper's findings.
+
+In this paper two severity levels were investigated (namely: *PDO* and *I* + *F*). However, different severity levels could be incorporated (e.g., fatality, severe injury, light injury, PDO, etc.) or different collisions types could be considered (e.g., angle, head-on, rear-end, sideswipe, etc.). The multivariate nature of such data sets is both logical and intuitive. Recent improvements in statistical tools allows for a more precise analysis which takes into account the correlations that exist among the different levels. These tools should be used to assist transportation engineers to better understand the relationships between the different modeling variables and techniques.
+
+# **References**
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Zotero/001_artiklid/Road Safety Indicators/elvikstrengtheningincentivesefficientroad2010.md

@@ -0,0 +1,302 @@
+---
+category: literaturenote
+citekey: elvikstrengtheningincentivesefficientroad2010
+title: "Strengthening incentives for efficient road safety policy priorities: The roles of cost–benefit analysis and road pricing"
+authors: "Elvik, Rune"
+year: 2010
+date: 2010-00-00 2010
+doi: 10.1016/j.ssci.2010.01.005
+publication: Safety Science
+url: "https://doi.org/10.1016/j.ssci.2010.01.005"
+zotero_key: PQ258R6J
+zotero_storage: 7GTAAZ86
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "Elvik, Rune"
+status: converted
+---
+![](_page_0_Picture_1.jpeg)
+
+## Contents lists available at [ScienceDirect](http://www.sciencedirect.com/science/journal/09257535)
+
+# Safety Science
+
+![](_page_0_Picture_4.jpeg)
+
+![](_page_0_Picture_5.jpeg)
+
+# Strengthening incentives for efficient road safety policy priorities: The roles of cost–benefit analysis and road pricing
+
+Rune Elvik \*
+
+Institute of Transport Economics, Gaustadalléen 21, NO-0349 Oslo, Norway
+
+#### article info
+
+Article history: Received 13 May 2009 Received in revised form 2 January 2010 Accepted 7 January 2010
+
+Keywords: Cost-benefit analysis Power Welfare Incentives Road safety policy Social dilemmas
+
+#### abstract
+
+This paper discusses how incentives for setting efficient priorities in road safety policy can be strengthened. Efficient priorities are characterised by the use of cost-effective road safety measures. Cost-effective road safety measures can be identified by means of cost-benefit analyses. Studies of the actual priorities in road safety policy, in particular in the Scandinavian countries, suggest that these priorities are inefficient, i.e. characterised by the non-use or sub-optimal use of cost-effective road safety measures as well as an extensive use of ineffective road safety measures. This occurs despite the fact that road safety policy analyses have included extensive cost-benefit analyses of road safety measures. It would thus appear that cost-benefit analyses do not necessarily generate a sufficient incentive to implement cost-effective road safety measures. Possible reasons for this are discussed in the paper. It is argued that a large part of the monetary benefits of road safety measures, as estimated in cost-benefit analyses, are not subject to market transactions, and do therefore not manifest themselves in the form of increased income or higher profits. While cost-benefit analyses are indispensable as a means of identifying cost-effective road safety measures, their influence on actual road safety policy needs to be strengthened by providing additional incentives for the use of cost-effective road safety measures. It is suggested that a system of road pricing could generate such incentives. A brief sketch of a hypothetical system of road pricing is given and some problems associated with the implementation of this system are discussed.
+
+> -2010 Elsevier Ltd. All rights reserved.
+
+## 1. Introduction
+
+In order to maintain progress in improving road safety, it is important to use cost-effective road safety measures. In this paper, the term cost-effective will be used to denote measures whose benefits (in monetary terms) are greater than their costs (in monetary terms). To identify cost-effective road safety measures, cost– benefit analysis is an indispensable tool [\(OECD, 2008\)](#page-7-0). Road safety policy analyses relying on cost-benefit analyses have been reported in several countries [\(Elvik, 1997, 2001, 2003, 2007; Elvik et al.,](#page-6-0) [1984; Elvik and Amundsen, 2000; OECD, 2008\)](#page-6-0). These analyses show that major improvements in road safety can be accomplished by implementing cost-effective road safety measures. The most recent analysis for Norway [\(Elvik, 2008a\)](#page-6-0) suggested that the number of road accident fatalities can be reduced by about 50% if all currently known cost-effective road safety measures are implemented by the year 2020.
+
+However, other studies [\(Elvik, 1993, 1995a, 2009a; Fridstrøm](#page-6-0) [and Elvik, 1997; Odeck, 1991, 1996; Jansson and Nilsson, 1989;](#page-6-0) [Nilsson, 1991; Nyborg, 1998; Elvik and Veisten, 2005; Helland](#page-6-0) [and Sørensen, 2009\)](#page-6-0) show that actual road safety policy, at least in Norway, is characterised by inefficient priorities. This means that policy involves both the use of measures that are not costeffective (i.e. benefits are smaller than costs) and the non-use or sub-optimal use of measures that are cost-effective. The existence of inefficient policies can be ascertained by examining the main findings of successive road safety policy analyses for Norway [\(Elvik](#page-6-0) [et al., 1984; Elvik, 1999, 2007\)](#page-6-0). In all these analyses, several main policy options were developed. Two of these options were to continue present policy or to base policy strictly on cost-benefit analysis.
+
+In the most recent of these analyses ([Elvik, 2007\)](#page-6-0), it was found that continuing present policy may reduce the number of road accident fatalities from 250 (mean 2003–2006) to 190 in 2020. Cost-effective use of road safety measures, based strictly on the results of cost-benefit analyses, may reduce the number of fatalities to 138 in 2020. In other words, current road safety policy in Norway does not make use of all opportunities for cost-effective road safety improvements. It should be added that this finding may not apply to all countries. A study in Great Britain [\(Nellthorp and Mac](#page-6-0)[kie, 2000](#page-6-0)) found that priorities between major road projects were to a large extent, although not slavishly, based on cost-benefit analysis. A recent Norwegian study [\(Odeck, 2009\)](#page-7-0) also indicated
+
+<sup>\*</sup> Tel.: +47 22 57 38 10; fax: +47 22 60 92 00. E-mail address: [re@toi.no](mailto:<xml_chg_old>kre@toi.no</xml_chg_old><xml_chg_new>re@toi.no</xml_chg_new>)
+
+that policy makers base their priorities on the factors that are included in cost-benefit analyses (travel time, safety, environmental amenities), but take account of these factors in non-monetary terms (impact assessments in Norway are required to state impacts both in natural units and in monetary terms). It is nevertheless relevant to ask the following questions:
+
+- 1. Why are the actual priorities in road safety policy inefficient? Does cost–benefit analysis generate sufficient incentives to implement cost-effective road safety measures?
+- 2. If cost–benefit analysis does not generate sufficient incentives for efficient policy priorities, how can stronger incentives for making policy conform more closely to the results of cost-benefit analyses be created?
+
+It should be noted that there are, in theory, very many reasons why actual road safety policy may not be based strictly on the results of cost–benefit analysis ([Elvik and Veisten, 2005\)](#page-6-0). It could, for example, be the case that implementing all cost-effective road safety measures would require substantially larger expenditures than current budgets allow for. However, road safety policy analyses in Norway [\(Elvik, 1999, 2007\)](#page-6-0) found that this was not the case. Current policy priorities in Norway are so inefficient that all costeffective road safety measures could be funded by reducing expenditures on ineffective measures and increasing expenditures on cost-effective measures, without having to increase total expenditures. This may of course be different in other countries. This paper will focus on two possible reasons why cost-benefit analyses may not create sufficient incentives to implement cost-effective road safety measures. The first of these concerns the nature of the monetary benefits of improved road safety and the possibilities of converting these benefits to increased income or larger profits. The second concerns the strength of the interests various stakeholders who may influence road safety have in improving road safety.
+
+## 2. Components of the monetary valuation of road safety and the nature of road safety benefits
+
+While different countries estimate the costs of road accidents in different ways, there is near unanimity among economists about how to estimate these costs for use in cost-benefit analysis. Guidelines for estimating road accident costs are given in a number of publications, including a report from the COST-programme [\(Alfaro](#page-6-0) [et al., 1994\)](#page-6-0) and reports from the ECMT and OECD [\(ECMT, 2001;](#page-6-0) [Pearce et al., 2006](#page-6-0)). These guidelines recommend using a combination of three approaches in order to cover all cost elements:
+
+- 1. The resource cost method, also referred to as the costs of restitution, is applied to estimate the direct monetary outlays associated with resources used as a result of accidents.
+- 2. The human capital method, which is applied to estimate the value of productive capacity lost as a results of accidents. Lost productive capacity is sometimes referred to as indirect costs of accidents.
+- 3. The willingness-to-pay method, which is used to estimate the ex ante demand for improving road safety, i.e. the gain in welfare (consumer surplus) that can be attained by reducing the number of accidents.
+
+[Fig. 1](#page-2-0) lists these components of the monetary valuation of road safety. The various components of valuation differ in terms of how they are manifested in economic transactions. The direct costs are real expenditures. In principle, these costs can be retrieved or at least roughly identified in the accounts of hospitals, insurance companies, the police, the courts, car repair shops and households. Estimates of lost productive capacity partly reflect monetary transactions; partly these costs are of a more abstract nature. In particular, lost productive capacity attributable to a fatality is usually estimated as the present value of future earnings. This represents the value of what the individual could have produced if alive; this can never be known with certainty and is therefore most appropriately interpreted as a loss of productive potential or capacity, not an actual loss of production.
+
+The actual loss of production resulting from accidents can be estimated by applying the friction cost method developed by Koopmanschap et al. ([Koopmanschap and Ineveld, 1992; Koopmanschap](#page-6-0) [et al., 1995](#page-6-0)). This method estimates the loss of production during the period it takes to hire new staff to replace an individual who leaves the labour force as a result of an accident. The estimates developed by Koopmanschap et al. indicate that the actual losses of production are only about 10% of the present value of the loss of productive capacity or potential. This does not mean that the loss of productive potential is not real; it simply means that this loss does not materialise as a decline in production.
+
+Willingness-to-pay for a reduced number of road accidents reflects the hypothetical demand for improved safety. It does not reflect any actual monetary transactions. This fact was clearly understood by the pioneers introducing the willingness-to-pay approach to the valuation of road safety. Thus, [Schelling \(1968\),](#page-7-0) page 143 wrote: ''Unexpected death has a hypothetical quality whether it is merely being talked about or money is being spent to prevent it." The willingness-to-pay for reducing statistical risks by an amount that corresponds to the prevention of one death has nothing to do with the ex post costs generated by the death of a known individual. The latter costs are at least two orders of magnitude smaller than the valuation of preventing a death. Thus, in countries that apply the willingness-to-pay approach for valuing road safety, this component normally represents more than half, in some cases nearly the whole, monetary value assigned to improving road safety [\(Elvik, 1995B\)](#page-6-0). The valuation of improved road safety in terms of willingness-to-pay is not subject to market transactions. This means that, although representing real benefits of improving road safety, it will not be realised in terms of added income or profits.
+
+## 3. Incentives and stakeholders in road safety policy
+
+#### 3.1. The concept of incentives
+
+Given the fact that a large part of the monetary benefits of improved road safety, as estimated in cost-benefit analyses, will not manifest itself as a monetary gain, it is necessary to ask whether various actors who can influence road safety have sufficiently strong incentives to do so, even if actual the monetary benefits obtained will be considerably smaller than the societal benefits as reflected in the valuation of improved safety. An incentive can be defined as any prospective benefit or reward favouring the choice of an option. Thus defined, an incentive can only motivate for action if it makes a noticeable difference in utility and if the actor is able to bring about the desired outcome of an action. The relevant questions therefore are:
+
+- 1. To what extent can various actors (households, businesses, health care providers, car manufacturers, government) influence road safety by means of actions under their control?
+- 2. How much would these actions influence the utility of these actors?
+
+The term ''utility" is applied in a very broad sense here: It refers to the level of satisfaction or welfare, including the level of support
+
+<span id="page-2-0"></span>![](_page_2_Figure_2.jpeg)
+
+Fig. 1. Components of the monetary valuation of improved road safety.
+
+given to actions taken by politicians. The following sections will briefly discuss the incentives of some actors to influence road safety.
+
+## 3.2. Household incentives to improve road safety
+
+Do households face strong incentives for improving road safety? According to the latest survey of household consumption expenditures in Norway [\(Statistics Norway, 2009\)](#page-7-0), only about 2.3% of expenditures can reasonably be interpreted as being attributable to road accidents. In other words, if road accidents were eliminated, an average Norwegian household would save about 2% on their household budget. No household can exercise 100% control of the risk it faces on the road. A more plausible estimate is that individual behaviour, with respect to, for example, speed [\(Elvik,](#page-6-0) [2008b](#page-6-0)), route choice or seat belt wearing can influence the risk of injury by, say, about 30%. Hence, by consistently adopting safe behaviour, a household might be able to save 30% of its accident costs, amounting to about 0.7% of the total household budget. This incentive must be regarded as quite weak.
+
+An additional problem is that some promising road safety measures that are cost-effective from a societal perspective are not cost-effective from a road user perspective. ISA (intelligent speed adaptation; technology making speeding impossible or at least unpleasant) is a case in point. The assessment of costs and benefits of ISA on new cars from a societal perspective and from a road user perspective are compared in [Table 1](#page-3-0).
+
+According to the societal perspective, the benefits consist of all savings in accident costs, from which the costs of additional travel time below the speed limit are subtracted. It was assumed that not all ISA-systems are perfect; hence, the mean speed of travel in a traffic stream in which all vehicles have ISA will be a little below the speed limit. This additional travel time has been included.
+
+According to a road user perspective, the analysis is quite different. Only 60% of accident savings are included, as the rest of accidents are external from the road user's point of view ([Elvik, 1994\)](#page-6-0). The full costs of reducing speed, including those attributable to the lowering of illegal speeds, have been included. While treating time saved by speeding (i.e. violating the speed limit) as a benefit is not appropriate in a cost–benefit analysis adopting a societal perspective ([Elvik, 2006\)](#page-6-0), it is clearly a benefit from a road user perspective; why else would drivers be speeding?
+
+The two perspectives give dramatically different results. From the societal perspective, benefits exceed costs by a wide margin. From a road user perspective, benefits are negative. Hence, unless a cost–benefit analysis somehow succeeded in persuading households to adopt a societal perspective, it is unlikely that it would make households buy ISA.
+
+#### 3.3. Business incentives to improve road safety
+
+Just as the average costs of road accidents represent a small share of an average household budget, the mean cost of an accident normally represents a very small share of the costs of a business firm. Thus, in a study of the costs of occupational accidents in the furniture industry, [Rundmo and Söderqvist \(1994\)](#page-7-0) found that the financial losses resulting from accidents amounted to 0.3% of the total payroll. Businesses themselves paid only about 20% of this; the rest was covered by the public sector. The purely financial incentive to prevent accidents was therefore almost non-existent; on the average a saving of 0.05% of the wage budget would be attained if accidents were eliminated.
+
+In short, businesses – at least in the furniture industry – hardly have noticeable costs as a result of accidents. According to [Rundmo](#page-7-0) [and Söderqvist \(1994\)](#page-7-0) firms kept a larger staff than they strictly speaking needed. They did so in order to keep production running smoothly in cases of illness. The normal rate of absence from work in many industries is between 5% and 10%; thus to keep activities progressing normally, surplus staff of at least this magnitude is needed. Keeping this staff of course costs a lot. But this cost has already been internalised by businesses; injuries that result from accidents have, in a sense, been paid for in advance and hardly generate any new cost. Since most of the cost of keeping surplus staff is attributable to illness not caused by accidents, the monetary incentive to improve safety is weak.
+
+[Osmundsen et al. \(2008\)](#page-7-0) discuss in general terms problems associated with implementing safety incentives in industry. They point out several difficulties that are likely to reduce the efficiency of incentives intended to promote safety, using Norwegian oil industry as a case.
+
+<span id="page-3-0"></span>Table 1 Costs and benefits of intelligent speed adaptation (ISA) as viewed from a societal and driver perspective.
+
+| Item of benefits or costs | Amounts in million NOK (1 NOK = 0.12 Euro in May 2009) if all cars have intelligent speed adaptation. Negative amounts are added costs |            |                                                                                  |  |  |
+|---------------------------|----------------------------------------------------------------------------------------------------------------------------------------|------------|----------------------------------------------------------------------------------|--|--|
+|                           | Societal perspective<br>Driver perspective<br>Comments                                                                                 |            |                                                                                  |  |  |
+| Accident savings          | 28.997                                                                                                                                 | 17.398     | About 40% of accident costs are external and not counted as a benefit by drivers |  |  |
+| Extra travel time         | <br>6402                                                                                                                               | <br>38.410 | Only reduction in legal speeds included according to societal perspective        |  |  |
+| Vehicle operating costs   | 720                                                                                                                                    | 720        | Car drivers will include all savings in vehicle operating costs                  |  |  |
+| Environmental benefits    | 2350                                                                                                                                   | 0          | Environmental benefits are external from drivers' point of view                  |  |  |
+| Total benefits            | 25.665                                                                                                                                 | <br>20.292 |                                                                                  |  |  |
+| Installation costs        | 9181                                                                                                                                   | 9181       | Costs are paid in full by drivers                                                |  |  |
+| Annual running costs      | 2333                                                                                                                                   | 2333       | Costs are paid in full by drivers                                                |  |  |
+| Total costs               | 11.514                                                                                                                                 | 11.514     |                                                                                  |  |  |
+| Benefit cost ratio        | 2.23                                                                                                                                   | <br>1.76   | Dramatic difference in results depending in perspective adopted                  |  |  |
+
+#### 3.4. Health care sector incentives to promote road safety
+
+Does the health sector have a strong incentive to improve road safety? A recent cost estimate for Norway ([Elvik, 2009B](#page-6-0)) indicates that the costs of treating traffic injury victims represent only about 1.5% of the total operating cost for hospitals in Norway. Thus, by eliminating road accidents, <2% of the total hospital budget could be saved.
+
+In practice, however, it is not very likely that hospital budgets would be cut by this amount if road accidents were eliminated. It is more likely that the resources now spent on treating traffic injury victims would be transferred to other types of medical treatment. There are waiting lists for many types of treatment; in principle these could be shortened if there were no road accidents. This is obviously a societal gain. But the gain would not materialise in the form of reduced spending on health care. Moreover, the health sector does not control any road safety measures and is therefore not in a position to reduce the costs by means of its own policies.
+
+## 3.5. Car manufacturer incentives to improve road safety
+
+Car manufacturers are today facing an incentive to improve road safety that is considerably stronger than it was only 15 years ago. One of the factors contributing to this is the remarkable success of the European New Car Assessment Programme (EuroNCAP) ([ETSC, 2009](#page-6-0)). EuroNCAP is an extensive programme for testing and rating the safety performance of new cars. The programme has become widely known among car owners, thanks in part to the support and publicity given to the programme by motoring organisations. EuroNCAP has attained high credibility because it is an independent programme providing objective assessments; it does not cater to the commercial interests of any particular car manufacturer. This gives the programme a vastly more authoritative status than any advertisement produced by a car manufacturer.
+
+EuroNCAP score has become a key element in the competition for car purchasers. Studies [\(Andersson, 2005\)](#page-6-0) show that consumers value car safety and are willing to pay for it. [Andersson \(2005\)](#page-6-0) estimated the implicit value of preventing a fatality to SEK 12 million (1 SEK = 0.10 Euro in December 2009). Car safety has improved greatly in recent years; occupants of new cars are far less likely to be killed or seriously injured in an accident of a given severity than occupants of older cars [\(Broughton, 2008; Martin and Len](#page-6-0)[guerrand, 2008](#page-6-0)).
+
+In principle, therefore, safety can be developed into a major competitive force in the marketplace, thus giving car manufacturers incentives to develop safer cars. Car manufacturers will, however, only offer safety technology they think will sell. ISAsystems, for example, are not offered by car manufacturers today.
+
+#### 3.6. Road authority incentives to promote road safety
+
+In all highly motorised countries, the road system has been greatly improved during the past 50 years or so. Many of these improvements are likely to have contributed to improving road safety. Do road authorities face strong incentives to improve road safety? Road authorities do face incentives, but these are partly of a different nature from those facing other stakeholders. In the first place, road authorities can be instructed by politicians to implement road safety measures. In the second place, the recent development of road assessment programmes, like EuroRAP, has made information more easily available to motorists about the safety of roads, thus putting pressure on road authorities to improve roads with a bad safety record. In the third place, it is not unreasonable to think that many traffic engineers take professional pride in designing safer roads and improving the safety of existing roads.
+
+Neither of these incentives is, however, derived from cost-benefit analysis. Although facing incentives to improve road safety, road authorities do not necessarily face a strong incentive to use their budgets as efficiently as possible. For Norway, there is evidence ([Nyborg, 1998](#page-6-0)) that road budgets are ample and clearly large enough to fund all cost-effective measures as well as quite a few measures that are not cost-effective. This may of course be different in other countries. Other studies ([Elvik, 1995a, 2009a](#page-6-0)) indicate that road authorities in Norway regard politicians as their principals and try to develop politically feasible investment programmes that will be widely supported by politicians. To a certain extent, policies designed to be widely supported will embody priorities not based strictly on efficiency.
+
+#### 3.7. Preliminary conclusions
+
+Based on the discussion above, it seems clear that cost-benefit analyses will not always create sufficient incentives for implementing cost-effective road safety measures. In the first place, the actual monetary gains resulting from road safety measures will be considerably smaller than the full societal benefits of such measures as estimated according to the willingness-to-pay for improving road safety. This does not mean that the benefits are not real, simply that they are not converted to a stream of cash by means of market transactions. In the second place, some of those who have a stake in road safety have such a small stake in it that they face weak incentives to act. Car manufacturers and road authorities face stronger incentives, and these incentives have probably become stronger in recent decades than they used to be. The incentives facing car manufacturers and road authorities are, however, of a general nature and do not ensure that these stakeholders will always promote the most efficient measures for improving road safety. It is reasonable to say that both car manufacturers and road authorities can be expected to continue their efforts to improve road safety, but not necessarily in the most cost-effective manner. Cost-benefit analyses therefore needs to be supported by stronger instruments of power in order to ensure that the priorities for improving road safety are as efficient as they can be. Can such instruments of power be imagined? Can a way be found to convert the hypothetical demand for road safety, as expressed in the willingness-to-pay for it, into an actual demand and thus generate stronger incentives for improving road safety?
+
+## 4. The prospects of a near perfect road pricing to generate demand for road safety
+
+## 4.1. Technology for road pricing
+
+Technological progress is rapidly making it possible to introduce a near perfect system of road pricing. In such a system, every road user would pay the marginal societal costs of road use per kilometre of travel. These costs would include:
+
+- 1. The cost of providing a certain road capacity.
+- 2. Road maintenance costs.
+- 3. Costs of specific road safety measures.
+- 4. Accident costs.
+- 5. Environmental costs.
+
+For each of these items a basic cost rate per kilometre of travel would be determined for each road. Each motor vehicle could then be fitted with a driving computer and a geographical positioning system that could record information regarding, for example:
+
+- 1. Route choice.
+- 2. Speed.
+- 3. Use of daytime running lights.
+- 4. Following distance.
+- 5. Use of indicators.
+- 6. Impact speed in case of an accident.
+
+The cost of the equipment needed to record these data is rapidly going down. The advantages of recording the data would be huge. One could, for example, in principle eliminate the problem of incomplete accident reporting and inaccurate information regarding where accidents take place.
+
+Enormous amounts of data would be produced by driving computers. A solution must be found to the problem of how to collect and process these data. There are many possibilities. One possibility would be to connect the fuel system electronically to the driving computer. The computer would write the data to a memory stick that would need to be removed from the car every time it needed to be refuelled. It would not be possible to open the lid to the fuel tank without removing the memory stick. To pay for the fuel, the memory stick would have to be inserted into a computer at each fuel station – the driver would then get a bill including both the fuel and the payment for using the road. A new memory stick would be handed to the driver as a receipt for the payment; this would then have to be inserted into the driving computer in order to be able to start the car.
+
+As outlined above, the driving computer would be an instrument for data collection only. It would not interfere with driver behaviour. Drivers would therefore still have the option of speeding; however, every instance of speeding would be detected and the driver would be charged a fee proportional to the risk involved in speeding plus a penalty intended as a deterrent.
+
+As far as pedestrians and cyclists are concerned, [Jansson \(1994\),](#page-6-0) in an analysis of the external cost of accidents, argues that these road users should not pay for using the roads, since motor vehicles are the main source of the risk they are facing. It will therefore be assumed that motorists will pay the costs of facilities intended for use by pedestrians or cyclists. This would be in their interest, as separate facilities for pedestrians and cyclists make it less likely that motorists will cause injuries to these road users.
+
+## 4.2. A simple illustration
+
+To illustrate how a system of road pricing might be operating, consider the estimates of the societal costs of travel given in [Table](#page-5-0) [2](#page-5-0). The table is based on [Erke and Elvik \(2006\)](#page-6-0) and on [Samstad et al.](#page-7-0) [\(2005\)](#page-7-0). The estimates in [Table 2](#page-5-0) include only the external effects of motorised travel by road, not the costs of road investments and maintenance.
+
+Consider, as an illustration a driver who is driving 1 km on a rural two lane road with a speed limit of 80 km/h. The basic charge for this driver would be NOK 0.973 km-<sup>1</sup> (1 NOK = 0.12 Euro as of December 2009). If the driver was speeding by 10%, i.e. going at a speed of 88 km/h, a surcharge would be added to reflect the cost of speeding. This cost would include an increase in accident risk, increased contribution to global warming and an increase of air pollution. Applying the Power Model ([Elvik, 2004, 2005\)](#page-6-0), the surcharge can be estimated to about 0.30 NOK for accidents and in total about 0.02 NOK for global warming and air pollution. The total charge per kilometre would then be about NOK 1.30 km-To this should be added a surcharge for road maintenance, as road wear increases as a function if speed.
+
+Faced by prices per kilometre of driving that vary depending on the baseline level of accident risk and depending on individual behaviour, drivers would soon discover that safe behaviour brings monetary rewards in the form of lower charges per kilometre. As part of such a system, road authorities could offer specific services to road users every year on every road. These services might, depending on the status of the road, include: resurfacing, renewing traffic signs, installing road lighting, changing the speed limit, or any other measure. At the beginning of each year, road authorities would contact all car owners who used the road at least once the past year and offer them a package of services and an estimate of the cost of these services. Payment for major investments would take the form of down-payments during a number of years, to avoid suddenly increasing road user charges drastically to fund a major project.
+
+Road users would indicate their willingness-to-pay for the services offered by purchasing memory sticks that contain different combinations of the measures. To prevent strategic behaviour in the form of free riding, services should be priced so that they could only be offered if everybody paid for them. The amount paid would depend on the frequency of use of the road. In case of insufficient demand, the services would not be performed.
+
+To stimulate demand, road users should be offered rebates once the measures offered had been implemented and found to reduce the accident rate. This would create strong incentives for road authorities not to introduce measures that would not be expected to reduce the accident rate and to evaluate rigorously whether measures implemented did in fact reduce the accident rate. A potential problem would be that a low number of accidents would make it difficult to evaluate the effects of small road safety schemes at a local level. To create a basis for meaningful evaluation, all projects of the same nature should therefore be pooled into a national data base. Evaluation studies should be performed by an independent body employing state-of-the-art techniques. Findings should always be published.
+
+## 5. Discussion
+
+Road safety has been greatly improved in many highly motorised countries the past 40 years, following a peak in the number of road accident fatalities around 1970. However, the current
+
+<span id="page-5-0"></span>Table 2 External costs of use of motor vehicles on public roads in Norway. NOK per kilometre of driving.
+
+| Traffic environment | Type of road           | Marginal external costs of motorised travel – NOK per vehicle kilometre (1 NOK = 0.12 Euro in May 2009) |                |               |               |
+|---------------------|------------------------|---------------------------------------------------------------------------------------------------------|----------------|---------------|---------------|
+|                     |                        | Accidents                                                                                               | Global warming | Air pollution | Traffic noise |
+| Rural               | Motorway, 100 km/h     | 0.224                                                                                                   | 0.176          | 0.047         | 0.000         |
+| Rural               | Motorway, 90 km/h      | 0.206                                                                                                   | 0.176          | 0.047         | 0.000         |
+| Rural               | Two lane road, 80 km/h | 0.750                                                                                                   | 0.176          | 0.047         | 0.000         |
+| Rural               | Two lane road, 70 km/h | 0.700                                                                                                   | 0.176          | 0.047         | 0.000         |
+| Rural               | Two lane road, 60 km/h | 0.650                                                                                                   | 0.176          | 0.047         | 0.000         |
+| Urban, small city   | Two lane road, 50 km/h | 0.900                                                                                                   | 0.176          | 0.173         | 0.510         |
+| Urban, major city   | Two lane road, 50 km/h | 0.900                                                                                                   | 0.176          | 0.397         | 0.518         |
+
+number of fatalities is still regarded as unacceptably high in most countries and ways of improving the efficiency of road safety policies are sought. Policy analyses indicate that, at least in Norway and Sweden, current road safety priorities are not as effective as theoretically possible, i.e. ineffective measures continue to be used and not all cost-effective measures are introduced.
+
+Cost-benefit analyses do not seem to generate sufficient incentives to implement cost-effective road safety measures. The purely monetary incentives for improving road safety facing households, business firms and the health care sector are weak. Most of the monetary benefits of improving road safety as estimated in costbenefit analyses represent a hypothetical demand for improved road safety. To generate stronger incentives for improving road safety, this hypothetical demand needs to be converted to an actual demand. In principle, this is now becoming possible in the form of road pricing systems in which road users pay all costs of road use. By applying information technology, it is in principle even possible to device road pricing systems that are responsive to road user behaviour. As an example, a computer recording speed would make it possible to put a price tag on speeding by applying known relationships between speed and the risk and severity of accidents.
+
+In a fully implemented road pricing system, road authorities would get all their funding from fees paid by road users. The level of service offered to road users would then depend directly on how much road users were willing to pay. Road authorities could test this by offering alternative packages of measures carrying different price tags. Successful road safety measures would lead to lower road user charges at a later date.
+
+If comprehensive road pricing were introduced, there would no longer be a need for cost-benefit analysis. The provision of road safety would ideally speaking match the demand for it, resulting in an optimal level of safety. Road users would be rewarded for improving safety by paying less for the use of roads; the safer the roads, the lower the road user charges. The system would be fair in sense that money would be raised from those who benefitted from the improvements.
+
+There are, however, several problems related to road pricing that need to be considered carefully before introducing it. More specifically, the following problems need to be discussed:
+
+- 1. Acceptability of the system and the need for designing it so that it does not impose inequitable financial burdens on road users.
+- 2. Whether a detailed monitoring of individual behaviour represents an unacceptable invasion of privacy.
+- 3. How to fund the costs for starting up the system.
+- 4. The prices to be charged by the system are not very precisely known.
+- 5. The need for charging prices which are higher than the marginal costs of road use.
+- 6. How to dispose of the revenue generated by the system.
+
+It is well known that road pricing is very unpopular and not always accepted by road users [\(Button and Verhoef, 1998; Schade](#page-6-0) [and Schlag, 2003\)](#page-6-0). Road pricing is often met with the objection that road users are already paying the societal costs of transport in terms of taxes on vehicles and motor fuel. At the aggregate level, this may well be correct, but the taxes imposed on vehicles and fuel do not reflect the marginal costs of driving. If correctly designed, a road pricing system would generate sufficient revenue to operate and extend the road system and compensate for the external effects of road use. To keep the system revenue neutral and to prevent it from adding to the total costs of keeping and operating a motor vehicle, offsetting changes in taxes on the purchase and ownership of motor vehicles, as well as motor fuel taxes could be introduced. The total economic burden placed on households and businesses would then remain unchanged.
+
+As discussed in this paper, the system would include a fairly detailed monitoring of road user behaviour. This is intended to generate incentives for safer behaviour, since unsafe road user behaviour is a major road safety problem. A detailed monitoring of road user behaviour may, however, be regarded as an invasion of privacy. There are legitimate concerns that the data generated by the system could be abused. If, as an example, a road user forgot to use the indicator when turning right at a junction, and then struck a pedestrian – who did not believe the car was turning as it did not indicate that it would – this fairly minor error could be used by an insurance company to deny the driver coverage for the damages to the pedestrian. This is clearly a serious concern, and the system should be designed so as to prevent such abuses. One way of doing so, would be to require the informed consent of every road user before data generated by the system were made available to, for example, insurance companies.
+
+There would be significant initial costs to start-up a system of road pricing. Installing driving computers and digital maps in every motor vehicle might cost, perhaps, a few hundred Euros per vehicle. Many road users would regard these expenses as a complete waste; they would see no benefits of a system whose most obvious effect would be to make them pay more for using the roads. If government, based on a careful impact assessment, found the benefits of road pricing to clearly exceed the costs, the possibility of subsidising the start-up cost of the system should be considered; in other words government would pay the start-up cost and road users would get it for free.
+
+The prices to be charged by a road pricing system are not very well known. In an initial phase, equilibrium prices would have to be determined by a process of trial-and-error. At the outset, prices should be based on the results of surveys of the willingness-to-pay for improving road safety, saving travel time and improving the environment. The system would then, in a sense, represent an empirical testing of the validity of the currently mostly hypothetical valuations of safety, travel time and environmental amenities. Willingness-to-pay surveys have been criticised for hypothetical bias: since respondents do not have to pay the amounts stated, they can be tempted to state higher amounts than they are really willing to pay, in order to be politically correct or satisfy their own notions of what a good citizen should do. There is, therefore, a significant risk that prices based on the results of willingness-to-pay surveys will be too high and that few will actually be willing to pay these <span id="page-6-0"></span>prices. The result might be a reduced traffic volume – which by itself might improve road safety – but which would not be the major objective of the system.
+
+Can a system of road pricing fund all the costs of maintaining, improving and expanding the road system? Jansson (1992) discussed this question in 1992, asking if it was at all conceivable that roads could be run commercially, by road users paying for using the roads. He concluded that this was in principle possible, but that strict marginal cost pricing would not be feasible, as it would lead to huge deficits. This is because there are large fixed costs in any road system; strict marginal cost pricing would not cover all fixed costs. To cover the fixed costs, prices higher than the marginal costs would have to be charged; alternatively government would have to subsidise the fixed costs.
+
+The revenue generated by a road pricing system should be spent in a way that did not undermine or distort the incentives generated by the system. The income generated by the road pricing system would be allocated between different recipients. Road authorities would get what they proposed in their budgets, provided road users were willing to pay for these budgets. The health care sector would be reimbursed for treating accident victims. Victims would be compensated both by insurance companies and the public sector, as is the case today. An option that deserves consideration is to overcharge speeding and other violations in order to generate a surplus. This surplus would then be paid back to law-abiding road users in order to reward them for their safe behaviour. That would make the reward for safe behaviour more tangible than it is when it manifests itself merely in the form of paying lower charges than violators do. Moreover, part of a surplus could be used to fund police enforcement.
+
+#### 6. Conclusions
+
+The main conclusions of the analyses presented in this paper can be summarised as follows:
+
+- 1. Current road safety policy is inefficient: not all road safety measures whose benefits are greater than the costs are implemented, and resources are spent on measures whose benefits are smaller than the costs.
+- 2. Cost–benefit analysis does not by itself generate sufficient incentives to implement cost-effective road safety measures. One reason for this is the fact that most of the benefits of improving road safety consist of gains in welfare that are not readily payable by means of market transactions. These gains are nevertheless real and improve social welfare.
+- 3. Households, business firms and the health sector in general face very weak incentives to improve road safety.
+- 4. Car manufacturers face incentives to improve safety to the extent that greater safety promotes the sales of cars.
+- 5. Road authorities face incentives to improve road safety, but these are of a general nature and do not necessarily favour using the most cost-effective measures to improve road safety.
+- 6. Road pricing is rapidly becoming more technically feasible. In principle, it is possible to design a system for road pricing that will generate incentives for improving road safety.
+- 7. There are, however, many potential problems associated with road pricing that need careful discussion before introducing such a system.
+
+## References
+
+Alfaro, J.-L., Chapuis, M., Fabre, F. (Eds.), 1994. COST 313. Socioeconomic Cost of Road Accidents. Final Report of the Action. EUR 15464 EN. European Commission, Brussels.
+
+- Andersson, H., 2005. Willingness to Pay for a Reduction in Road Mortality Risk. Evidence from Sweden. Lund Economic Studies Number 126. Department of Economics, Lund University, Lund.
+- Broughton, J., 2008. Car driver casualty rates in Great Britain by type of car. Accident Analysis and Prevention 40, 1543–1552.
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Zotero/001_artiklid/Road Safety Indicators/evansfatalaccidentsrailwaylevel2011.md

@@ -0,0 +1,405 @@
+---
+category: literaturenote
+citekey: evansfatalaccidentsrailwaylevel2011
+title: Fatal accidents at railway level crossings in Great Britain 1946–2009
+authors: "Evans, Andrew W."
+year: 2011
+date: 2011-00-00 2011
+doi: 10.1016/j.aap.2011.04.019
+publication: "Accident Analysis & Prevention"
+url: "https://doi.org/10.1016/j.aap.2011.04.019"
+zotero_key: 9432RQ2M
+zotero_storage: GRPARC3D
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "Evans, Andrew W."
+status: converted
+---
+Contents lists available at [ScienceDirect](http://www.sciencedirect.com/science/journal/00014575)
+
+# Accident Analysis and Prevention
+
+journal homepage: [www.elsevier.com/locate/aap](http://www.elsevier.com/locate/aap)
+
+![](_page_0_Picture_5.jpeg)
+
+# Fatal accidents at railway level crossings in Great Britain 1946–2009
+
+Andrew W. Evans <sup>∗</sup>
+
+Centre for Transport Studies, Department of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, United Kingdom
+
+# article info
+
+Article history: Received 15 November 2010 Received in revised form 17 February 2011 Accepted 14 April 2011
+
+Keywords: Railways Roads Level crossings Safety Accidents Fatalities
+
+# abstract
+
+This paper investigates fatal accidents and fatalities at level crossings in Great Britain over the 64-year period 1946–2009. The numbers of fatal accidents and fatalities per year fell by about 65% in the first half of that period, but since then have remained more or less constant at about 11 fatal accidents and 12 fatalities per year. At the same time other types of railway fatalities have fallen, so level crossings represent a growing proportion of the total. Nevertheless, Britain's level crossing safety performance remains good by international standards.
+
+The paper classifies level crossings into three types: railway-controlled, automatic, and passive. The safety performance of the three types of crossings has been very different. Railway-controlled crossings are the best-performing crossing type, with falling fatal accident rates. Automatic crossings have higher accident rates per crossing than railway controlled or passive crossings, and the accident rates have not decreased. Passive crossings are by far the most numerous, but many have low usage by road users. Their fatal accident rate has remained remarkably constant over the whole period at about 0.9 fatal accidents per 1000 crossings per year.
+
+A principal reason why fatal accidents and fatalities have not fallen in the second half of the period as they did in the first half is the increase in the number of automatic crossings, replacing the safer railway controlled crossings on some public roads. However, it does not follow that this replacement was a mistake, because automatic crossings have advantages over controlled crossings in reducing delays to road users and in not needing staff.
+
+Based on the trends for each type of crossing and for pedestrian and non-pedestrian accidents separately, in 2009 a mean of about 5% of fatal accidents were at railway controlled crossings, 52% were at automatic crossings, and 43% were at passive crossings. Fatalities had similar proportions. About 60% of fatalities were to pedestrians.
+
+A simple comparison of automatic railway level crossings and signalised road intersections found that in 2005 the numbers of fatalities per 1000 crossings or intersections were similar.
+
+© 2011 Elsevier Ltd. All rights reserved.
+
+# **1. Introduction**
+
+This paper investigates the safety performance of railway level crossings in Great Britain over the long-term from 1946 to 2009. A reason for concern about level crossings is that their safety performance is not improving, or improving only slowly. The lower curve in [Fig. 1](#page-1-0) is a simple plot of the average number of fatalities per year at level crossings in Great Britain in five-year intervals from 1946 to 2009. The number of fatalities per year fell substantially in the first half of this period from 42.6 in 1946–1950 to 11.8 in 1971–1975,
+
+Abbreviations: AHB, automatic half barrier (level crossing); ALCRM, all level crossings risk model; CSI, Common Safety Indicator; DfT, Department for Transport; ERA, European Railway Agency; GB, Great Britain; HMRI, Her Majesty's Railway Inspectorate; LC, level crossing; Nped, non-pedestrian accident; ORR, Office of Rail Regulation; Ped, pedestrian accident; RSSB, Rail Safety and Standards Board.
+
+but it has remained more or less constant since then, and was 10.8 in 2006–2009. At the same time, other railway fatalities have fallen, so level crossing fatalities are becoming more prominent and represent an increasing proportion of the total. The 42.6 level crossing fatalities per year in 1946–1950 represented 11% of all railway fatalities (excluding trespassers and suicides), but the 10.8 level crossing fatalities per year in 2006–2009 represented 46% of all railway fatalities. Good quality data on level crossing numbers, fatalities and fatal accidents are available for Great Britain since 1946, and the aim of this paper is to explore what can be learned from a longterm analysis of these data. The paper is confined to fatal accidents and fatalities to avoid complications from changing definitions and under-recording of non-fatal injuries.
+
+Although 95% of fatalities at level crossings are to road users, either pedestrians or road vehicle occupants, the long-term development of level crossing fatalities does not mirror those in road accidents generally. The upper curve in [Fig. 1](#page-1-0) plots the average number fatalities per year in road accidents, not including
+
+<sup>∗</sup> Corresponding author. Tel.: +44 020 7594 6043; fax: +44 020 7594 6102. E-mail address: [a.evans@imperial.ac.uk](mailto:a.evans@imperial.ac.uk)
+
+<span id="page-1-0"></span>![](_page_1_Figure_2.jpeg)
+
+**Fig. 1.** Level crossing and road fatalities per year in five-year intervals: Great Britain: 1946–2009.
+
+level crossing accidents, measured in units of 100. Road fatalities increased in the first half of the period at the time when level crossing fatalities were falling, and decreased in the second half of the period at the time when level crossing accidents were about constant. Another notable difference is that the proportion of fatalities to pedestrians is higher at level crossings than in road accidents generally. (The proportions of fatalities to pedestrians in 1946–2009 were 56% at level crossings and 36% in other road accidents.) Therefore, it seems that the factors influencing level crossing fatalities are different from those influencing road accidents.
+
+This paper is about Great Britain, but it is useful at the outset to place the performance of Great Britain in a European context, using data from the 'Common Safety Indicators' (CSIs) assembled by the European Railway Agency [\(ERA, 2010\).](#page-8-0) Compared with most other European countries, the United Kingdom (which is Great Britain plus Northern Ireland) has a good record. In 2008, the UK had fewer level crossing (LC) fatalities than France or Germany (14 compared with 42 and 52, respectively), fewer LC fatalities per million population (0.26 compared with 0.65 and 0.67), fewer LC fatalities per 1000 level crossings (2.1 compared with 2.9 and 4.8), fewer LC fatalities per railway route-kilometre (0.45 compared with 1.46 and 1.67), and fewer LC fatalities per billion train-kilometres (26 compared with 79 and 50).
+
+The paper continues as follows. Section 2 considers the numbers and types of level crossings in Britain. Section [3](#page-2-0) considers fatalities and fatal accidents at level crossings. Section [4](#page-3-0) uses a simple statistical model to analyse the data. Section [5](#page-5-0) presents the results of the modelling. Section [6](#page-7-0) compares fatal accidents and fatalities at automatic level crossings and signalised road intersections in 2005. Section [7](#page-7-0) presents conclusions. [Appendix A](#page-7-0) gives additional statistical results.
+
+## **2. Numbers and types of level crossings**
+
+The railway safety regulator in Britain, formerly HM Railway Inspectorate (HMRI) and now the Office of Rail Regulation (ORR), records the numbers and types of level crossings on the national railway system in its annual report ([HMRI, annual\),](#page-8-0) and has done so at least since 1946. The official classification of level crossing types has changed over the years: in 1946 there were four types; in recent years there have been twelve. However, they may reasonably be grouped into three broad types, which are used in this paper. These are the following.
+
+![](_page_1_Figure_9.jpeg)
+
+**Fig. 2.** Numbers of level crossings: Great Britain: 1946–2009.
+
+- (1) Railway-controlled crossings. At these crossings, the opening and closing of the crossing to the railway or the road is controlled by a member of the railway staff, who is a signaller or crossing-keeper. The operation of the crossing is now almost always interlocked with the railway signalling, so that it is not possible to clear the signals for a train unless and until the crossing is closed to the road. Such crossings traditionally had large swinging gates, some of which remain in service. Modern railway-controlled crossings have lifting full barriers, either operated by a signaller at the site, or operated remotely and supervised by Closed Circuit Television.
+- (2) Automatic crossings. These crossings are operated by the passage of trains without the intervention of railway staff. When a train approaching the crossing reaches a 'strike-in' point, it triggers the operational cycle: first there is a warning to road users; then the crossing is closed to road users; then the train passes; and finally the crossing opens to the road again. The minimum permissible time in Britain between the train striking-in and its reaching the crossing is 27 s ([Health](#page-8-0) [and Safety Executive, 1996, p](#page-8-0)age 15). The best-known type of automatic crossing is the automatic half barrier (AHB), which has flashing lights and barriers covering only the approach side of the road. The reason for having only half barriers is to provide an escape route for any vehicle or person already on the crossing when the barriers fall. There are various other types of automatic crossing, including some with lights but no barriers.
+- (3) Passive crossings, including footpath crossings. Some of these are called 'user-worked' crossings in Britain. These crossings have no active warnings of the approach of trains, so that the safety of persons or vehicles crossing depends on their own vigilance and behaviour. Sometimes telephones are provided to enable users to phone the railway signaller to check that the line is clear. Passive crossings account for the great majority of level crossings: they are typically on private roads, on farms, or on footpaths. Many, but not all, are little used; some usage is seasonal or can change with land use.
+
+Almost all the crossings on public roads are either railwaycontrolled or automatic. They typically have much higher usage than passive crossings.
+
+[Table 1](#page-2-0) and Fig. 2 show the average numbers of crossings of each type on the main line railway system of Great Britain in 5-year
+
+<span id="page-2-0"></span>**Table 1** Average number of level crossings in 5-year periods: 1946–2009.
+
+| Period          | Railway controlled | Automatic | Passive | All    |
+|-----------------|--------------------|-----------|---------|--------|
+| 1946–1950       | 4148               |           | 22,902  | 27,050 |
+| 1951–1955       | 4186               |           | 22,124  | 26,310 |
+| 1956–1960       | 4360               |           | 20,298  | 24,658 |
+| 1961–1965       | 3823               | 14        | 19,225  | 23,062 |
+| 1966–1970       | 2036               | 220       | 12,884  | 15,141 |
+| 1971–1975       | 1635               | 307       | 9820    | 11,762 |
+| 1976–1980       | 1582               | 394       | 9004    | 10,980 |
+| 1981–1985       | 1325               | 523       | 8475    | 10,323 |
+| 1986–1990       | 1021               | 729       | 7379    | 9129   |
+| 1991–1995/96    | 930                | 779       | 7254    | 8963   |
+| 1996/97–2000/01 | 880                | 782       | 6656    | 8318   |
+| 2001/02–2005    | 865                | 800       | 6293    | 7958   |
+| 2006–2009       | 813                | 720       | 5144    | 6677   |
+
+**Table 2** Fatalities at level crossings: all railways: Great Britain: 1946–2009.
+
+| Period          | Pedestrians | Occupants of road vehicles | Railway staff | Railway passengers | All  |
+|-----------------|-------------|----------------------------|---------------|--------------------|------|
+| 1946–1950       | 126         | 78                         | 9             | 0                  | 213  |
+| 1951–1955       | 100         | 59                         | 1             | 0                  | 160  |
+| 1956–1960       | 70          | 59                         | 9             | 0                  | 138  |
+| 1961–1965       | 68          | 72                         | 4             | 0                  | 144  |
+| 1966–1970       | 45          | 52                         | 9             | 8                  | 114  |
+| 1971–1975       | 37          | 19                         | 3             | 0                  | 59   |
+| 1976–1980       | 37          | 25                         | 5             | 0                  | 67   |
+| 1981–1985       | 26          | 23                         | 0             | 0                  | 49   |
+| 1986–1990       | 40          | 33                         | 1             | 8                  | 82   |
+| 1991–1995/96    | 42          | 24                         | 0             | 0                  | 66   |
+| 1996/97–2000/01 | 41          | 10                         | 0             | 0                  | 51   |
+| 2001/02–2005    | 37          | 21                         | 3             | 5                  | 66   |
+| 2006–2009       | 31          | 12                         | 0             | 0                  | 43   |
+| 1946–2009       | 700         | 487                        | 44            | 21                 | 1252 |
+
+periods over the 64 years 1946–20091. There were about 27,050 in 1946–1950, and about 6680 in 2006–2009. The reduction is partly the result of long-term policies to eliminate crossings where possible, and partly because the national railway route length roughly halved during the period. The fastest reduction in the numbers of level crossings occurred in the late 1960s, when many railway routes were closed as a matter of policy [\(British Railways](#page-8-0) [Board, 1963\).](#page-8-0) The number of crossings per route-km was 0.85 in 1946–1950 and 0.42 in 2006–2009.
+
+Table 1 shows that in 1946–1950 all crossings were either railway-controlled or passive. Automatic crossings were not introduced into Great Britain until the early 1960s, although they were then fairly common elsewhere in Europe (see [Ministry of](#page-8-0) [Transport, 1968, S](#page-8-0)ection I; [Hall and Van der Mark, 2008\).](#page-8-0) The number of railway-controlled crossings steadily declined from about 4150 in 1946–1950 to 813 in 2006–2009. This was because of a mixture of crossing closures, line closures, and conversions of crossings to automatic. The remaining number of railway-controlled crossings in Britain is high by European standards, many countries having none ([Rail Safety and Standards Board, 2006\).](#page-8-0) It will be seen later that railway-controlled crossings are relatively safe, and that may partially account for the good safety record at level crossings in Britain. The number of automatic crossings grew from zero in 1956–1960 to 800 in 2001/02–2005, and fell back to 720 in 2006–2009. The number of passive crossings has steadily declined, from about 22,900 in 1946–1950 to 5140 in 2006–2009.
+
+# **3. Fatalities and fatal accidents at level crossings**<sup>2</sup>
+
+Fatalities to level crossing users and staff are classified and recorded by HMRI in the following four groups.
+
+- (1) Pedestrians
+- (2) Occupants of road vehicles
+- (3) Railway staff
+- (4) Railway passengers
+
+In this context railway passengers are those on board trains: people outside trains who are intending to travel or who have travelled are classified as pedestrians.
+
+Table 2 gives the numbers of fatalities at level crossings by 5 year period in each of these groups. There were a total of 1252 fatalities in the 64 years, an average 19.6 per year. Of these, 700 (56%) were pedestrians, 487 (39%) were occupants of road vehicles, including two-wheeled vehicles and farm vehicles, 44 (4%) were railway staff, and 21 (2%) were railway passengers. The railway passenger fatalities occurred in just three accidents—at Hixon in 1968, Lockington in 1986 and Ufton Nervet in 2004. The proportion of pedestrian fatalities in Britain may be relatively high by international standards; there are little data on this, but one international example is the USA, where only 18% of road user fatalities at level crossings were pedestrians in 2001 [\(Mok and Savage, 2005,](#page-8-0) page 868). That may be because of relatively less pedestrian activity in the USA.
+
+<sup>1</sup> In fact, as indicated by the row labels, Table 1 and later tables include 10 periods of 5 years, 1 period of 5¼years, 1 period of 4¾years and 1 period of 4 years. The¼ and ¾ years arise because HMRI switched its reporting period from calendar years up to 1990 to fiscal years (1 April to 31 March) from 1991/92 to 2003/04, and back to calendar years in 2005. The changing periods have been taken into account in the calculations of the paper.
+
+<sup>2</sup> It should be noted that there is a slight mismatch between the number of level crossings discussed in Section [2](#page-1-0) and the numbers of fatalities and fatal accidents in
+
+Section 3. The former are confined to the national rail system, but the latter cover all railways. There are a sizeable number of level crossings off the national system, but many of these are on heritage railways and are little used. A small number of the fatalities discussed in Section 3 were not on the national system. In the rest of the paper we disregard this distinction.
+
+<span id="page-3-0"></span>The HMRI annual reports do not explicitly give the numbers of fatal accidents at level crossings, as distinct from fatalities, but they do mention many individual accidents, especially those with more than one fatality. In a previous project, [Evans \(2003\)id](#page-8-0)entified all multiple-fatality accidents mentioned in HMRI reports, including those at level crossings. If one makes the assumption that all multiple-fatality accidents are explicitly mentioned, it is then possible to deduce the numbers of single-fatality accidents, and hence the total numbers of fatal accidents.
+
+[Table 3](#page-4-0) shows the results of doing this. The bottom line of [Table 3](#page-4-0) shows the distribution of fatalities in fatal level crossing accidents in Great Britain in 1946–2009: there were 76 accidents with more than one fatality, from which it is deduced that there were 1029 single-fatality accidents and 1105 fatal accidents overall. This implies that the mean number of fatalities per fatal accident was 1.133. The worst accident was in 1947 at Burton Agnes level crossing, on the Hull–Scarborough line, when a train struck an army lorry, with 12 fatalities in the lorry. The second worst accident was in 1968 at Hixon level crossing, on the Colwich–Stoke-on-Trent line, when a train struck a slow-moving road transporter loaded with an electrical transformer, leading to 11 fatalities on the train.
+
+Multiple-fatality accidents may have fatalities to people in more than one of the four categories above: for example, an accident may cause fatalities both to occupants of road vehicles and to staff or passengers on trains. However, it happens that there have been no accidents in which there were fatalities both to pedestrians and to people in other categories. This makes it possible unambiguously to divide accidents into those with pedestrian fatalities and those with other fatalities, labelled henceforth as 'pedestrian' and 'nonpedestrian' accidents. The great majority of the fatalities of the nonpedestrian accidents are occupants of vehicles (road or rail), but these accidents also include a small number of fatalities to railway staff struck by trains while manually operating gates, especially in the early years. [Table 3](#page-4-0) shows the distribution of fatalities in the two classes of accident. Almost all the pedestrian accidents were singlefatality, and all the most serious accidents were non-pedestrian. Of all fatal accidents, 692 (63%) were pedestrian and 413 (37%) were non-pedestrian.
+
+[Table 4](#page-4-0) shows the numbers of pedestrian and non-pedestrian accidents at each of the three types of crossing in 5-year periods from 1946 to 2009. The right-hand panel of [Table 4](#page-4-0) shows that the total numbers of accidents per year in both categories fell in the first 30 years 1946–1975, but did not fall much in 1976–2009. The overall numbers of accidents per year are plotted in [Fig. 4](#page-6-0) (below).
+
+[Table 5](#page-4-0) gives the number of fatal accidents at each type of crossing per year per 1000 crossings. It can be seen that the overall fatal accident rate has not changed very much over time from its long-term average of 1.17 accidents per year per 1000 crossings. The accident rate at railway-controlled crossings has fallen; that at passive crossings has remained more or less constant at about 0.9 accidents per year per 1000 crossings; that at automatic crossings is both higher and, if anything, rising over time. Fig. 3 shows the data points for each type of crossing.
+
+#### **4. Analysis**
+
+The analysis in this paper considers fatal accident rates per 1000 crossings per year and trends in these over time by level crossing type and accident type (pedestrian and non-pedestrian). The analysis does not aim to estimate risks at individual crossings, for which various models have been developed, including [Austin and](#page-8-0) [Carson \(2002\)](#page-8-0) for the United States and the All Level Crossing Risk Model (ALCRM) ([Rail Safety and Standards Board, 2010\)](#page-8-0) for Great Britain. These models are used for informing decisions about which level crossings should be upgraded. The ALCRM has some 200 input
+
+![](_page_3_Figure_9.jpeg)
+
+**Fig. 3.** Fatal accidents per 1000 crossings: 1946–2009.
+
+variables, including the numbers of trains, road vehicles and pedestrians using the crossing per day.
+
+For this paper we have little data on the usage of crossings, and in any case usage varies greatly from one crossing to another. Nevertheless, in interpreting the results, it is useful to be aware that usage systematically varies between crossing types. The Rail Safety and Standards Board [\(RSSB, 2004,](#page-8-0) [Table 4\)](#page-4-0) gives some useful information on average crossing usage by crossing type, excluding footpath crossings. Their data suggest that for railway-controlled crossings, the average number of trains per day is about 70, the average number of road vehicle users is about 1200 and the average number of pedestrians is about 160. For automatic crossings, the average number of trains per day is about 60, the average number of road vehicle users is about 1000 and the average number of pedestrians is about 80. After making reasonable guesses of the amount of footpath use, the average number of trains at passive crossings is about 55 per day, the average number of road vehicle users is only about 4, and the average number of pedestrians is about 25. Therefore, the most marked difference in usage is between controlled and automatic crossings on one hand, with an average of 1000–1200 road vehicles per day and passive crossings on the other hand, with only 4 road vehicles per day. This is a reflection of the fact that controlled and automatic crossings are generally on public roads, whereas passive crossings are generally on private roads, farms, and footpaths. Passive crossings have low numbers of fatal accidents per crossing per year, as shown in Fig. 3, but their low usage implies that they have the highest risk per road vehicle-traverse.
+
+In order to model accident trends by crossing type and accident type, we have fitted the following model to the data in [Table 4.](#page-4-0)
+
+$$y_{ijt} = \alpha_{ij}c_{it} \exp(\beta_{ij}t) \tag{1}$$
+
+where yijt is the mean number of accidents of type j per year at crossings of type i in year t (measured with 1966 = 0); (i = 1, 2, 3; j = 1, 2). cit is the number of crossings of type i in year t; ˛ij are parameters measuring the mean number of accidents of type j per year at crossings of type i in year 0. ˇij are parameters measuring the annual proportionate rate of change in the number of accidents of type j per crossing per year at crossings of type i.
+
+The model assumes that the mean numbers of fatal accidents at crossings of each type are directly proportional to the numbers of crossings of that type, cit. Following [Mok and Savage \(2005\), w](#page-8-0)e have also investigated fitting the model with accidents assumed proportional to a power of cit, not necessarily equal to 1. However, for no type of crossing or type of accident was the power significantly different from 1, so we have retained direct proportionality.
+
+<span id="page-4-0"></span>**Table 3** Distributions of fatalities in fatal level crossing accidents: Great Britain: 1946–2009.
+
+|                          | Number of accidents with given number of fatalities |    |    |   |   |   |   |   |   |    |    | Fatalities | Fatalities/accident |      |       |
+|--------------------------|-----------------------------------------------------|----|----|---|---|---|---|---|---|----|----|------------|---------------------|------|-------|
+|                          | 1                                                   | 2  | 3  | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12         | All                 |      |       |
+| Pedestrian accidents     | 685                                                 | 6  | 1  |   |   |   |   |   |   |    |    |            | 692                 | 700  | 1.012 |
+| Non-pedestrian accidents | 344                                                 | 43 | 15 | 3 | 1 | 3 |   |   | 1 | 1  | 1  | 1          | 413                 | 552  | 1.337 |
+| All accidents            | 1029                                                | 49 | 16 | 3 | 1 | 3 | 0 | 0 | 1 | 1  | 1  | 1          | 1105                | 1252 | 1.133 |
+
+**Table 4** Fatal accidents at level crossings: all railways: Great Britain: 1946–2009.
+
+| Period          |     | Railway controlled |     |     | Automatic |     |     | Passive |     |     | All crossings |      |  |
+|-----------------|-----|--------------------|-----|-----|-----------|-----|-----|---------|-----|-----|---------------|------|--|
+|                 | Ped | Nped               | All | Ped | Nped      | All | Ped | Nped    | All | Ped | Nped          | All  |  |
+| 1946–1950       | 47  | 25                 | 72  | 0   | 0         | 0   | 79  | 28      | 107 | 126 | 53            | 179  |  |
+| 1951–1955       | 35  | 9                  | 44  | 0   | 0         | 0   | 65  | 41      | 106 | 100 | 50            | 150  |  |
+| 1956–1960       | 17  | 17                 | 34  | 0   | 0         | 0   | 53  | 38      | 91  | 70  | 55            | 125  |  |
+| 1961–1965       | 26  | 15                 | 41  | 0   | 0         | 0   | 42  | 41      | 83  | 68  | 56            | 124  |  |
+| 1966–1970       | 12  | 7                  | 19  | 0   | 4         | 4   | 32  | 36      | 68  | 44  | 47            | 91   |  |
+| 1971–1975       | 11  | 5                  | 16  | 4   | 0         | 4   | 22  | 12      | 34  | 37  | 17            | 54   |  |
+| 1976–1980       | 7   | 6                  | 13  | 1   | 7         | 8   | 29  | 13      | 42  | 37  | 26            | 63   |  |
+| 1981–1985       | 2   | 2                  | 4   | 3   | 11        | 14  | 21  | 7       | 28  | 26  | 20            | 46   |  |
+| 1986–1990       | 1   | 1                  | 2   | 9   | 21        | 30  | 27  | 8       | 35  | 37  | 30            | 67   |  |
+| 1991–1995/96    | 3   | 0                  | 3   | 10  | 12        | 22  | 29  | 7       | 36  | 42  | 19            | 61   |  |
+| 1996/97–2000/01 | 4   | 0                  | 4   | 8   | 7         | 15  | 27  | 3       | 30  | 39  | 10            | 49   |  |
+| 2001/02–2005    | 5   | 0                  | 5   | 15  | 15        | 30  | 16  | 6       | 22  | 36  | 21            | 57   |  |
+| 2006–2009       | 3   | 0                  | 3   | 9   | 8         | 17  | 18  | 1       | 19  | 30  | 9             | 39   |  |
+| 1946–2009       | 173 | 87                 | 260 | 59  | 85        | 144 | 460 | 241     | 701 | 692 | 413           | 1105 |  |
+
+Ped = accidents involving fatalities only to pedestrians.
+
+Nped = accidents involving fatalities only to other classes of person.
+
+**Table 5** Fatal accidents per year per 1000 crossings: Great Britain: 1946–2009.
+
+| Period          | Railway-controlled | Automatic | Passive crossings | All  |
+|-----------------|--------------------|-----------|-------------------|------|
+| 1946–1950       | 3.47               |           | 0.93              | 1.32 |
+| 1951–1955       | 2.10               |           | 0.96              | 1.14 |
+| 1956–1960       | 1.56               |           | 0.90              | 1.01 |
+| 1961–1965       | 2.15               | 0.00      | 0.86              | 1.08 |
+| 1966–1970       | 1.87               | 3.63      | 1.06              | 1.20 |
+| 1971–1975       | 1.96               | 2.60      | 0.69              | 0.92 |
+| 1976–1980       | 1.64               | 4.06      | 0.93              | 1.15 |
+| 1981–1985       | 0.60               | 5.35      | 0.66              | 0.89 |
+| 1986–1990       | 0.37               | 7.83      | 0.90              | 1.40 |
+| 1991–1995/96    | 0.65               | 5.65      | 0.99              | 1.36 |
+| 1996/67–2000/01 | 0.91               | 3.84      | 0.90              | 1.18 |
+| 2001/02–2005    | 1.22               | 7.89      | 0.74              | 1.51 |
+| 2006–2009       | 0.92               | 5.91      | 0.92              | 1.46 |
+| 1946–2009       | 1.89               | 5.62      | 0.90              | 1.17 |
+
+This differs from Mok and Savage, who found powers of less than 1 in the USA.
+
+The results in this paper are based on the assumption that the accident data are Poisson-distributed, though because the data are 'overdispersed' for the Poisson distribution we have also explored the use of the negative binomial distribution. [Appendix A](#page-7-0) gives results for the negative binomial corresponding to those given in this section for the Poisson distribution. The use of the negative binomial distribution makes no difference to the results of the statistical tests, and only small differences to the parameter estimates.
+
+In fitting the model, we have assumed that all the ˛ijs are different, with no particular structure. We then explore the structure of the trend parameters ˇ: in particular we explore whether the trend parameters are different for the different types of crossing and accidents. [Table 6](#page-5-0) gives the main statistical results and test statistics for variants of the model used for estimating these trends. Model variant (a) assumes that the trend ˇ is zero for all types of crossings and accidents; variant (b) assumes a common non-zero ˇ for all types of crossing and accidents; variant (c) assumes differentˇs for different accident types but not for different crossing types (ˇ1<sup>j</sup> =ˇ2<sup>j</sup> =ˇ3j); variant (d) assumes different ˇs for different crossing types but not for different accident types (ˇi<sup>1</sup> =ˇi2); variant (e) assumes that all six ˇs are different.
+
+The scaled deviance in [Table 6](#page-5-0) is the measure of goodness of fit of the model variants to the data; a large scaled deviance indicates a poor fit. If the data are indeed generated in the way presumed in the model (that is Poisson-distributed with a time-dependent mean), the scaled deviance would be approximately -2-distributed with mean equal to the number of degrees of freedom. It can be seen that the fit is not good for any of the variants: the data are 'overdispersed'. To test whether one model variant fits the data significantly better than another, we compare the difference in the scaled deviances of the two variants with the -2-distribution with degrees of freedom equal to the difference in degrees of freedom between the variants. For example, variant (e) fits significantly better than variant (d) because the reduction in the scaled deviance of 20.0 in moving from (d) to (e) is larger even than the upper 0.1% point of the -2-distribution with 3 degrees of freedom (which is 16.27). On the basis of such tests, variant (e) is significantly the best-fitting model, indicating that the trends are different for
+
+<span id="page-5-0"></span>**Table 6** Statistical results from fitting Poisson log-linear models to the accident data.
+
+| Variant of model                                       | Degrees of freedom | Scaled deviance | Estimate of trend parameter (standard error in brackets)                                                                                                                                                                                                                                                                                                                                   |
+|--------------------------------------------------------|--------------------|-----------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
+| (a) No trend                                           | 66                 | 171.4           | Assumed zero for all types of crossing and accidents                                                                                                                                                                                                                                                                                                                                       |
+| (b) Common trend                                       | 65                 | 162.2           | −0.57% (0.19%) p.a. for all types of crossing and accidents                                                                                                                                                                                                                                                                                                                                |
+| (c) Separate trends for accident types                 | 64                 | 147.6           | −0.05% (0.23%) p.a. for pedestrian accidents<br>−1.59% (0.33%) p.a. for non-pedestrian accidents                                                                                                                                                                                                                                                                                           |
+| (d) Separate trends for LC types                       | 63                 | 132.2           | −2.58% (0.47%) p.a. for railway-controlled crossings<br>+1.34% (0.77%) p.a. for automatic crossings<br>−0.19% (0.22%) p.a. for passive crossings                                                                                                                                                                                                                                           |
+| (e) Separate trends for LC types and<br>accident types | 60                 | 112.2           | −2.17% (0.55%) p.a. for pedestrians at controlled crossings<br>−3.50% (0.89%) p.a. for non-pedestrians at controlled crossings<br>+3.49% (1.30%) p.a. for pedestrians at automatic crossings<br>+0.00% (0.97%) p.a. for non-pedestrians at automatic crossings<br>+0.37% (0.26%) p.a. for pedestrians at passive crossings<br>−1.39% (0.41%) p.a. for non-pedestrians at passive crossings |
+
+each combination of crossing type and accident type. In the work below we adopt model (e), and estimate the mean numbers of accidents per crossing as the sum of those to pedestrians and nonpedestrians.
+
+Conclusions from the modelling in Table 6 on the trends in fatal accidents per crossing per year are the following.
+
+- Taken together, fatal accidents per crossing per year show a significant downward trend, but the trend is small, especially compared with other long-term improvements in rail safety (see, for example, [Evans, 2007\).](#page-8-0)
+- The trend for pedestrian accidents per crossing per year taken together is significantly worse than that for non-pedestrian (mostly road vehicle) accidents
+- The trend in accidents per crossing per year is significantly downward at railway-controlled crossings, about flat at passive crossings, and non-significantly upward (as well as higher) at automatic crossings.
+
+[Fig. 3](#page-3-0) plots the modelled and observed numbers of fatal accidents per crossing per year by type of crossing. The observed data are from [Table 5.](#page-4-0) The modelled curves are the sum of those for pedestrian and non-pedestrian accidents from model variant (e). The figure clearly illustrates the different trends for the different types of crossing.
+
+The following are plausible explanations for the different levels and trends in fatal accidents per crossing per year.
+
+- On railway-controlled crossings, the accident rates have declined. This may be first because the methods operating crossings have improved: in particular, barriers have replaced many gates, some of which require staff to go on to the tracks. Secondly, the protection offered by the railway signalling systems, which are interlocked with the crossings, has improved, just as railway signalling has improved generally.
+- On automatic crossings accident rates are higher than on railwaycontrolled crossings and have not declined, even though the average crossing usage is broadly similar. Accidents rates are higher because the primary responsibility for the safe operation of automatic crossings rests with road users in observing the warnings indicating approaching trains. Furthermore, if there is a mishap, such as a road vehicle stalling or a pedestrian falling on the crossing, the users are not protected by the railway signals as they are at railway-controlled crossings.
+- The safe operation of passive crossings also depends on the vigilance and use of correct procedures by road and footpath users. However, their accident rate per crossing is much lower than for automatic crossings, primarily because, not being on public roads, their usage is lower. However, their accident rate has not declined: it is a remarkable empirical finding in [Fig. 3](#page-3-0) and
+
+[Table 5](#page-4-0) that the fatal accident rate has remained about constant at about 0.9 per 1000 passive crossings over the whole period of 64 years, despite investigations to improve them ([Rail Accident](#page-8-0) [Investigation Branch, 2009\).](#page-8-0)
+
+As an extension to fitting model (1) to the accident data, we explored adding further explanatory variables to supplement or replace the time trend. Variables tested were train-kilometres per route-kilometre (as an indicator of the intensity of trains), road motor vehicle-kilometres (as an indicator of the intensity of road traffic), and road fatalities per year (as an indicator of general road safety performance). We have not found convincing relationships between accidents per crossing and these variables. Some reasons may be the following. First, as noted above and shown in [Fig. 3,](#page-3-0) the safety performance and trends of the different crossing types have been different, so one might not expect accidents per crossing to be well modelled by general variables such as those above. Secondly, a majority of the level crossing accidents are to pedestrians, but variables related to traffic and road accidents are dominated by motor vehicles. Thirdly, there is an interesting argument put forward by [Stott \(1987\)](#page-8-0) and again by [Heavisides and Barker \(2008\)](#page-8-0) and by [RSSB \(2010\)](#page-8-0) that one should not expect a linear relationship between motor vehicle accidents and road traffic flow at automatic level crossings. Rather, the relationship is gamma-shaped, in which accidents rise linearly with traffic at low flows, but then reach a maximum and fall off at higher flows. This is because after a train has initiated the crossing sequence, at high road traffic flows the first road vehicle to arrive is likely to arrive before the train; it then stops and its presence to some degree protects later road vehicles against colliding with the train. At lower road traffic flows, it is more likely that the first vehicle arrives at the same time as the train, with greater risk of collision.
+
+## **5. Mean accidents and fatalities per year**
+
+[Fig. 4](#page-6-0) plots the results of combining the modelled trends in accidents per crossing from [Fig. 3](#page-3-0) with the numbers of crossings in [Table 1](#page-2-0) and [Fig. 1](#page-1-0) to give the modelled trends in fatal accidents per year by type of crossing and in total. [Fig. 4](#page-6-0) also shows the overall observed numbers of fatal accidents per year from the data in [Table 4.](#page-4-0)
+
+[Table 7](#page-6-0) shows modelled trends, accident rates per thousand crossings, numbers of crossings, modelled numbers of accidents, and estimated fatalities in 2009. The estimated numbers of fatalities per fatal accident are assumed to be different for the two types of accident, and constant over time. They are taken from [Table 3.](#page-4-0)
+
+Conclusions from [Fig. 4](#page-6-0) and [Table 7](#page-6-0) are the following.
+
+• The estimated mean numbers of fatal accidents and fatalities at level crossings in 2009 were 10.0 and 11.2, respectively. (The
+
+<span id="page-6-0"></span>**Table 7** Modelled fatal accidents and fatalities: Great Britain 2009.
+
+| Type of crossing                    | Type of fatal<br>accident           | Average rate of<br>change in fatal<br>accidents per<br>crossing | Estimated mean<br>fatal accidents per<br>1000 crossings<br>2009 | Number of<br>crossings 2009 | Estimated mean<br>fatal accidents per<br>year 2009 | Fatalities per fatal<br>accident | Estimated mean<br>fatalities per year<br>2009 |
+|-------------------------------------|-------------------------------------|-----------------------------------------------------------------|-----------------------------------------------------------------|-----------------------------|----------------------------------------------------|----------------------------------|-----------------------------------------------|
+| Railway controlled                  | Pedestrian                          | −2.2% p.a.                                                      | 0.47                                                            | 808                         | 0.38                                               | 1.01                             | 0.39                                          |
+| Railway controlled                  | Non-pedestrian                      | −3.5% p.a.                                                      | 0.13                                                            | 808                         | 0.10                                               | 1.34                             | 0.14                                          |
+| Railway controlled                  | All                                 |                                                                 |                                                                 |                             | 0.48                                               |                                  | 0.52                                          |
+| Automatic                           | Pedestrian                          | +3.5% p.a.                                                      | 3.92                                                            | 717                         | 2.81                                               | 1.01                             | 2.84                                          |
+| Automatic                           | Non-pedestrian                      | 0.0% p.a.                                                       | 3.32                                                            | 717                         | 2.38                                               | 1.34                             | 3.18                                          |
+| Automatic                           | All                                 |                                                                 |                                                                 |                             | 5.19                                               |                                  | 6.03                                          |
+| Passive                             | Pedestrian                          | +0.4% p.a.                                                      | 0.68                                                            | 5067                        | 3.44                                               | 1.01                             | 3.49                                          |
+| Passive                             | Non-pedestrian                      | −1.4% p.a.                                                      | 0.17                                                            | 5067                        | 0.87                                               | 1.34                             | 1.16                                          |
+| Passive                             | All                                 |                                                                 |                                                                 |                             | 4.31                                               |                                  | 4.64                                          |
+| All types<br>All types<br>All types | Pedestrian<br>Non-pedestrian<br>All |                                                                 |                                                                 | 6592<br>6592                | 6.64<br>3.35<br>9.99                               | 1.01<br>1.34                     | 6.72<br>4.47<br>11.19                         |
+
+![](_page_6_Figure_4.jpeg)
+
+**Fig. 4.** Fatal accidents per year at level crossings: 1946–2009.
+
+actual numbers in that year were 11 and 13, respectively, but there is considerable variation from year to year.)
+
+- At railway-controlled crossings the number of fatal accidents per year has fallen greatly over the long term, and had reached low levels in 2009. The fall is partly because the number of such crossings has fallen (shown in[Table 1an](#page-2-0)d[Fig. 2\),](#page-1-0) and partly because the accident rate has fallen (shown in [Fig. 3](#page-3-0) and discussed in Section [4\).](#page-3-0) Railway-controlled crossings are estimated to have accounted for a mean of only about 5% of level crossing fatal accidents and fatalities in 2009. Most of these are pedestrians.
+- At automatic level crossings the number of fatal accidents per year has risen over the long term. This is partly because of the increase in the numbers of such crossings since their introduction in the early 1960s, and partly because their accident rate has been rising for pedestrians. As shown in [Fig. 3, t](#page-3-0)heir accident rate per crossing is higher than for the other types of crossing. In 2009, automatic crossings accounted for means of 52% of fatal accidents and 54% of fatalities at level crossings.
+- At passive crossings (including footpath crossings), the number of fatal accidents per year has fallen over the long term. This is entirely due to the fall in the numbers of such crossings. Their mean accident rate remained remarkably constant at rather less
+
+**Table 8** Fatal accidents and fatalities at automatic level crossings and signalised road intersections: Great Britain 2005.
+
+|                                                                        | Road   | Rail |
+|------------------------------------------------------------------------|--------|------|
+| Estimated number of signalised<br>intersections/automatic<br>crossings | 14,300 | 762  |
+| Number of fatal accidents 2005                                         | 121    | 5.13 |
+| Number of fatalities 2005                                              | 126    | 6.01 |
+| Fatal accidents per 1000<br>intersections/crossings                    | 8.5    | 6.7  |
+| Fatalities per 1000<br>intersections/crossings                         | 8.8    | 7.9  |
+
+than 1 per 1000 crossings per year, the majority being pedestrian accidents. Although their accident rate is low, the large number of passive crossings means that they accounted for a substantial proportion of all accidents in 2009: 43% of fatal accidents and 41% of fatalities.
+
+• The above counteracting trends for the different crossing types mean that, as shown in Fig. 4, the total numbers of fatal accidents at level crossings have remained almost unchanged for about 30 years at a mean of about 11 per year.
+
+It follows that the principal reason why the number of fatal accidents has not declined since the early 1970s is the replacement of railway controlled by automatic crossings. However, it does not follow that this was a mistake, because automatic crossings have a number of important advantages over railway-controlled ones, which are generally the main alternative. The main advantages of automatic crossings are the following.
+
+- They need no staff to operate them.
+- They have much shorter cycle times than railway-controlled crossings, and thus cause less delay and capacity loss to road traffic. That is because railway-controlled crossings are interlocked with the signals. If a train is to run under clear signals, the time interval between the closure of the crossing to the road for an approaching train and the arrival of the train at the crossing is much longer for railway-controlled crossings than for automatic crossings. Thus the delay and the road capacity reduction at railway-controlled level crossings may be substantial.
+
+<span id="page-7-0"></span>**Table 9** Statistical results from fitting negative binomial log-linear models to the accident data.
+
+| Variant of model                       | Degrees of freedom | Difference in −2LLa from (a) | Estimate of trend parameter (standard error in brackets)        |
+|----------------------------------------|--------------------|------------------------------|-----------------------------------------------------------------|
+| (a) No trend                           | 66                 | 0                            | Assumed zero for all types of crossing and accidents            |
+| (b) Common trend                       | 65                 | −7.2                         | −0.80% (0.30%) p.a. for all types of crossing and accidents     |
+| (c) Separate trends for accident types | 64                 | −18.2                        | −0.03% (0.35%) p.a. for pedestrian accidents                    |
+|                                        |                    |                              | −2.01% (0.48%) p.a. for non-pedestrian accidents                |
+| (d) Separate trends for LC types       | 63                 | −24.9                        | −2.50% (0.56%) p.a. for railway-controlled crossings            |
+|                                        |                    |                              | +1.55% (0.91%) p.a. for automatic crossings                     |
+|                                        |                    |                              | −0.33% (0.33%) p.a. for passive crossings                       |
+| (e) Separate trends for LC types and   | 60                 | −42.2                        | −1.95% (0.63%) p.a. for pedestrians at controlled crossings     |
+| accident types                         |                    |                              | −3.68% (1.00%) p.a. for non-pedestrians at controlled crossings |
+|                                        |                    |                              | +3.53% (1.43%) p.a. for pedestrians at automatic crossings      |
+|                                        |                    |                              | +0.14% (1.10%) p.a. for non-pedestrians at automatic crossings  |
+|                                        |                    |                              | +0.49% (0.37%) p.a. for pedestrians at passive crossings        |
+|                                        |                    |                              | −1.75% (0.55%) p.a. for non-pedestrians at passive crossings    |
+
+<sup>a</sup> <sup>−</sup>2LL = minus twice the log likelihood.
+
+Thus a balance has to be struck between the benefits of railwaycontrolled crossings and those of automatic ones. Intermediate types of crossing are possible with modern technology. It is possible that the retention of a relative large number of railway-controlled crossings in Britain is a partial explanation for Britain's relatively good safety performance at level crossings.
+
+### **6. Comparison of accidents at automatic level crossings and signalised road junctions**
+
+There is evidence that a high proportion of level crossing accidents is associated with errors or violations by road users (for example, [RSSB, 2009\).](#page-8-0) This is not surprising, given that most level crossing accidents occur at automatic or passive crossings, where the primary responsibility for safe use rests with road users. Railway operators tend to have a poor view of road users' behaviour at level crossings, and this is backed up by some well-known video clips of very dangerous behaviour by road users. Nevertheless, it is not clear whether road user behaviour is worse on at level crossings than on the roads generally.
+
+This section presents a small piece of data to address this by comparing the fatal accident and fatality rates at automatic rail level crossings with their nearest road equivalent, signalised intersections. [Table 8](#page-6-0) gives data on the numbers of intersections/crossings, and fatal accidents and fatalities at these locations in Great Britain in 2005. The rail data are the modelled estimates of the means for 2005 from the fitted model in Section [4. T](#page-3-0)he road fatality data (121 fatal accidents; 126 fatalities) are taken from a special table produced for the writer by the Department of Transport (DfT) from the official road fatality data [\(DfT, annual\).](#page-8-0) The number of signalised road intersections is based on an estimate by the County Surveyors' Society of 12,300 in 2000, increased by 3% per year to 2005 (DfT, personal communication).
+
+The bottom two lines of [Table 8](#page-6-0) show that the estimated fatal accidents and fatalities per intersection or crossing were similar.
+
+#### **7. Conclusions**
+
+This paper investigates fatalities and fatal accidents at level crossings in Great Britain over the 64-year period 1946–2009. The numbers of fatal accidents and fatalities per year fell by about 65% in the first half of that period, but since then have remained more or less constant at about 11 fatal accidents and 12 fatalities per year. At the same time other types of railway fatality have fallen, so level crossings represent a growing proportion of the total. Nevertheless, Britain's level crossing safety performance remains good by international standards.
+
+The paper classifies level crossing types into three groups: railway-controlled, automatic, and passive. At the beginning of the period all crossings were either railway controlled or passive. Automatic crossings were not introduced into Britain until the early 1960s, replacing other types, but many railway-controlled crossings remain. As in most countries, by far the largest numbers of crossings are passive; most of these are not on public roads, but on private roads, farms, and footpaths. The total number of crossings has fallen by about 75% over the period, due partly to rail route closures and partly to closures of individual crossings, with or without replacement by bridges.
+
+The safety performance of the three types of crossings has been very different. Railway-controlled crossings are the best-performing crossing type, with falling fatal accident rates. Automatic crossings have higher accident rates per crossing than railway controlled or passive crossings, and the accident rates have not decreased. They have advantages over railway-controlled crossings on public roads in not needing staff and imposing less delay on road users. Nevertheless, they are less safe, so a balance has to be struck between safety, cost and delay. Passive crossings are by far the most numerous, but many have low usage by road users. Their fatal accident rate has remained remarkably constant over the whole period at about 0.9 fatal accidents per 1000 crossings per year.
+
+A principal reason why fatal accidents and fatalities have not fallen in the second half of the period as they did in the first half is the increase in the number of automatic crossings, replacing the safer railway controlled crossings on some public roads. However, it does not follow that this replacement was a mistake, because of the advantages of automatic crossings above.
+
+Based on the trends for each type of crossing and for pedestrian and non-pedestrian accidents separately, in 2009 means of 5% of fatal accidents were at railway controlled crossings, 52% were at automatic crossings, and 43% were at passive crossings. Fatalities had similar proportions. About 60% of fatalities were to pedestrians.
+
+A simple comparison of automatic railway level crossings and signalised road intersections found that in 2005 the numbers of fatalities per 1000 crossings or intersections were similar.
+
+### **Appendix A.**
+
+The results in Section [4](#page-3-0) of the paper are based on the assumption that the numbers of accidents are Poisson-distributed, even though they are 'overdispersed'. A common alternative to the Poisson distribution is to assume that the data have a negative binomial distribution. Table 9 gives results for the negative binomial distribution corresponding to those for the Poisson distribution in [Table 6. T](#page-5-0)here is no absolute measure of goodness of fit for the negative binomial distribution corresponding to the scaled deviance, but the differences in minus twice the log likelihoods between the model variants have the same properties as the differences
+
+0952 9.
+
+Railways, Paris.
+
+<span id="page-8-0"></span>in the scaled deviances. On this basis model variant (e) remains the best fitting variant, and all significance tests lead to the same conclusions. The right-hand column of [Table 9](#page-7-0) shows that the parameter estimates with the negative binomial are close to those with the Poisson distribution; the standard errors are somewhat larger.
+
+#### **References**
+
+7110 3308 0.
+
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+Health and Safety Executive, 1996. Railway Safety Principles and Guidance: Part 2, Section E: Guidance on level crossings. HS(G)153/6. HSE Books, ISBN:0 7176
+
+Heavisides, J., Barker, J., 2008. Impact of traffic flow on level crossing risk. In: Paper Presented at the 10th World level Crossing Symposium ,. International Union of
+
+- Mok, S.C., Savage, I., 2005.Why has safety improved at rail-highway grade crossings? Risk Analysis 25 (4), 867–879.
+- Rail Accident Investigation Branch, 2009. Investigation into safety at user worked crossings. Report 13/2009, RAIB, Derby, UK.
+- Rail Safety and Standards Board, 2004. Road vehicle level crossings special topic report. RSSB, London.
+- Rail Safety and Standards Board, 2006. The cost of level crossings—an international benchmarking exercise. Research Project T364, RSSB, London.
+- Rail Safety and Standards Board, 2009. Annual Safety Performance Report 2008. RSSB, London.
+- Rail Safety and Standards Board, 2010. Development of the All Level Crossing Risk Model: a History. Report prepared by A D Little. RSSB, London.
+- Stott, P.F., 1987. Automatic Open Level Crossings: A Review of Safety. Her Majesty's Stationery Office, London, ISBN:0 11 550831 7.

Zotero/001_artiklid/Road Safety Indicators/fucomparisonthresholddeterminationmethods2021.md

@@ -0,0 +1,408 @@
+---
+category: literaturenote
+citekey: fucomparisonthresholddeterminationmethods2021
+title: Comparison of threshold determination methods for the deceleration rate to avoid a crash (DRAC)-based crash estimation
+authors: "Fu, Chuanyun; Sayed, Tarek"
+year: 2021
+date: 2021-00-00 2021
+doi: 10.1016/j.aap.2021.106051
+publication: "Accident Analysis & Prevention"
+url: "https://doi.org/10.1016/j.aap.2021.106051"
+zotero_key: XPJ7HC4U
+zotero_storage: A845NAKI
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "Fu, Chuanyun"
+status: converted
+---
+![](_page_0_Picture_1.jpeg)
+
+Contents lists available at [ScienceDirect](www.sciencedirect.com/science/journal/00014575)
+
+# Accident Analysis and Prevention
+
+journal homepage: [www.elsevier.com/locate/aap](https://www.elsevier.com/locate/aap)
+
+![](_page_0_Picture_5.jpeg)
+
+# Comparison of threshold determination methods for the deceleration rate to avoid a crash (DRAC)-based crash estimation
+
+![](_page_0_Picture_7.jpeg)
+
+Chuanyun Fu a,b, \*, Tarek Sayed <sup>b</sup>
+
+- <sup>a</sup> *School of Transportation and Logistics, Southwest Jiaotong University, China* <sup>b</sup> *Department of Civil Engineering, The University of British Columbia, Canada*
+- ARTICLE INFO
+
+*Keywords:*  Traffic conflicts Crash estimation DRAC MADR Bayesian hierarchical framework Extreme value theory
+
+## ABSTRACT
+
+There is an increased interest in the use of traffic conflicts as a surrogate safety measure and several traffic conflict indicators have been developed. One of these indicators is the deceleration rate to avoid a crash (DRAC). Generally, the greater the DRAC value, the higher the crash risk and a crash would occur when the DRAC exceeds the maximum available deceleration rate (MADR). It is noted that the MADR varies considerably for individual vehicles and depends on many factors such as the pavement conditions, vehicle weight, tire, and the braking system. Previous studies usually either set a specific value for the MADR or randomly sample values from a truncated normal distribution of MADR. However, little is known about which threshold determination approach is better. Therefore, this study aims to compare the threshold determination approaches for DRAC-based crash estimation applying Bayesian hierarchical extreme value modeling. Using traffic conflict and crash data collected from four signalized intersections in the city of Surrey, several Bayesian hierarchical models are developed for five specific values of MADR and values from two truncated normal distributions of MADR. The crash frequencies estimated from these models were compared with observed crashes. The results show that, in terms of DRACbased crash estimation accuracy, the truncated normal distribution N(8.45, 1.4<sup>2</sup> )I(4.23, 12.68) of MADR outperforms other determination methods of MADR. Moreover, in terms of DRAC-based crash estimation accuracy and precision, the use of multisite Bayesian hierarchical models outperforms the at-site models. The truncated normal distribution N(8.45, 1.42 )I(4.23, 12.68) of MADR is therefore recommended for DRAC-based crash estimation.
+
+#### **1. Introduction**
+
+The problems associated with the use of crash data in road safety analysis are well-documented [\(Sayed and Zein, 1999\)](#page-8-0). There are quality and availability problems associated with crash data. As well, the use of crash data in safety analysis is a reactive approach. Crashes need to be observed over a prolonged time period to identify safety problems and to correct them. Therefore, the development of surrogate safety measures such as traffic conflicts for use in safety analysis has attracted considerable research interest. Compared to traffic crashes, traffic conflicts occur more frequently, can be easily observed, and provide better insight into the collision failure mechanism ([Sayed and Zein, 1999](#page-8-0)).
+
+Over the past decades, a number of traffic conflict indicators have been established and used in traffic safety analysis. Examples of most widely used conflict indicators include temporal and spatial proximity indicators and deceleration-based indicators. Several researchers have explicitly recognized the deceleration rate to avoid a crash (DRAC) as a useful surrogate safety measure [\(Archer, 2005](#page-8-0)). The DRAC is the rate at which a following vehicle must decelerate to avoid a collision with the leading vehicle ([Zheng and Sayed, 2019a](#page-9-0)). It is defined as the differential speed between a following vehicle and its leading vehicle divided by their closing time ([Cooper and Ferguson, 1976;](#page-8-0) [Gettman and Head,](#page-8-0)  [2003\)](#page-8-0). Compared to the other surrogate safety measures, such as time to collision (TTC) and the post encroachment time (PET), the DRAC has some advantages, since it could reflect the evasive action (e.g., required deceleration) of the following vehicle to come to a timely stop or reach the corresponding speed of the leading vehicle and thereby avoid a collision ([Cunto and Saccomanno, 2008](#page-8-0)).
+
+The greater the DRAC value the higher the crash risk, and a crash would occur if the DRAC exceeds the maximum available deceleration rate (MADR). Therefore, the crash risk based on DRAC can be calculated given a MADR. Since the MADR is unique for individual vehicles and
+
+<sup>\*</sup> Corresponding author at: School of Transportation and Logistics, Southwest Jiaotong University, China. *E-mail addresses:* [fcy1128@mail.ubc.ca](mailto:fcy1128@mail.ubc.ca) (C. Fu), [tsayed@civil.ubc.ca](mailto:tsayed@civil.ubc.ca) (T. Sayed).
+
+depends on pavement conditions, vehicle weight, tire and braking system, and other factors, it is usually assumed to follow a truncated normal distribution N(8.45, 1.4<sup>2</sup> ), with an upper limit of 12.68 m/s2 and a lower limit of 4.23 m/s2 ([Cunto and Saccomanno, 2008](#page-8-0)). Several studies have investigated the crash risk based on DRAC by mainly using the extreme value distribution (EVT) and the truncated normal distribution. The former treats the conflict extremes characterized by DRAC as a random variable, while the latter treats the MADR as a random variable. Additionally, a threshold needs to be developed to identify traffic conflict extremes for use in the establishment of the EVT model based on DRAC.
+
+Previous studies used different specific values for MADR to conduct DRAC-based traffic conflict safety evaluation. A value of 8 m/s2 for MADR was considered as a conservative value that all vehicles could reach in one previous study [\(Ceunynck, 2017\)](#page-8-0). [Wang et al. \(2019\)](#page-8-0)  employed the MADR values of 8 m/s2 and 12 m/s2 for crash estimation from the bivariate extreme value models, respectively. In the study by ([Zheng et al., 2019b](#page-9-0)), the mean value (i.e., 8.45 m/s<sup>2</sup> ) of the truncated normal distribution N(8.45, 1.42 )I(4.23, 12.68) of MADR was selected as the threshold for crash occurrence, which was applied to develop the bivariate extreme value models for crash estimation. It is noted that a specific value of MADR may lead to DRAC-based crash underestimation or overestimation at some sites. Therefore, [Zheng and Sayed \(2019a\)](#page-9-0)  used the values of DRAC sampled from the fitted extreme value distribution and the values of MADR sampled from a given truncated normal distribution N(8.45, 1.4<sup>2</sup> )I(4.23, 12.68) to calculate the DRAC-based crash risk. As well, [Fu et al. \(2020\)](#page-8-0) determined the values of MADR for DRAC-based crash estimation by sampling from the truncated normal distribution N(8.45, 1.4<sup>2</sup> )I(4.23, 12.68).
+
+In addition to the extreme value distribution, the truncated normal distribution is also used to estimate the crash risk based on DRAC. In other words, the MADR is regarded as a random variable and is assumed to follow a truncated normal distribution. The crash risk can be calculated as the probability of the MADR being less than the DRAC. [Meng](#page-8-0)  [and Weng \(2011\)](#page-8-0) evaluated the rear-end crash risk measured by DRAC at work zones. They assumed that the MADR of cars and trucks followed truncated normal distributions N(8.45, 1.4<sup>2</sup> )I(1.23, 12.68) and N(6.82, 1.4<sup>2</sup> )I(0.60, 10.05), respectively. This approach was also applied to investigate the work zone rear-end crash risk based on DRAC for different vehicle-following patterns ([Weng et al., 2014](#page-8-0)), assess the performance of two microscopic safety indices (i.e., DRAC and TTC) on safety evaluation for expressways [\(Qu et al., 2014](#page-8-0)), and explore the rear-end crash risk based on DRAC and TTC in work zone merging areas ([Weng et al., 2015](#page-8-0)). With the updated data of the braking performance of various automobiles, a new truncated normal distribution of MADR N (9.7, 1.3<sup>2</sup> )I(4.2, 12.7) was obtained ([Wang and Stamatiadis, 2013](#page-8-0), [2014\)](#page-8-0). The two studies employed the distribution of MADR to calculate the probability of MADR being less than the required braking rate to avoid a crash conditional on the reaction time being less than the TTC.
+
+The review of previous studies using DRAC in road safety analysis shows that limited research has been undertaken on selecting which threshold determination approach for DRAC-based traffic conflict analysis (i.e., setting specific values or distributions of MADR) would yield the best results in terms of accuracy and precision.
+
+Therefore, the objective of this study is to compare the threshold determination approaches for DRAC-based crash estimation in terms of accuracy and precision. For the comparison, a Bayesian hierarchical extreme value model that combines traffic conflict extremes from different sites, incorporates the impact of various covariates, and considers the unobserved site-specific heterogeneity is developed.
+
+The structure of this paper is organized as follows: Section 2 presents the data used in this study. Section 3 provides details of the proposed Bayesian hierarchical extreme value model, including the generalized extreme value model, the Bayesian hierarchical structure, the model estimation method, the model choice, and the crash estimation approach. The model estimation results, model comparisons, and variables interpretation are discussed in Section [4](#page-4-0). The last section, Section [5](#page-8-0), presents the conclusions of this study and the recommended future work.
+
+## **2. Data description**
+
+The data used for this study include video data and crash data. The video data were collected from four signalized intersections in the city of Surrey, British Columbia, Canada. They are the intersections of 72 Ave & 128 St, 72 Ave & 132 St, 64 Ave & King George Blvd, and Fraser Hwy & 168 St (see [Fig. 1](#page-2-0)).
+
+Video data were collected by cameras that focus on the approaches where most of rear-end conflicts occur. Computer vision techniques were applied to identify signal cycles, extract vehicle trajectories, and generate space-time diagram of vehicles from the video footages. The detailed video processing procedures are presented in ([Essa and Sayed,](#page-8-0)  [2018,](#page-8-0) [2019](#page-8-0)). The DRAC was then automatically calculated from the extracted vehicle trajectories. It is noted that the conflict indicator is computed continuously (i.e., frame by frame and one second = 30 frames) over time for an event, and the maximum value is selected for DRAC. For each pair of consecutive vehicles on the through lane, the DRAC could be acquired. Additionally, three traffic parameters at the signal cycle level were extracted from the space-time diagram, including: traffic volume (V, vehicles/lane/cycle) which is the number of vehicles per cycle on the studied lane; shock wave area (A, km s) which is a triangle area where it is the state II of classical four traffic flow states theory ([May, 1990\)](#page-8-0), as illustrated in [Fig. 2](#page-2-0); and platoon ratio (P) which is defined as the proportion of all vehicles arriving during green multiplied by the ratio of the signal cycle length to the effective green time of the subject movement [\(Highway Capacity Manual, 2000\)](#page-8-0).
+
+In this study, only DRAC was utilized to characterize traffic conflicts. It is calculated as ([Cooper and Ferguson, 1976](#page-8-0); [Gettman and Head,](#page-8-0)  [2003\)](#page-8-0):
+
+$$DRAC_{F,I} = \frac{\left(v_{F,I} - v_{L,I}\right)^2}{2\left(x_{L,I} - x_{F,I} - D_L\right)} \tag{1}$$
+
+where, *vF,t*and *vL,t*are speeds of following vehicle and leading vehicle at time *t*, respectively; *xF,t*and *xL,t*are positions of following vehicle and leading vehicle at time *t*, respectively; *DL* is the length of leading vehicle.
+
+It is noted that there may be zero or even no values of DRAC for a pair of consecutive vehicles. Therefore, only events with DRAC *>* 0 m/s2 were considered as candidate traffic conflicts for the following analysis. A total of 2202 events with DRAC values were obtained from 416 signal cycles, which is on average 5.3 events per cycle. The summary statistics of traffic conflict and crash data are shown in [Table 1.](#page-3-0)
+
+Three years of crash data (2013–2015) at the four signalized intersections in the city of Surrey, British Columbia was used. The data, provided by the Insurance Corporation of British Columbia, included the information such as location, date, time, crash type, and crash severity, among others. Since the crash data is used to assess the performance of the proposed model, only rear-end crashes that occurred in the through lanes at the target approaches were selected. Moreover, since rear-end conflicts were observed in the daytime period, only rear-end crashes happened during the daytime were kept. Eventually, a total of 43 rearend crashes remained, as presented in [Table 1.](#page-3-0)
+
+#### **3. Model development**
+
+# *3.1. Generalized extreme value model*
+
+In this study, the generalized extreme value (GEV) distribution is fitted based on the block maxima (BM) extremes. The observations are aggregated into fixed blocks, and the maxima of each block is treated as extreme ([Coles, 2001;](#page-8-0) [Zheng et al., 2018](#page-9-0)). Suppose that *X*1*, X*2*,* ⋯*, Xn* is a sequence of independent random variables having a common distribution function and *Mn* = max{*X*1*, X*2*,* ⋯*, Xn*} represents the block maxima.
+
+<span id="page-2-0"></span>![](_page_2_Picture_2.jpeg)
+
+**Fig. 1.** Study intersections and corresponding approaches.
+
+![](_page_2_Figure_4.jpeg)
+
+**Fig. 2.** Classical four different traffic flow states at signalized intersections.
+
+If there exist sequences of constants {*an >* 0} and {*bn*} such that
+
+$$\Pr\{(M_n - b_n)/a_n \le z\} = G(z) \text{ as } n \to \infty$$
+ (2)
+
+where, *G* is a non-degenerate distribution function. It is a member of GEV family [\(Coles, 2001\)](#page-8-0), which is given by:
+
+$$G(z) = exp\left\{ -\left[1 + \xi \frac{(z - \mu)}{\sigma}\right]^{-1/\xi} \right\}$$
+(3)
+
+defined on the set {*z* : 1 + *ξ*(*z* − *μ*)*/σ >* 0}, where *μ* is the location parameter, − ∞ *< μ <* ∞; *σ* is the scale parameter, *σ >* 0; *ξ* is the shape parameter, − ∞ *< ξ <* ∞.
+
+# *3.2. Bayesian hierarchical structure*
+
+A Bayesian hierarchical structure is developed for the univariate extreme value model, which has three layers: data layer, process layer, and prior layer [\(Zheng and Sayed, 2019b; Zheng et al., 2019a;](#page-9-0) [Fu et al.,](#page-8-0)  [2020;](#page-8-0) [Zheng and Sayed, 2020](#page-9-0)).
+
+## *3.2.1. Data layer*
+
+A GEV distribution given by Eq. (2) is employed to model the data at the first layer of hierarchy, which is
+
+$$G(z_{ij} < z; \mu_i, \sigma_i, \xi_i) = exp \left\{ -\left[1 + \xi_i \frac{(z - \mu_i)}{\sigma_i}\right]^{-1/\xi_i} \right\}$$
+(4)
+
+where, *zij* is the *j* th recorded block maxima at site *i*, with *i* = 1*,* 2*,* ⋯*, m*  and *j* = 1*,*2*,*⋯*,ni*; (*μ<sup>i</sup> , σi, ξi*) represent the parameters at site *i*. Given that *zij* corresponds to the block maxima, it can be depicted by the GEV distribution whose parameters are dependent on the site. To ensure a positive scale parameter, the *σ* is reparameterized as *ψ* = log*σ*. Therefore, the Eq. (4)
+
+can be rewritten as:
+
+$$G(z_{ij} < z; \mu_i, \sigma_i, \xi_i) = exp \left\{ -\left[1 + \xi_i \frac{(z - \mu_i)}{\exp(\psi_i)}\right]^{-1/\xi_i} \right\}$$
+ (5)
+
+<span id="page-3-0"></span>**Table 1**  Summary statistics of data.
+
+| Data information                         |                                 | 72 Ave &<br>128 St                           | 72 Ave &<br>132 St                | 64 Ave &<br>King<br>George<br>Blvd | Fraser<br>Hwy &<br>168 St            |
+|------------------------------------------|---------------------------------|----------------------------------------------|-----------------------------------|------------------------------------|--------------------------------------|
+| Video was recorded in                    |                                 | March 28,<br>2012<br>(10− 12 am;<br>2− 4 pm) | April 3,<br>2012<br>(9− 12<br>am) | June 10,<br>2015 (1− 5<br>pm)      | June 10,<br>2015 (9<br>am − 1<br>pm) |
+| Number of cycles                         |                                 | 130                                          | 72                                | 103                                | 111                                  |
+|                                          |                                 | 928                                          | 303                               | 436                                | 535                                  |
+| Event counts<br>DRAC value<br>(m/s2<br>) | Mean<br>Min<br>Max              | 2.05<br>0.00<br>7.10                         | 1.81<br>0.16<br>6.38              | 2.41<br>0.01<br>5.98               | 2.60<br>0.06<br>6.70                 |
+| V (vehicle                               | Mean                            | 13.52                                        | 13.43                             | 11.62                              | 13.71                                |
+| count per                                | Min                             | 2                                            | 7                                 | 4                                  | 3                                    |
+| cycle)                                   | Max                             | 28                                           | 25                                | 18                                 | 23                                   |
+| A (km⋅s)                                 | Mean                            | 1.38                                         | 0.96                              | 1.19                               | 1.10                                 |
+|                                          | Min                             | 0.00                                         | 0.00                              | 0.00                               | 0.00                                 |
+|                                          | Max                             | 4.45                                         | 2.90                              | 3.03                               | 5.66                                 |
+| P                                        | Mean                            | 1.10                                         | 1.07                              | 1.40                               | 1.12                                 |
+|                                          | Min                             | 0                                            | 0.14                              | 0.00                               | 0.32                                 |
+|                                          | Max                             | 1.88                                         | 1.72                              | 2.11                               | 1.75                                 |
+| Observed<br>crashes                      | 2013<br>2014<br>2015<br>Average | 8<br>3<br>3<br>4.7                           | 0<br>1<br>0<br>0.3                | 9<br>7<br>2<br>6.0                 | 4<br>3<br>3<br>3.3                   |
+
+#### *3.2.2. Process layer*
+
+A latent Gaussian process underlying extremes is characterized through developing a structure that connects the parameters in the data layer with certain covariates. The identity link function is used to build the connection. It is noted that since it is hard to precisely estimate the shape parameter *ξ* of GEV distribution, it is not possible to model *ξ* as a smooth function of certain covariates. Hence, the shape parameter *ξ* is hypothesized to be unknown but not influenced by covariates during the process [\(Coles, 2001](#page-8-0); [Cooley et al., 2006\)](#page-8-0). As such, the GEV distribution parameter can be expressed as:
+
+$$\begin{cases} \mu_i = \beta_{\mu 0} + \beta_{\mu} \mathbf{X} \\ \psi_i = \beta_{\mu 0} + \beta_{\psi} \mathbf{X} \\ \xi_i = \beta_{20} \end{cases}$$
+
+$$\tag{6}$$
+
+where, *βμ*0, *βψ*0, and *βξ*0 are intercepts; **X** is the vector of covariates; **β***<sup>μ</sup>* and **β***ψ*are the vectors of estimated parameters of covariates. In fact, there usually seems to be additional heterogeneity that is not directly addressed by covariates. In order to capture the additional unobserved heterogeneity, random error terms are also introduced as:
+
+$$\begin{cases} \mu_{i} = \beta_{\mu 0} + \beta_{\mu} \mathbf{X} + \varepsilon_{\mu i} \\ \psi_{i} = \beta_{\psi 0} + \beta_{\psi} \mathbf{X} + \varepsilon_{\psi i} \\ \xi_{i} = \beta_{20} + \varepsilon_{\xi i} \end{cases}$$
+(7)
+
+where, *εμi*, *εψi*, and *εξi* are random effects reflecting between-site variation, which are consistent for extremes in the same site but vary between different sites. Therefore, the model for the process layer can be expressed in the following form of a random intercept:
+
+$$\begin{cases} \mu_{i} = \beta_{\mu i} + \beta_{\mu} \mathbf{X} \\ \psi_{i} = \beta_{\psi i} + \beta_{\psi} \mathbf{X} \\ \xi_{i} = \beta_{\xi i} \end{cases}$$
+(8)
+
+where, *βμi*, *βψi*, and *βξi*are site-specific random intercepts.
+
+#### *3.2.3. Prior layer*
+
+In this layer, priors are assigned to site-specific random intercepts and the estimated parameters of covariates for characterizing the latent process. It is hypothesized that each parameter in this layer is independent to the others. Due to no available prior information regarding how the parameters of GEV distribution are associated with covariates, uninformative priors for these parameters, i.e., {*βμi*, *βψi*, **β***μ*, **β***<sup>ψ</sup>* }, are adopted. They are hypothesized to be normally distributed with zero mean and large variance, i.e., *N*(0*,*106). It is worth noting that the GEV model is sensitive to its shape parameter, so an improper defined prior would lead to a convergence issue during the model estimation. According to the previous road safety studies such as [\(Songchitruksa and](#page-8-0)  [Tarko, 2006\)](#page-8-0) and ([Zheng et al., 2014](#page-9-0)), the estimated shape parameters are usually within the range of (-1.0, 1.0). Therefore, the priors for shape parameters are assumed to follow a uniform distribution, i.e., Unif(-1.0, 1.0).
+
+## *3.3. Model estimation method*
+
+In the above-mentioned three-layer hierarchical model, according to the Bayes theorem, the posterior inference for the univariate Bayesian hierarchical extreme value model parameters **θ** given the data **Ω** is
+
+$$p(\mathbf{\theta}|\mathbf{\Omega}) \propto \underbrace{p_1(\mathbf{\Omega}|\mathbf{\theta}_1) p_2(\mathbf{\theta}_1|\mathbf{\theta}_2) p_3(\mathbf{\theta}_2)}_{Data} \underbrace{p_{rocess} p_{rior}}_{Process}$$
+(9)
+
+where, *p*(**θ**|**Ω**) is the posterior distribution of the parameter **θ**; *ps* is the density function associated with layer *s* (*s* = 1*,* 2*,* 3) of the hierarchical model and depends on parameters **θ***v*(*v* = 1*,*2).
+
+The density associated with the data layer is written as:
+
+$$p_{1}(\mathbf{Z}|\boldsymbol{\theta}_{1}) = \prod_{i=1}^{m} \prod_{j=1}^{n_{1}} \left(\frac{1}{\exp\left(\boldsymbol{y}_{i}\right)}\right) \exp \left\{ -\left[1 + \xi_{i} \frac{\left(z_{ij} - \mu_{i}\right)}{\exp\left(\boldsymbol{y}_{i}\right)}\right]^{-1/\xi_{i}} \right\} \left[1 + \xi_{i} \frac{\left(z_{ij} - \mu_{i}\right)}{\exp\left(\boldsymbol{y}_{i}\right)}\right]^{-1-1/\xi_{i}}$$
+
+$$(10)$$
+
+where, **θ1** = [**μ***,* **ψ***,* **ξ**] *<sup>T</sup>*; *m* is the number of study sites (i.e., intersections); *ni* is the number of blocks at site *i*. According to the GEV parameters specified in Eq. (8), the density related to the process layer is obtained as:
+
+$$\begin{split} p_{2}(\boldsymbol{\theta}_{1}|\boldsymbol{\theta}_{2}) &= \frac{1}{\delta_{\mu}\sqrt{2\pi}} \exp\left[-\frac{(\mu-\mu_{i})^{2}}{2\delta_{\mu}^{2}}\right] \times \frac{1}{\delta_{\psi}\sqrt{2\pi}} \exp\left[-\frac{(\psi-\psi_{i})^{2}}{2\delta_{\psi}^{2}}\right] \\ &\times \frac{1}{\delta_{\xi}\sqrt{2\pi}} \exp\left[-\frac{(\xi-\xi_{i})^{2}}{2\delta_{\xi}^{2}}\right] \end{split} \tag{11}$$
+
+where, **θ2** = [**βμ***,* **βψ***,* **βξ**] *<sup>T</sup>*. With the priors specified, the density associated with the prior layer is given by
+
+$$p_3(\mathbf{\theta}_2) = p_{\beta_{\mu}}(\beta_{\mu}) \times p_{\beta_{\psi}}(\beta_{\psi}) \times p_{\beta_{\xi}}(\beta_{\xi})$$
+(12)
+
+The posterior distributions of model parameters can be inferred by virtue of Markov Chain Monte Carlo (MCMC) simulation using Gibbs Sampling.
+
+#### *3.4. Model choice*
+
+When developing the univariate Bayesian hierarchical extreme value model with relating the parameters of GEV distribution to several covariates, there will be many models to choose from. In the Bayesian framework, the Deviance Information Criterion (DIC) is commonly adopted to compare models. The basic principle of DIC is parsimony, obtaining the simplest model that explains as much of the variation in the data as possible ([Spiegelhalter et al., 2002\)](#page-8-0). The DIC is computed as follows:
+
+$$DIC = \overline{D} + n_D \tag{13}$$
+
+where, *D* is the posterior mean deviance that measures the model fitting and *nD* is the effective number of parameters in the model. Generally, a smaller DIC value indicates a better model. It is also suggested that a difference greater than 10 can definitely rule out the model with the higher DIC value, a difference ranging from 5 to 10 is considered sub<span id="page-4-0"></span>stantial, and a difference less than 5 makes the models competitive ([El-Basyouny and Sayed, 2012b; 2012a](#page-8-0)).
+
+## *3.5. Crash estimation method*
+
+When the GEV (*μ, σ, ξ*) is fitted based on the data from individual sites, it is called the at-site model. As well, it is called the multisite model when the GEV (*μ, σ, ξ*) is fitted based on the data from several sites simultaneously. In this study, a traffic conflict is characterized by DRAC. A crash would occur if the DRAC exceeds the MADR [\(Cunto and Sac](#page-8-0)[comanno, 2008](#page-8-0)). As such, with the fitted GEV distribution of maximum DRAC, the risk of crash can be calculated as:
+
+$$R_{i} = \Pr\{Z_{i} \ge MADR\} = 1 - G_{i}(MADR)$$
+
+$$= 1 - \exp\left\{-\left[1 + \xi_{i}^{MADR} - \mu_{i}\right]^{-1/\xi_{i}}\right\}$$
+(14)
+
+where, *Ri* is the risk of crash for block *i*; *Xi* is the maximum DRAC in block *i*; *Gi*(⋅) is the fitted univariate Bayesian hierarchical extreme value distribution for block *i*. Five specific values (i.e., 7 m/s2 , 8 m/s<sup>2</sup> , 8.5 m/ s 2 , 9.7 m/s2 , and 12 m/s2 ) of MADR are employed to calculate the risk of crash, respectively. As well, two truncated normal distributions (i.e., N (8.45, 1.4<sup>2</sup> )I(4.23, 12.68) and N(9.7, 1.3<sup>2</sup> )I(4.23, 12.68)) of MADR are used to generate the sampled values of MADR for crash risk calculation.
+
+#### **4. Results and discussions**
+
+#### *4.1. Model estimation results*
+
+With the maximum values of DRAC from different signal cycles of four signalized intersections, the multisite Bayesian hierarchical extreme value models were developed. The estimations of the proposed models were conducted using WinBUGS ([Lunn et al., 2000](#page-8-0)). Two separate chains for each model parameter with diverse initial values were set to run 50,000 iterations and the first 20,000 iterations were discarded as burn-in samples. The posterior estimates were acquired from the remaining 30,000 iterations. The model convergence was checked by calculating the Gelman-Rubin statistic of two chains for each parameter and visually examining the trace plots of parameter chains ([Gelman and](#page-8-0) 
+
+[Rubin, 1992](#page-8-0); [El-Basyouny and Sayed, 2009; Zheng and Ismail, 2017\)](#page-8-0).
+
+Four multisite Bayesian hierarchical models were established: BHM\_GEV(0,0,0), BHM\_GEV(1,0,0), BHM\_GEV(0,1,0), and BHM\_GEV (1,1,0). All the four models have site-specific random error terms for the location parameter, scale parameter, and shape parameter. BHM\_GEV (0,0,0) is the multisite stationary Bayesian hierarchical model without covariates. BHM\_GEV(1,0,0) and BHM\_GEV(0,1,0) are the multisite nonstationary Bayesian hierarchical models with the three covariates added to the location parameter and scale parameter separately. BHM\_GEV (1,1,0) is the multisite non-stationary Bayesian hierarchical model with covariates added to both location parameter and scale parameter simultaneously, and only significant covariates are included in this model. The estimation results of four multisite Bayesian hierarchical models are presented in Table 2.
+
+As shown in Table 2, the DIC values are 1562.089, 1394.052, 1543.146, and 1384.523 for the multisite BHM\_GEV(0,0,0), multisite BHM\_GEV(1,0,0), multisite BHM\_GEV(0,1,0), and multisite BHM\_GEV (1,1,0), respectively. In general, the stationary model has a greater DIC value than those of non-stationary models. The smallest DIC difference between stationary model and non-stationary models is 18.943, which shows that the non-stationary models considerably outperform the stationary model. This also confirms that the introduced covariates in the non-stationary models explain significant variations in the observed data. Moreover, the multisite BHM\_GEV(1,1,0) has the smallest DIC value, which indicates that it is the best fitted model and better than other models in terms of goodness of fit.
+
+## *4.2. Covariates interpretation*
+
+As discussed in [\(Zheng et al., 2019a](#page-9-0)), it is not straightforward to interpret the influences of covariates on safety, since they directly impact the location parameter and scale parameter of the GEV distribution. The location and scale parameters determine the shape convexity of GEV distribution, which includes the part of the distribution where most crash events are located. Given a specific MADR, an illustration of GEV distributions of DRAC with different location parameters and scale parameters is presented in [Fig. 3](#page-5-0). Given the fixed scale parameter and shape parameter, the GEV distribution with a smaller location parameter is farther away from the crash risk area, implying higher safety level. Similarly, given the fixed location parameter and
+
+**Table 2**  Estimation results of multisite Bayesian hierarchical models.
+
+|                 |        | BHM_GEV(0,0,0) |        | BHM_GEV(1,0,0) |        | BHM_GEV(0,1,0) |        | BHM_GEV(1,1,0) |        |
+|-----------------|--------|----------------|--------|----------------|--------|----------------|--------|----------------|--------|
+| Model parameter |        | Mean           | S.D.   | Mean           | S.D.   | Mean           | S.D.   | Mean           | S.D.   |
+|                 | βμ0[1] | 2.9090**       | 0.1612 | 1.5410**       | 0.3118 | 2.5930**       | 0.1714 | 1.6250**       | 0.2769 |
+| μ               | βμ0[2] | 2.0830**       | 0.1330 | 0.9711**       | 0.3025 | 2.0100**       | 0.1287 | 1.0950**       | 0.2840 |
+|                 | βμ0[3] | 2.7340**       | 0.1910 | 1.7710**       | 0.3607 | 2.4670**       | 0.1963 | 1.6880**       | 0.3364 |
+|                 | βμ0[4] | 2.9670**       | 0.1978 | 1.6910**       | 0.3202 | 2.7480**       | 0.1962 | 1.7450**       | 0.2965 |
+|                 | βμ(V)  | –              | –      | 0.0999**       | 0.0182 | –              | –      | 0.0825**       | 0.0202 |
+|                 | βμ(A)  | –              | –      | 0.6016**       | 0.0878 | –              | –      | 0.7287**       | 0.1088 |
+|                 | βμ(P)  | –              | –      | − 0.6242**     | 0.2183 | –              | –      | − 0.5974**     | 0.2060 |
+|                 | βΨ0[1] | 0.4562**       | 0.0794 | 0.2203**       | 0.0694 | 0.1955         | 0.1457 | − 0.0259       | 0.0999 |
+| ψ =             | βΨ0[2] | 0.0150         | 0.0972 | 0.0362         | 0.0900 | − 0.2311       | 0.1580 | − 0.1767       | 0.1128 |
+| log(σ)          | βΨ0[3] | 0.5244**       | 0.0929 | 0.2391**       | 0.0833 | 0.3245*        | 0.1634 | 0.0179**       | 0.1092 |
+|                 | βΨ0[4] | 0.5208**       | 0.0966 | 0.2511**       | 0.0866 | 0.2907**       | 0.1509 | 0.0651**       | 0.1023 |
+|                 | βΨ(V)  | –              | –      | –              | –      | 0.0167**       | 0.0091 | –              | –      |
+|                 | βΨ(A)  | –              | –      | –              | –      | 0.1309**       | 0.0497 | 0.1619**       | 0.0524 |
+|                 | βΨ(P)  | –              | –      | –              | –      | − 0.0964       | 0.0926 | –              | –      |
+|                 | βξ0[1] | − 0.2369**     | 0.0893 | − 0.2131**     | 0.0521 | − 0.3069**     | 0.0688 | − 0.1450**     | 0.0586 |
+|                 | βξ0[2] | 0.0318         | 0.0851 | − 0.1363*      | 0.0690 | − 0.0458       | 0.0833 | − 0.1611**     | 0.0754 |
+| ξ               | βξ0[3] | − 0.4058**     | 0.1055 | − 0.2970**     | 0.0812 | − 0.4181*      | 0.0838 | − 0.2333**     | 0.0767 |
+|                 | βξ0[4] | − 0.2262**     | 0.1275 | − 0.1135**     | 0.1005 | − 0.3026**     | 0.0954 | − 0.1304       | 0.0946 |
+| D               |        | 1550.000       |        | 1380.000       |        | 1530.000       |        | 1370.000       |        |
+| nD              |        | 12.089         |        | 14.052         |        | 13.146         |        | 14.523         |        |
+| DIC             |        | 1562.089       |        | 1394.052       |        | 1543.146       |        | 1384.523       |        |
+
+Note: "–" means the covariate is not included; S.D. is the standard deviation; "\*" and "\*\*" mean the covariate is significant at 0.1 and 0.05 level, respectively; "V" is the traffic volume; "A" is the shock wave area; and "P" is the platoon ratio.
+
+<span id="page-5-0"></span>![](_page_5_Figure_2.jpeg)
+
+**Fig. 3.** Illustration of GEV distributions with different location and scale parameters.
+
+shape parameter, the GEV distribution with a smaller scale parameter has a skinny shape, and its tail area within the crash risk area becomes narrower, indicating higher safety level as well.
+
+According to the results from the best fitted model, multisite BHM\_GEV(1,1,0), all the three covariates are significantly related to the location parameter of GEV distribution, while only one covariate is significantly associated with the scale parameter of GEV distribution. Specifically, the traffic volume and shock wave area are positively related to the location parameter of GEV distribution, whereas the platoon ratio is negatively associated with the location parameter of GEV distribution. Moreover, the shock wave area is positively related to the scale parameter of GEV distribution. Both the greater traffic volume and shock wave area will increase the location parameter, which yields more expected number of crashes. However, a greater platoon ratio will decrease the location parameter, and thus produce less expected number of crashes. Similarly, a greater shock wave area will increase the scale
+
+parameter, which generates more expected number of crashes.
+
+#### *4.3. Comparison of threshold determination methods for DRAC*
+
+The best fitted model, multisite BHM\_GEV(1,1,0), was used to predict the annual number of crashes for each intersection, where *T* = 365 × 12 = 4380, and t = 4, 3, 4, and 4 for intersections of 72 Ave & 128 St, 72 Ave & 132 St, 64 Ave & King George Blvd, and Fraser Hwy & 168 St, respectively. Five specific values (i.e., 12 m/s<sup>2</sup> , 9.7 m/s<sup>2</sup> , 8.5 m/s<sup>2</sup> , 8 m/s<sup>2</sup> , and 7 m/s2 ) and two truncated normal distributions (i.e., N(9.7, 1.3<sup>2</sup> )I(4.23,12.68) and N(8.45, 1.42 )I(4.23,12.68)) for MADR were used. In addition, the uncertainties of estimated crashes were determined directly in WinBUGS during the model posterior inference via different quantiles, and this is also an advantage of Bayesian inference that can incorporate all uncertainties in the data and model parameters ([El-Basyouny and Sayed, 2012b;](#page-8-0) [Zheng and Sayed, 2020\)](#page-9-0). The crash estimation results from the multisite BHM\_GEV(1,1,0) are shown in Table 3. In the table, the 95% confidence intervals (95% C.I.) of observed crashes are also presented, given that the observed crashes at each intersection are just one observation of the underlying process ([Zheng and Sayed, 2020](#page-9-0)). By hypothesizing that the observed crashes follow the Poisson distribution, the 95% C.I.s were computed as { *λ* : <sup>1</sup> 2*nχ*<sup>2</sup> <sup>2</sup>*y*0*,*0*.*<sup>975</sup> ≤ *λ* ≤ <sup>1</sup> 2*nχ*<sup>2</sup> <sup>2</sup>(*y*0+1)*,*0*.*025} , where *n* = 3 is the number of years for crash data collection, and *y*0 is the total number of crashes in the 3-year period for an intersection [\(Songchitruksa and Tarko, 2006\)](#page-8-0).
+
+As shown in Table 3, there are three intersections where the estimated crashes from multisite BHM\_GEV(1,1,0) using the MADR of 12 m/ s 2 are smaller than the observed crashes and outside the 95% confidence intervals of the observed crashes. Similar results are obtained from multisite BHM\_GEV(1,1,0) using the MADR of 9.7 m/s2 . There are two intersections where the estimated crashes from multisite BHM\_GEV (1,1,0) using the MADR of 8.5 m/s2 are smaller than the observed crashes and outside the 95% confidence intervals of the observed crashes, whereas the estimated crashes of other two intersections are within the 95% confidence intervals of the observed crashes. The multisite BHM\_GEV(1,1,0) using the MADR of 8 m/s2 generates crash underestimation at two intersections with the estimated crashes outside the 95% confidence intervals of the observed crashes, while produces crash overestimation at one intersection with the estimated crashes
+
+**Table 3**  Crash estimation results of multisite Bayesian hierarchical models with different thresholds.
+
+outside the 95% confidence intervals of the observed crashes. Although the multisite BHM\_GEV(1,1,0) using the MADR of 7 m/s2 yields the estimated crashes inside the 95% confidence intervals of the observed crashes at two intersections, it produces serious crash overestimations at other two intersections. The estimated crashes from multisite BHM\_GEV (1,1,0) using the values of MADR sampled from a truncated normal distribution N(9.7, 1.32 )I(4.23, 12.68) are similar to those from multisite BHM\_GEV(1,1,0) using a specific value of 8.5 m/s2 for MADR. However, the estimated crashes from multisite BHM\_GEV(1,1,0) using the values of MADR sampled from a truncated normal distribution N(8.45, 1.42 )I (4.23, 12.68) are all within the 95% confidence intervals of the observed crashes.
+
+The results of crash estimation indicate that in terms of accuracy, the multisite BHM\_GEV(1,1,0) using the sampled values for MADR is better than the one using a specific value for MADR. This is due to the MADR varying with the vehicle, pavement, and environmental conditions at different sites. A larger specific value of MADR would lead to crash underestimation at some sites, while a smaller specific value of MADR would generate crash overestimation at these sites. By using the multisite BHM\_GEV(1,1,0), the comparison of estimated crashes among different MADR values is presented in Fig. 4. In terms of crash estimation accuracy, among 16 different specific values of MADR, the best ones are 7.5 m/s2 , 8.4/8.5/8.6 m/s<sup>2</sup> , 6.8 m/s2 , and 8.7 m/s2 for the four intersections, respectively. According to the 95% confidence interval of observed crashes, the ranges of appropriate MADR are 7.2–7.8 m/s2 , 7.3–8.6 m/s2 , 6.6–7.1 m/s<sup>2</sup> , 8.2–9.5 m/s2 for the four intersections, respectively. Therefore, it is hard to find an appropriate specific value or range of MADR for DRAC-based crash estimation at all these intersections.
+
+Additionally, the multisite BHM\_GEV(1,1,0) using the values of MADR sampled from a truncated normal distribution N(8.45, 1.4<sup>2</sup> )I (4.23, 12.68) outperforms the one with the sampled values of MADR from a truncated normal distribution N(9.7, 1.32 )I(4.23, 12.68). Crash underestimation at two intersections from the multisite BHM\_GEV (1,1,0) using the values of MADR sampled from a truncated normal distribution N(9.7, 1.3<sup>2</sup> )I(4.23, 12.68) may be a result of the inappropriate upper and lower limits of such a truncated normal distribution. Therefore, in terms of crash estimation accuracy, it is recommended to determine the value of MADR by sampling from the truncated normal distribution N(8.45, 1.42 )I(4.23, 12.68).
+
+# *4.4. Comparison of multisite and at-site Bayesian hierarchical models*
+
+The at-site Bayesian hierarchical models were developed for each site by following the same procedure as the multisite Bayesian hierarchical models. All the three covariates were also considered in the model development. Those at-site Bayesian hierarchical models with the smallest DIC values were recognized as the best fitted models, and their estimation results are shown in [Table 4.](#page-7-0) It can be seen that the sign of significant covariates of the at-site models is the same as the multisite BHM\_GEV(1,1,0), but the significance of covariates are varying across the sites.
+
+With the values of MADR sampled from the truncated normal distribution N(8.45, 1.42 )I(4.23, 12.68), the best fitted at-site models were employed to predict the annual crash frequencies, which were then compared to the observed crashes and the estimated crashes from the
+
+![](_page_6_Figure_9.jpeg)
+
+**Fig. 4.** Comparison of estimated crashes among different MADR values (m/s2 ).
+
+<span id="page-7-0"></span>**Table 4**  Estimation results of the best at-site Bayesian hierarchical models.
+
+|                 | 72 Ave & 128 St |                | 72 Ave & 132 St |                | 64 Ave & King George Blvd |                | Fraser Hwy & 168 St |                |        |
+|-----------------|-----------------|----------------|-----------------|----------------|---------------------------|----------------|---------------------|----------------|--------|
+| Model parameter |                 | BHM_GEV(1,1,0) |                 | BHM_GEV(1,1,0) |                           | BHM_GEV(1,0,0) |                     | BHM_GEV(1,1,0) |        |
+|                 |                 | Mean           | S.D.            | Mean           | S.D.                      | Mean           | S.D.                | Mean           | S.D.   |
+| μ               | βμ0             | 1.5760**       | 0.4281          | 1.3260**       | 0.1477                    | 1.2050**       | 0.6346              | 0.6576**       | 0.4479 |
+|                 | βμ(V)           | 0.1327**       | 0.0324          | –              | –                         | 0.0989**       | 0.0453              | 0.0902**       | 0.0354 |
+|                 | βμ(A)           | 0.3402**       | 0.1334          | 1.0380**       | 0.1929                    | 1.0350**       | 0.1997              | 1.0670**       | 0.2185 |
+|                 | βμ(P)           | − 0.7599**     | 0.3658          | –              | –                         | − 0.5886**     | 0.3608              | –              | –      |
+| log(σ)          | βΨ0             | − 0.1577**     | 0.2235          | − 0.5869**     | 0.1421                    | 0.1947**       | 0.0815              | 0.0088         | 0.1445 |
+|                 | βΨ(V)           | 0.0237*        | 0.0141          | –              | –                         | –              | –                   | –              | –      |
+|                 | βΨ(A)           | –              | –               | 0.5125**       | 0.1159                    | –              | –                   | 0.2181**       | 0.1110 |
+|                 | βΨ(P)           | –              | –               | –              | –                         | –              | –                   | –              | –      |
+| ξ               | βξ0             | − 0.1373**     | 0.0673          | − 0.1592*      | 0.0797                    | − 0.2525**     | 0.0748              | − 0.1391       | 0.0946 |
+| D               |                 | 430.000        |                 | 200.000        |                           | 330.000        |                     | 390.000        |        |
+| nD              |                 | 5.868          |                 | 4.451          |                           | 5.153          |                     | 6.082          |        |
+| DIC             |                 | 435.868        |                 | 204.451        |                           | 335.153        |                     | 396.082        |        |
+
+Note: "–" means the covariate is not included; S.D. is the standard deviation; "\*" and "\*\*" mean the covariate is significant at 0.1 and 0.05 level, respectively; "V" is the traffic volume; "A" is the shock wave area; and "P" is the platoon ratio.
+
+multisite BHM\_GEV(1,1,0), respectively. The results of the comparison are presented in Table 5. The estimated crashes of four intersections from the multisite BHM\_GEV(1,1,0) are all within the 95% confidence intervals of the observed crashes, while the estimated crashes of only one intersection from the at-site model are within the 95% confidence intervals of the observed crashes. Moreover, the estimated crashes of three intersections from the multisite BHM\_GEV(1,1,0) are closer to the observed crashes than those from the at-site models. Additionally, the 95% confidence intervals of estimated crashes from the multisite BHM\_GEV(1,1,0) are narrower than those from the at-site Bayesian hierarchical models. This indicates that as compared to the at-site Bayesian hierarchical models, the multisite BHM\_GEV(1,1,0) distinctly improves crash estimation in terms of accuracy and precision. Such significant improvement is probably due to synthesizing the strengths across different sites for model estimation.
+
+However, it is noted that the confidence intervals of estimated crashes from the multisite BHM\_GEV(1,1,0) are still much wider than the 95% Poisson intervals of observed crashes. As discussed in one previous study [\(Zheng et al., 2019a\)](#page-9-0), the large uncertainty in crash estimation based on the multisite Bayesian hierarchical model is mainly a result of the paucity of data. On one hand, the short-term observation period of three-four hours may not completely reflect the daily/weekly/seasonal variation of traffic in one year. On the other hand, any uncertainty in the estimated risk of crashes during the traffic conflict observation period will be magnified by at least *T/t* = 365 × 12*/*4 = 1095 times. From this point of view, the precision issue can be handled with a larger data sample collected from a longer observation period.
+
+**Table 5**  Crash estimate comparison between multisite model and at-site models.
+
+| Site                         | Observed | crashes per year | per year | Multisite model<br>estimated crashes | At-site models<br>estimated crashes<br>per year |             |  |
+|------------------------------|----------|------------------|----------|--------------------------------------|-------------------------------------------------|-------------|--|
+|                              | Mean     | 95%<br>C.I.      | Mean     | 95% C.I.                             | Mean                                            | 95% C.I.    |  |
+| 72 Ave & 128<br>St           | 4.7      | [2.6,<br>7.8]    | 6.7      | [0.0,505.5]                          | 8.3                                             | [0.0,647.6] |  |
+| 72 Ave & 132<br>St           | 0.3      | [0.0,<br>1.9]    | 1.9      | [0.0,174.9]                          | 1.1                                             | [0.0,176.2] |  |
+| 64 Ave & King<br>George Blvd | 6.0      | [3.6,<br>9.5]    | 4.4      | [0.0,440.1]                          | 2.7                                             | [0.0,492.5] |  |
+| Fraser Hwy &<br>168 St       | 3.3      | [1.6,<br>6.1]    | 5.6      | [0.0,479.6]                          | 13.2                                            | [0.0,969.6] |  |
+
+## *4.5. Comparison of extreme value distribution and truncated normal distribution*
+
+Given that the MADR follows a truncated normal distribution N (8.45, 1.402 ), with a lower limit of 4.23 m/s2 and an upper limit of 12.68 m/s2 ([Cunto and Saccomanno, 2008\)](#page-8-0), the risk of crash can also be calculated as:
+
+$$R_{i} = \Pr(MADR \le DRAC_{i}) = \frac{\Phi(\frac{DRAC_{i} - \mu_{MADR}}{\sigma_{MADR}}) - \Phi(\frac{C_{MADR} - \mu_{MADR}}{\sigma_{MADR}})}{\Phi(\frac{U_{MADR} - \mu_{MADR}}{\sigma_{MADR}}) - \Phi(\frac{C_{MADR} - \mu_{MADR}}{\sigma_{MADR}})}$$
+(15)
+
+where, *μMADR* and *σMADR* are the mean and standard deviation of MADR distribution (here refers to a truncated normal distribution); *LMADR* and *UMADR* are the lower and upper limits of MADR; *Φ*(⋅) is the cumulative distribution function of the standard normal distribution.
+
+Based on Eq. (15), the estimated crashes for each site were obtained and compared to the observed crashes and the estimated crashes from the multisite BHM\_GEV(1,1,0) using the values of MADR sampled from the truncated normal distribution N(8.45, 1.4<sup>2</sup> )I(4.23, 12.68), respectively. The comparison results are shown in Table 6. The estimated crashes from the Bayesian hierarchical extreme value distribution are closer to the observed crashes than those from the truncated normal distribution. This confirms that the Bayesian hierarchical extreme value distribution is more suitable to fit the traffic conflict extremes than the truncated normal distribution.
+
+**Table 6**  Crash estimate comparison between Bayesian hierarchical extreme value and truncated normal distributions.
+
+| Site                         | per year | Observed crashes |      | Estimated crashes<br>from extreme value<br>distribution per year | Estimated<br>crashes from<br>truncated<br>normal<br>distribution per<br>year |             |
+|------------------------------|----------|------------------|------|------------------------------------------------------------------|------------------------------------------------------------------------------|-------------|
+|                              | Mean     | 95% C.<br>I.     | Mean | 95% C.I.                                                         | Mean                                                                         | 95%<br>C.I. |
+| 72 Ave & 128 St              | 4.7      | [2.6,<br>7.8]    | 6.7  | [0.0,505.5]                                                      | 9.3                                                                          | –           |
+| 72 Ave & 132 St              | 0.3      | [0.0,<br>1.9]    | 1.9  | [0.0,174.9]                                                      | 4.3                                                                          | –           |
+| 64 Ave & King<br>George Blvd | 6.0      | [3.6,<br>9.5]    | 4.4  | [0.0,440.1]                                                      | 3.8                                                                          | –           |
+| Fraser Hwy & 168<br>St       | 3.3      | [1.6,<br>6.1]    | 5.6  | [0.0,479.6]                                                      | 14.7                                                                         | –           |
+
+## <span id="page-8-0"></span>**5. Conclusions**
+
+This study compared the threshold determination methods (i.e., setting specific values or distributions of MADR) for DRAC-based crash estimation using Bayesian hierarchical extreme value modeling. The crash data and traffic conflicts defined by DRAC were collected from four signalized intersections in the city of Surrey, British Columbia, Canada. Four multisite Bayesian hierarchical models were developed, including a stationary model and three non-stationary models. For comparison purposes, the at-site non-stationary models for four sites were also developed separately. As well, the estimated crashes from a truncated normal distribution of MADR for four sites were calculated. The estimated crashes from the best fitted multisite Bayesian hierarchical model with five specific values (i.e., 7 m/s<sup>2</sup> , 8 m/s<sup>2</sup> , 8.5 m/s<sup>2</sup> , 9.7 m/s<sup>2</sup> , and 12 m/s2 ) of MADR and two truncated normal distributions (i. e., N(8.45, 1.42 )I(4.23, 12.68) and N(9.7, 1.3<sup>2</sup> )I(4.23, 12.68)) of MADR were compared to the observed crashes, respectively. With the best threshold determination approach, the estimated crashes from the best fitted multisite Bayesian hierarchical model were compared to those from the best fitted at-site non-stationary models and the truncated normal distribution, respectively.
+
+The results show that, in terms of DRAC-based crash estimation accuracy, (i) the truncated normal distribution N(8.45, 1.4<sup>2</sup> )I(4.23, 12.68) of MADR outperforms both the truncated normal distribution N(9.7, 1.3<sup>2</sup> )I(4.23, 12.68) of MADR and the specific values (i.e., 7 m/s2 , 8 m/s2 , 8.5 m/s2 , 9.7 m/s<sup>2</sup> , and 12 m/s<sup>2</sup> ) of MADR; (ii) the Bayesian hierarchical extreme value distribution outperforms the truncated normal distribution. In terms of DRAC-based crash estimation accuracy and precision, the multisite Bayesian hierarchical model is better than the at-site Bayesian hierarchical models. Moreover, finding specific appropriate values of MADR to use for DRAC-based crash estimation at all intersections is difficult. Additionally, it is also found that during a signal cycle, more vehicles and greater shock wave area will generate higher crash risks, whereas a greater platoon ratio will produce a lower crash risk.
+
+In conclusion, this study highlights the difference in DRAC-based crash estimation with different thresholds. It also demonstrates the usefulness and advantages of the Bayesian hierarchical extreme value modeling in crash estimation compared to the truncated normal distribution. However, some limitations in this study merit further investigations. Firstly, the traffic conflicts are observed during a short period and from only four signalized intersections. Data from more sites and longer observation periods can be used to confirm the results of this study. Furthermore, only rear-end traffic conflicts and crashes are used. Other types of traffic conflicts and crashes need to be investigated. Secondly, as to a truncated normal distribution of MADR, its parameters (e.g., lower limit, upper limits, mean, and standard error) need to be further investigated, since the MADR is subject to various vehicles, road, and environmental conditions. Third, other distributions of MADR can be investigated. Fourth, to avoid a collision, the driver of the following vehicle may change lane instead of braking heavily. The evasion maneuvers mainly dependent on the severity level of the conflict. Similar to the deceleration to safety time (Hupfer, 1997), the conflict level can be determined based on DRAC which can be investigated in future studies.
+
+# **CRediT authorship contribution statement**
+
+**Chuanyun Fu:** Conceptualization, Methodology, Investigation, Validation, Writing - original draft. **Tarek Sayed:** Conceptualization, Methodology, Data curation, Supervision, Writing - review & editing.
+
+# **Declaration of Competing Interest**
+
+None.
+
+## **Acknowledgments**
+
+This study was jointly supported by the China Scholarship Council (CSC) and the National Natural Science Foundation of China (Grant No. 71801182).
+
+#### **References**
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Zotero/001_artiklid/Road Safety Indicators/garnowskifactorsrelatedcaraccidents2011.md

@@ -0,0 +1,413 @@
+---
+category: literaturenote
+citekey: garnowskifactorsrelatedcaraccidents2011
+title: On factors related to car accidents on German Autobahn connectors
+authors: "Garnowski, Martin; Manner, Hans"
+year: 2011
+date: 2011-00-00 2011
+doi: 10.1016/j.aap.2011.04.026
+publication: "Accident Analysis & Prevention"
+url: "https://doi.org/10.1016/j.aap.2011.04.026"
+zotero_key: DFHFPG6A
+zotero_storage: RENKHK6A
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "Garnowski, Martin"
+status: converted
+---
+Contents lists available at [ScienceDirect](http://www.sciencedirect.com/science/journal/00014575)
+
+# Accident Analysis and Prevention
+
+journal homepage: [www.elsevier.com/locate/aap](http://www.elsevier.com/locate/aap)
+
+![](_page_0_Picture_5.jpeg)
+
+# On factors related to car accidents on German Autobahn connectors
+
+Martin Garnowski a, Hans Manner <sup>b</sup>,<sup>∗</sup>
+
+- <sup>a</sup> FedEx Express Europe, Middle East, Indian Subcontinent and Africa, Cologne, Germany
+- <sup>b</sup> Department of Economic and Social Statistics, University of Cologne, Meister-Ekkehart-Str. 9, 50937 Cologne, Germany
+
+#### article info
+
+Article history: Received 7 January 2011 Received in revised form 15 April 2011 Accepted 24 April 2011
+
+Keywords: Highway connectors German Autobahn Accident causes Negative binomial regression Random parameters
+
+#### abstract
+
+We make an attempt to identify factors that explain accidents on German Autobahn connectors. To find these factors we perform an empirical study making use of count data models with fixed and random coefficients. The findings are based on a set of 197 ramps, which we classify into three distinct types of ramps. For these ramps, accident data is available for a period of 3 years (January 2003 until December 2005). The negative binomial model with some random coefficients proved to be an appropriate model in our cross-sectional setting for detecting factors that are related to accidents. The most significant variable is a measure of the average daily traffic. For geometric variables, not only continuous effects were found to be significant, but also threshold effects indicating the exceedance of certain values.
+
+© 2011 Elsevier Ltd. All rights reserved.
+
+## **1. Introduction**
+
+The traffic on German highways, the so-called "Autobahn", has been increasing drastically over the past years and is expected to grow further in the future, due to Germany's central geographical position in Europe. The increase in traffic surpasses not only the economic growth, but also the speed of construction of roads. If the road network is not expanded significantly, the increasing number of vehicles on German Autobahns will certainly lead to an increasing number of accidents. Due to limitations in the potential expansions of the Autobahn, particularly in the short run, an important task is to identify accident factors and their influence on accident probabilities. This information could give suggestions for low-cost, short-term improvements for the prevention of accidents on existing Autobahn segments. One of the most dangerous situations for car drivers on Autobahns is the weaving out of the flow of traffic via a road connector. In the years 2003–2005 nearly 8000 accidents happened on road connectors on Autobahns in the administrative district Düsseldorf, which has an extremely dense Autobahn network and is the region we focus on in this study. Due to the safety-standards on Autobahns "only" 10 of these accidents were fatal, however, the economic damage caused by accidents is remarkable.
+
+Several studies found that about 90% of all accidents are at least partially caused by human failure, see, e.g. [Treat et al. \(1977\).](#page-7-0) As driver behavior is influenced by the whole environment, the aim of road construction should be to construct road sites that prevent or forgive human errors. The problem with road connectors is that each of them is constructed differently according to distinct traffic volumes or geographical constraints. The key question is which factors cause drivers to make mistakes. The aim of our study is to find a model that explains the number or the probability of accidents at various types of Autobahn connectors. This is a statistical problem. However, due to the nature of the problem, the use of standard linear regression models is inappropriate, as argued by [Jovanis and Chang \(1986\)](#page-7-0) and [Miaou and Lum \(1993\). T](#page-7-0)he variable of interest, namely the number of accidents during a given time interval, suggests the use of count data models.
+
+[Miaou and Lum \(1993\),](#page-7-0) who investigated the relationship between truck accidents and roadway geometries, and [Pickering](#page-7-0) [et al. \(1986\)](#page-7-0) used the Poisson regression model to study accident data. [Hauer et al. \(1988\), o](#page-7-0)n the other hand, introduced the more appropriate negative binomial model to find that traffic flow and various road characteristics have a significant effect on the number of accidents on signalized intersections in Toronto. Another study applying the negative binomial model to determine the causes of car accidents is [Shankar et al. \(1995\), w](#page-7-0)ho analyzed accidents on a section of the Interstate 90 near Seattle. Both Poisson and negative binomial models require a cross sectional setting. [Chin and](#page-7-0) [Quddus \(2003\)fo](#page-7-0)und that panel count data models have the advantage that they are able to deal with spatial or temporal effects in contrast to cross sectional count data models. They analyzed different types of accidents on signalized intersections in Singapore using a set of variables containing geometric variables, traffic volume variables and regulatory controls. Another paper applying panel data techniques to study accident data is [Shankar et al. \(1998\).](#page-7-0) As accident data typically tends to have more zero-observations
+
+<sup>∗</sup> Corresponding author. Tel.: +49 221 470 4130; fax: +49 221 470 5084. E-mail addresses: [mgarnowski@fedex.com](mailto:mgarnowski@fedex.com) (M. Garnowski), [manner@statistik.uni-koeln.de](mailto:manner@statistik.uni-koeln.de) (H. Manner).
+
+<span id="page-1-0"></span>than are predicted by standard count data models, zero-inflated models have been introduced into traffic accident research. For example, [Shankar et al. \(1997\)](#page-7-0) investigated accidents on arterials in Washington with two years of accident data and concluded that zero-inflated models have a great flexibility in uncovering processes affecting accident frequencies on roadway sections. For run-off-roadway accidents on a section of a highway in Washington State [Lee and Mannering \(2002\)](#page-7-0) got promising results applying zero-inflated models in contrast to standard models. However, [Washington et al. \(2003\)](#page-7-0) and [Lord et al. \(2005\)](#page-7-0) provide arguments against the use of zero-inflated models in the analysis of accident data. Recently, [Anastasopoulos and Mannering \(2009\)](#page-7-0) and [El-Basyouny and Sayed \(2009\)](#page-7-0) introduced count data models with random parameters to account for unobserved heterogeneity and found that these models perform very well. For more on regression models with count data we refer to, among others, [Cameron and](#page-7-0) [Trivedi \(1986\); Lord et al. \(2005\); Lord and Mannering \(2010\)](#page-7-0) and [Kibria \(2006\).](#page-7-0)
+
+None of the above-mentioned studies analyzes data on highway connectors, but the statistical techniques and explanatory variables that they use are similar to the ones used here.We make an attempt to find an appropriate model for our dataset of 3 years of accidents on Autobahn connectors in the administrative district Düsseldorf (approximately a fifth of the area of North Rhine-Westphalia). In our analysis, we consider more than 60 Autobahn connectors with 197 ramps in an area of approximately 2300 km2, using traffic data and geometric variables both in continuous form and allowing for threshold effects, which are represented by dummies indicating the exceedance of certain threshold values.
+
+The remainder of the paper is organized as follows. In the next section we describe ourmethodology. In Section[3](#page-2-0) we introduce and explain our dataset, followed by the presentation of the empirical results in Section [4. F](#page-4-0)inally, Section [5](#page-6-0) concludes our paper.
+
+#### **2. Methodology**
+
+As our variable of interest, the number of accidents on highway connectors, is a count variable, linear regression models are not an appropriate tool for our analysis. Instead, we make use of count data regressionmodels that have been designed for the specific purpose of modeling discrete count variables. The benchmark model for count data is the Poisson regression model, which is derived from the Poisson distribution. We assume a cross sectional setting with n independent observations, the ith of which being (yi, **x**i), where yi is the number of occurrences of the event of interest and **x**<sup>i</sup> is a vector of regressors that determine the number of accidents yi. The Poisson regression model is defined by
+
+$$f(y_i|\mathbf{x}_i,\beta) = \frac{e^{-\lambda_i}\lambda_i^{y_i}}{y_i!}, \qquad y_i = 0, 1, 2, \dots$$
+ (2.1)
+
+where<sup>i</sup> > 0 is the intensity or rate parameter of observationi. Equation (2.1) measures the probability of yi occurrences of an event during a unit of time. In this model, the mean and the variance are the same, which is called the equidispersion-property of the Poisson distribution. The intensity parameter <sup>i</sup> is assumed to depend on the regressors through
+
+$$\lambda_i = \exp(\mathbf{x}_i'\beta),\tag{2.2}$$
+
+where the log-linear dependence of <sup>i</sup> on **x**<sup>i</sup> assures that the intensity parameter is always positive. It is crucial that the conditional mean equation is correctly specified and that the assumption of equidispersion is satisfied. In the case of overdispersion, maximum likelihood estimation (MLE) t-statistics are inflated, which can lead to too optimistic conclusions about the statistical significance of regressors. The assumption that yi is Poisson distributed can be relaxed considerably as studied in [Gourieroux et al. \(1984a,b\).](#page-7-0) Given a correctly specifiedmean, the pseudo MLEbased on a density from the linear exponential family (LEF) is consistent. This allows the assumption of equidispersion to be relaxed either by allowing for specific variance functions or by leaving the form of the variance unspecified. In the latter case standard errors can be obtained by a robust sandwich or bootstrap estimator.
+
+As the assumption of equidispersion is unlikely to hold in reality, a natural extension of the model is to allow for unobserved heterogeneity. Unobserved heterogeneity arises when the covariates do not account for the full amount of individual heterogeneity. An extension of the Poisson model that allows for unobserved heterogeneity and overdispersion is the negative binomial regression (NB) model. The NB model can be obtained by writing
+
+$$\lambda_i = \exp(\mathbf{x}_i'\boldsymbol{\beta} + \varepsilon_i), \tag{2.3}$$
+
+where exp (εi) follows a gamma distribution with mean 1 and variance ˛. For this reason it is also called the Poisson-gamma model. The density of the NB distribution is given by
+
+$$f(y_i|\mathbf{x}_i,\beta,\alpha) = \frac{\Gamma(\alpha^{-1}+y_i)}{\Gamma(\alpha^{-1})y_i!} \left(\frac{\alpha^{-1}}{\alpha^{-1}+\lambda_i}\right)^{\alpha^{-1}} \left(\frac{\lambda_i}{\alpha^{-1}+\lambda_i}\right)^{y_i}.$$
+ (2.4)
+
+The variance of this distribution is:
+
+$$V[y_i|\lambda_i,\alpha] = \lambda_i(1+\alpha\lambda_i) > \lambda_i.$$
+
+i
+
+Thus, for ˛> 0, this model allows for overdispersion. The NB regression is also estimated by MLE and, as it is also a member of LEF, it is robust to distributional misspecifications. However, if the model is misspecified the maximum likelihood standard errors are in general inconsistent and either robust sandwich or bootstrap standard errors should be used.
+
+One possibility to allow for heterogeneity across observations (possibly caused by unobserved factors) is to let all or some of the parameters be random. Random parameter count data models for accident data have been proposed by [Anastasopoulos and](#page-7-0) [Mannering \(2009\)](#page-7-0) and [El-Basyouny and Sayed \(2009\). T](#page-7-0)he random parameters are written as
+
+$$\beta_i = \beta + \varphi_i, \tag{2.5}$$
+
+where ϕ<sup>i</sup> is a random variable with density g(·). The most popular choice is the normal distribution with mean 0 and variance 2, which we also use in this paper. Conditional on the random components, the intensity parameters are given by <sup>i</sup>|ϕi = exp(**x** i ˇ) and <sup>i</sup>|ϕi = exp(**x** ˇ + εi) for the Poisson and negative binomial regression, respectively. The log-likelihood of the random parameter model can be obtained by integrating out ϕ<sup>i</sup> from the joint density of yi and ϕi:
+
+$$\ln L = \sum_{i=1}^{n} \ln \int_{\varphi_i} g(\varphi_i) f(y_i | \varphi_i) d\varphi_i.$$
+ (2.6)
+
+As this integral cannot be evaluated analytically and numerical integration is computational infeasible when the number of random parameters goes beyond one or two, [Anastasopoulos and](#page-7-0) [Mannering \(2009\)](#page-7-0) suggest to evaluate it by simulation. However, instead of using pseudo random numbers the integral above is evaluated using so called scrambled Halton sequences. Halton sequences are non-random sequences that cover the domain of integration more uniformly than random numbers and lead to a more precise evaluation of the integral with fewer draws. We refer to [Train \(1999\)](#page-7-0) and [Bhat \(2001, 2003\)](#page-7-0) for details on Halton sequences and their use in simulated maximum likelihood. Note that we treat a parameter as random when its estimated variance is significantly different from zero.
+
+In order to decide between the competing models, it is important to test for overdispersion in the data. Besides comparing the <span id="page-2-0"></span>sample mean and variance, a simple formal test can be performed by noting that the NB model reduces to the Poisson model when ˛= 0. Thus, the null hypothesis of equidispersion can be tested by estimating the NB and Poisson models and performing a likelihood ratio (LR) test for H<sup>0</sup> :˛= 0. Since ˛ is restricted to be positive the LR statistic asymptotically has probability mass of a half at zero and a half 2(1) distribution above 0. The critical value is then <sup>2</sup> <sup>1</sup>−2ı(1) when testing at level ı.
+
+The fit of competing models can be measured by the (McFadden) pseudo-R<sup>2</sup> given by
+
+$$1 - \frac{\ln \mathsf{L}_1}{\ln \mathsf{L}_0} \tag{2.7}$$
+
+where ln L<sup>1</sup> is the log-likelihood of the full model and ln L<sup>0</sup> is the log-likelihood of the model without any regressors. Additionally, potentially non-nestedmodels can be compared by looking at information criteria. The most popular ones are the Akaike Information Criterion (AIC) proposed by [Akaike \(1973\)](#page-7-0) and defined as
+
+$$AIC = -2 \ln L + 2k, \tag{2.8}$$
+
+and the Bayesian Information criterion (BIC) proposed by [Schwarz](#page-7-0) [\(1978\)](#page-7-0) and given by
+
+$$BIC = -2 \ln L + (\ln n)k, \tag{2.9}$$
+
+where k is the number of parameters in the model. The BIC places a larger penalty on additional regressors and thus leads to the selection of more parsimonious models.
+
+The estimated coefficients of the above models can be interpreted as semi-elasticities and, in contrast to linear regression coefficients, the response does not stay constant with varying regressors. For dummy variables the conditional mean of the dependant variable is exp(ˇˆ <sup>j</sup>) times larger if the dummy variable is one. The marginal effect is different for each observation i, but we consider both the average marginal effect ("Avg") and the marginal effect evaluated at the average ("At Avg"), which are calculated as
+
+$$\frac{1}{n}\sum_{i=1}^{n}\frac{\partial \mathsf{E}[y_{i}|\mathbf{x}_{i}]}{\partial x_{ij}} = \frac{1}{n}\sum_{i=1}^{n}\beta_{j}\exp(\mathbf{x}_{i}'\beta) \tag{2.10}$$
+
+and
+
+$$\frac{\partial \mathbf{E}[\mathbf{y}_i|\mathbf{x}]}{\partial \mathbf{x}_j}\bigg|_{\tilde{\mathbf{x}}} = \beta_j \exp(\tilde{\mathbf{x}}'\beta),$$
+ (2.11)
+
+respectively, where **x**¯ denotes the vector of sample means of the regressors.
+
+# **3. Data**
+
+In this section we describe important terms and introduce our dataset. Further details about the data are available from the authors upon request.
+
+#### 3.1. Clarification of terms
+
+We distinguish between the terms connector, ramp and curve. Fig. 1 shows a schematic picture of a connector for two Autobahns. This connector consists of 8 ramps and each ramp consists of at least one curve. One has to distinguish between different types of connectors, namely clover leaves which connect two Autobahns as in Fig. 1 and diamond interchanges which connect an Autobahn with a minor road as in[Fig. 2. T](#page-3-0)he schematic pictures present only two possible shapes of connectors as their form varies due to construction constraints.
+
+The ramps can be categorized as tangents, loops, egress-ramps and drive-up ramps. Drive-up ramps are not considered here, because many variables that can be gathered for the other types
+
+![](_page_2_Picture_20.jpeg)
+
+**Fig. 1.** Clover leaf.
+
+of ramps cannot be found for this type. Furthermore, significantly fewer accidents occur on these ramps due to a lower permitted driving speed. Thus, we only consider ramps on which cars leave a specific Autobahn and change onto another Autobahn or a minor road. For the sake of simplicity tangent ramps, loop-ramps and egress-ramps will be called T-ramps, O-ramps and E-ramps, respectively.
+
+## 3.2. Data description
+
+Our data contains the following information: details on individual accidents, traffic flow data and geometrical properties of the ramps. We describe each type in turn.
+
+Accident data: The raw data on accidents was provided by the "Autobahnpolizei Düsseldorf", the highway police for the district Düsseldorf. The dataset contains detailed information for all reported accidents on Autobahns in the administrative district in the time period from January 2003 to December 2005. This amounts to a total of 39,032 accidents (12,887 in 2003, 13,433 in 2004 and 12,712 in 2005). This detailed information includes the exact time of the accident, its location, type of vehicle, number of vehicles involved, the severity and type of the accident, information on the driver, sight conditions, and road sleekness. Out of nearly 40,000 reported accidents, we filtered out the accidents that happened on ramps of the various connectors. Given the constraints imposed by the datasets we had a total of 197 ramps under investigation of which 95 were E-ramps, 33 were O-ramps and 69 were T-ramps. After the filtering process a total of 3048 accidents were analyzed. Due to the fact that we are interested in modeling the aggregated counts over a certain period of time at a particular location, the detailed information on the accidents is disregarded in this study.
+
+[Table 1](#page-3-0) shows some descriptive statistics for accidents on the different types of ramps. The significant difference in the mean of accident numbers for the different types of ramps is eye-catching and suggests the existence of heterogeneity across ramp types.
+
+A phenomenon that is often present in accident data analysis is the predominance of zero-observations, which calls for the use of zero inflated models, i.e. count data models that explicitly account for the presence of a large number of zero-observations. [Lord et al.](#page-7-0)
+
+<span id="page-3-0"></span>![](_page_3_Figure_2.jpeg)
+
+**Fig. 2.** Diamond interchange.
+
+**Table 1** Descriptive statistics, accidents, whole sample period.
+
+| Variable                          | All ramps | E-ramps | O-ramps | T-ramps |
+|-----------------------------------|-----------|---------|---------|---------|
+| Min number of accidents on a ramp | 0         | 0       | 0       | 0       |
+| Max number of accidents on a ramp | 103       | 76      | 99      | 103     |
+| Mean number of accidents per ramp | 15.32     | 10.97   | 15.86   | 21.03   |
+| Mode                              | 4         | 4       | 2       | 4       |
+| Median                            | 9         | 7       | 11      | 12      |
+| Standard deviation                | 18.53     | 12.01   | 18.56   | 23.84   |
+| Variance                          | 343.33    | 144.20  | 344.48  | 568.44  |
+| Inter quartile range              | 15        | 12      | 18      | 25      |
+| Total number of accidents         | 3048      | 1042    | 555     | 1451    |
+| Number of ramps                   | 197       | 95      | 33      | 69      |
+| Number of zero-accident ramps     | 10        | 5       | 1       | 4       |
+
+[\(2005\)](#page-7-0) concluded that excess zeros indicate an inappropriate choice of time scale. Referring to Table 1, for neither ramp-type the mode is zero. We have only 10 zero-observations out of the 197 ramps (5 E-ramps, 1 O-ramp and 4 T-ramps). On the other hand, on 35 ramps, 25 ormore accidents happened in our sample period of three years. Furthermore, [Cheng andWashington \(2005\)fo](#page-7-0)und that three years of crash-history data provides an appropriate crash history duration, which initially motivated our choice of the data period. Therefore we decided against the use of zero inflated models in our analysis.
+
+Traffic flow data: The traffic flow data was provided by the "Landesbetrieb Straßenbau Nordrhein-Westfalen", the institution responsible for the planning, construction and maintenance of the Autobahn in the area of North Rhine-Westphalia.
+
+The traffic volume is counted automatically by induction loops that additionally recognize the length of passing cars and categorizes them into the groups of cars smaller or larger than 7.50 m. We will use the term passenger cars for the former and trucks for the latter group.
+
+The raw dataset contained daily data for all induction loops on Autobahns in the administrative district Düsseldorf for the period from the 4th of March 2005 to the 7th of March 2006, from which the traffic volume on the connectors of interest was extracted. Note that the sample period is not exactly the same as that of the accident data. However, we believe that the available data captures the essential information on the amount of traffic and can be used without any reservations.
+
+For our cross sectional analysis we calculated the average daily traffic (abbreviated ADT) for each ramp. For ramp i the ADT is defined as:
+
+$$ADT_{i} = \frac{1}{T_{i}} \sum_{t=1}^{T_{i}} TV_{i,t},$$
+(3.1)
+
+where TVi,<sup>t</sup> is the traffic volume on ramp i on day t and Ti is the number of daily observations available for ramp i. We also calculated the percentage of trucks on each ramp. Table 2 shows some descriptive statistics for the variable ADT. It is imminent that there is a large spread in the distribution of traffic volume on the various ramps.
+
+Geometry data: The geometry data was collected manually by using aerial photos of the ramps of interest. Details on how the variables were constructed are available from the authors upon request. [Table 3](#page-4-0) presents a list of the geometry variables along with their descriptive statistics.
+
+Next, a number of dummy variables were constructed that are shown in [Table 4.](#page-4-0)
+
+Finally, we have information on the surface types on the ramps. Three different types of surfaces have to be distinguished, namely, melted or mastic asphalt (MA), found on 57 ramps, mastic asphalt using chipping (MAC), found on 136 ramps, and asphaltic concrete
+
+**Table 2** Descriptive statistics ADT, whole sample period.
+
+| Average daily traffic (ADT) |           |
+|-----------------------------|-----------|
+| All vehicles (ADTTotal)     |           |
+| Mean                        | 6630.8    |
+| Maximum                     | 28,178.47 |
+| Minimum                     | 579.26    |
+| Standard deviation          | 4579.36   |
+| Passenger cars (ADTPC)      |           |
+| Mean                        | 5173.95   |
+| Maximum                     | 25,094.72 |
+| Minimum                     | 472.57    |
+| Standard deviation          | 3582.56   |
+| Trucks (ADTTrucks)          |           |
+| Mean                        | 1456.85   |
+| Maximum                     | 15,844.4  |
+| Minimum                     | 51.94     |
+| Standard deviation          | 2051.49   |
+
+<span id="page-4-0"></span>**Table 3** Descriptive statistics of geometry variables.
+
+| Variable                                   | Minimum | Maximum | Mean   | Stand.Dev. |
+|--------------------------------------------|---------|---------|--------|------------|
+| Length of the ramp (m)                     | 49.56   | 1868.15 | 335.12 | 243.95     |
+| Length of the deceleration lane (m)        | 0.00    | 902.24  | 258.00 | 158.08     |
+| Total width of the lanes on the ramp (m)   | 3.30    | 8.19    | 4.93   | 1.13       |
+| Width per lane (m)                         | 3.02    | 7.16    | 4.33   | 0.73       |
+| Width of the shoulder lane (m)             | 0.00    | 4.81    | 2.14   | 1.40       |
+| Radius steepest curve (m)                  | 28.43   | 1428.47 | 164.78 | 195.56     |
+| Total deflection angle (◦)                 | 0.00    | 305.15  | 115.78 | 92.75      |
+| Absolute total deflection angle (◦)        | 4.32    | 305.15  | 148.29 | 83.97      |
+| Angle of the steepest curve (◦)            | 3.76    | 302.00  | 119.86 | 86.47      |
+| Length of the steepest curve (m)           | 30.05   | 1259.25 | 205.49 | 155.90     |
+| Number of lanes on the ramp                | 1       | 2       | 1.17   | 0.38       |
+| Number of inflection points on the ramp    | 0       | 4       | 0.59   | 0.86       |
+| Position of the steepest curve on the ramp | 1       | 4       | 1.45   | 0.72       |
+| Number of curves on the ramp               | 1       | 6       | 1.72   | 0.93       |
+| Number of lanes on the autobahn leaving    | 1       | 3       | 2.48   | 0.51       |
+
+**Table 4** Descriptive statistics dummy variables.
+
+| Variable                                | Mean | Stand.Dev. |
+|-----------------------------------------|------|------------|
+| Right Autobahn lane becomes decel. lane | 0.06 | 0.24       |
+| A curve gets steeper                    | 0.24 | 0.43       |
+| A curve gets less steep                 | 0.13 | 0.34       |
+| Incline on the ramp                     | 0.50 | 0.50       |
+| Decline on the ramp                     | 0.54 | 0.50       |
+| Trees inside                            | 0.87 | 0.33       |
+| Trees outside                           | 0.78 | 0.42       |
+| Crossing lane at the access of the ramp | 0.22 | 0.42       |
+| Crossing lane at the exit of the ramp   | 0.22 | 0.41       |
+| Median between Autobahn and decel. lane | 0.38 | 0.49       |
+
+(AC) found on 4 ramps. Without going into details, according to [Richter and Heindel \(2004\)](#page-7-0) the main advantages of the different surface types are: MA is known to have a good grip, with the tradeoff of being a loud surface type. AC has the worst grip, but it is the cheapest of the three surface types. Roads build out of MAC are very durable and thus MAC is perfect for roads with high traffic density.
+
+# 3.3. Missing information
+
+There are a number of potential variables that may have been useful for the analysis but could not be collected. First of all, we did not have any information on traffic signs located on the connectors. On German Autobahns as well as on ramps there is no mandatory speed limit. However, on several ramps there are speed limit signs. "Slippery road"-signs can also be found on several ramps.
+
+Next, the aerial photos we used for the collection of our geometry variables did not give us any information on standing guardrails on the ramps. However, the effect of guardrails on accidents is a complex issue since guardrails may increase the frequency of property damage, but reduce the severity of accidents.1
+
+Another shortcoming of our dataset was the short period of our traffic flow variable, not allowing us for a substantiated panel data approach and hence making us ignore information on seasonality. Since a panel approach was not conducted, weather variables have not been used in our research. As the area of the connectors investigated is quite small (around 2300 km2), we think there are no significant differences in weather conditions for aggregated data. Nevertheless, in a panel approach it might have been interesting to take weather into consideration, not only to explain cross-sectional differences, but also to explain seasonality.
+
+Finally, the information we had on the road surface was also quite rudimentary. Without doubt, not only the type of the surface, but also the age of the surface has an impact on the grip of the road and thus an influence on the accident frequency.
+
+# **4. Empirical results**
+
+In this section we present the results of our empirical analysis. Section [4.1](#page-5-0) presents the estimation result. Their interpretation can be found in Section [4.2.](#page-6-0)
+
+Before we present our results we would like to note the following. First, Table 5 presents all variables we use along with their abbreviations. Second, for the regressions, the unit of measurement was changed to thousands of cars for all ADT-variables and to hundreds of meters for the radius in order to avoid unreadably small regression results.
+
+**Table 5** Abbreviations of variables in the dataset.
+
+| Variable                                         | Abbrevation             |
+|--------------------------------------------------|-------------------------|
+| Number of accidents                              | nb acc                  |
+| Length of the ramp                               | length ramp             |
+| Length of the deceleration lane                  | length decel            |
+| Total width of the lanes on the ramp             | width lanes             |
+| Width per lane                                   | width per lane          |
+| Width of the shoulder lane                       | width should            |
+| Radius steepest curve                            | radius                  |
+| Total deflection angle                           | angle tot               |
+| Absolute total deflection angle                  | angle abs               |
+| Angle of the steepest curve                      | angle steepest          |
+| Length of the steepest curve                     | length steepest         |
+| Number of lanes on the ramp                      | nb lanes                |
+| Number of inflection points on the ramp          | nb infl                 |
+| Position of the steepest curve on the ramp       | pos steepest            |
+| Number of curves on the ramp                     | nb curves               |
+| Number of lanes on the Autobahn leaving          | nb autob lanes          |
+| Dummy – Right Autobahn lane becomes decel. lane  | D autob decel           |
+| Dummy – A curve gets steeper                     | D steeper               |
+| Dummy – A curve gets less steep                  | D less steep            |
+| Dummy – Incline on the ramp                      | D incline               |
+| Dummy – Decline on the ramp                      | D decline               |
+| Dummy – Trees inside                             | D trees in              |
+| Dummy – Trees outside                            | D trees out             |
+| Dummy – Crossing lane at the access of the ramp  | D cross access          |
+| Dummy – Crossing lane at the exit of the ramp    | D cross exit            |
+| Dummy – Median between Autobahn and decel. lane  | D median                |
+| Average daily traffic passenger cars             | ADT pc                  |
+| Average daily traffic trucks                     | ADT trucks              |
+| Truck percentage                                 | truck perc              |
+| Threshold Dummy – Length deceleration lane       | T length decelthreshold |
+| Threshold Dummy – Width of the lanes             | T width lanesthreshold  |
+| Threshold Dummy – Position of the steepest curve | T pos steepestthreshold |
+| Threshold Dummy – Radius of the steepest curve   | T radiusthreshold       |
+
+<sup>1</sup> We would like to thank an anonymous referee for pointing this out.
+
+<span id="page-5-0"></span>**Table 6** Estimation results.
+
+| Variable             | Fixed parameters model |             | Random parameters model |             |  |
+|----------------------|------------------------|-------------|-------------------------|-------------|--|
+|                      | Coefficient            | Std. Errors | Coefficient             | Std. Errors |  |
+| Constant             | −0.9091                | 0.4791      | −1.2067                 | 0.4690      |  |
+| ln(ADT pc)           | 0.7363                 | 0.0988      | 0.8130                  | 0.1030      |  |
+| truck perc           | 0.8954                 | 0.4194      | 1.2078                  | 0.4114      |  |
+| ln(angle abs)        | 0.2685                 | 0.0840      | 0.2838                  | 0.0780      |  |
+| D steeper            | 0.3435                 | 0.1661      | 0.2364                  | 0.1776      |  |
+| RC                   |                        |             | 0.5989                  | 0.1925      |  |
+| T length decel180    | 0.4831                 | 0.1409      | 0.4352                  | 0.1382      |  |
+| RC                   |                        |             | 0.5071                  | 0.1381      |  |
+| T width lanes3.90    | 0.4333                 | 0.1824      | 0.4057                  | 0.1942      |  |
+| T pos steepest1      | 0.3115                 | 0.1470      | 0.2246                  | 0.1527      |  |
+| RC                   |                        |             | 0.5012                  | 0.1765      |  |
+| Dispersion parameter | 0.6267                 | 0.0719      | 0.2909                  | 0.1160      |  |
+| ln L                 | −689.86                |             |                         | −685.99     |  |
+| AIC                  | 1397.7                 |             | 1395.9                  |             |  |
+| BIC                  | 1427.3                 |             | 1435.4                  |             |  |
+| Pseudo-R2            |                        | 0.0672      |                         | 0.0725      |  |
+
+#### 4.1. Estimation results
+
+We consider the negative binomial (NB) regression both with fixed and with (possibly) random coefficients (RC). A coefficient is treated as random when its estimated standard deviation RC is significantly different from 0. Since the negative binomial model nests the Poisson regression model when ˛= 0 the null hypothesis of a Poisson Model, and hence the null hypothesis of equidispersion, can be tested using the LR test as described in Section [2. W](#page-1-0)e computed this LR statistic for all estimated models and it turned out that the test has p-values of virtually zero for all the model specifications we considered. An exception is the RC model with random intercept, in which case the fit of the Poisson regression is almost identical to the fit of the NB model. This is not surprising as the NB model and the Poisson model with random intercept are very similar differing only in the error distributions.
+
+Preliminary estimates of the NB regression reveal that from our initial set of variables only ADT pc, ln(angle abs), truck perc and D steeper are statistically significant. Alternatively, the radius can be used instead of ln(angle abs), as these two variables have a correlation of about −0.76. In the next step of our analysis, we test for the different functional forms of the regressor ADT pc in order to allow for nonlinearities. We consider two variations, first by adding a quadratic term to the initial model and second by working with the natural logarithm of ADT pc. Both choices clearly improve the model fit as indicated by the pseudo-R<sup>2</sup> and information criteria. However, there is no clear evidence whether the squared form is to be preferred over the logarithmic form. In order to get an additional evaluation criterion we conducted the LR-test for non-nested models proposed by [Vuong \(1989\). T](#page-7-0)he null hypothesis of equivalence of the models cannot be rejected in favor of any of the specifications. However, as it has one parameter less to estimate we continue working with the logarithmic form.
+
+Next, we want to investigate the heterogeneity across the different ramp types suggested by the descriptive statistics. Ideally, a separate regression should be estimated for each ramp type, but given the small number of observations for the individual ramp types the results would not be reliable. Therefore we consider dummy variables for each ramp type (skipping the intercept to avoid multicollinearity) and perform a likelihood ratio test to see if the model fit improved. The improvement in fit is not significant so we dropped the dummies from the model.
+
+As none of the remaining variables were found to have additional significant effects in explaining accident frequencies we investigate whether there are possible threshold effects. By this we mean the effect when variables are larger than some (predetermined) value and we consider these to capture potential nonlinearities. To identify the thresholds we create dummy variables that for values exceeding the supposed threshold value and zero otherwise. By varying the threshold value and comparing the information criteria and the pseudo-R<sup>2</sup> we try to determine the actual value of the threshold. The notation of the threshold variables is as follows: A "T" in front of the variable indicates that this is a dummy measuring the threshold and the index-number shows the value of the threshold. This means that the variable is 1 for values larger than the threshold and zero otherwise. Three variables seem to have a threshold effect, namely the length of the deceleration lane (length decel), the total width of the lane(s) (width lanes) and the position of the steepest curve (pos steepest).
+
+We would like to note two things concerning our final model: (i) the variable width lanes measures the total width of the officially accessible lanes without accounting for the width of a possible shoulder lane. We also investigated a possible threshold effect of the total width of the official road together with the shoulder lane (i.e. the whole possibly accessible road). However no significant effect could be found. (ii) the variable T pos steepest1 takes on the value one if the first curve is not the steepest curve on the ramp.
+
+The following step in the analysis is to allow for random coefficients. We estimate the model using 500 Halton draws to simulate the log-likelihood function. Initially, all model parameters are allowed to vary randomly, but we treat parameters as fixed when the estimated variance of the random coefficient RC is not significantly different from 0. Only the variables D steeper, T length decel180 and T pos steepest1 have random coefficients. Furthermore, in the random coefficient model no additional variables from our dataset have a significant (fixed or random) effect on the number of accidents.
+
+Table 6 presents the estimation results of our model with fixed and random coefficients. First of all, it is noticeable that the random coefficient specification only leads to a small improvement in the model fit, which is in contrast to the findings of [Anastasopoulos](#page-7-0) [andMannering \(2009\). N](#page-7-0)evertheless, a likelihood ratio test suggests that the improvement in fit is significant with a p-value of about 0.05. The BIC, on the other hand, indicates that the simpler version of the model with fixed parameters is more suitable. Furthermore, the estimated dispersion parameter˛of the binomial distribution is much smaller for the random coefficient model, which is likely due to the fact that the heterogeneity of the random coefficients picks up some of the heterogeneity originally captured by the dispersion parameter. The parameter estimates are mostly very similar across the models, with the exception that the parameter of the variable truck perc changes when allowing for random coefficients. How-
+
+<span id="page-6-0"></span>**Table 7** Marginal effects.
+
+| Variable          |             | Fixed parameters model |        |             | Random parameters model |        |  |
+|-------------------|-------------|------------------------|--------|-------------|-------------------------|--------|--|
+|                   | Coefficient | Avg                    | At Avg | Coefficient | Avg                     | At Avg |  |
+| ln(ADT pc)        | 0.74        | 11.14                  | 8.89   | 0.81        | 10.53                   | 8.32   |  |
+| truck perc        | 0.90        | 13.55                  | 10.82  | 1.21        | 15.64                   | 12.36  |  |
+| ln(angle abs)     | 0.27        | 4.06                   | 3.24   | 0.28        | 3.67                    | 2.90   |  |
+| D steeper         | 0.34        | 5.20                   | 4.15   | 0.24        | 3.06                    | 2.42   |  |
+| T length decel180 | 0.48        | 7.31                   | 5.84   | 0.44        | 5.64                    | 4.45   |  |
+| T width lanes3.90 | 0.43        | 6.56                   | 5.23   | 0.41        | 5.25                    | 4.15   |  |
+| T pos steepest1   | 0.31        | 4.71                   | 3.76   | 0.22        | 2.91                    | 2.30   |  |
+
+ever, for the variables that have random coefficients, the estimates are a bit lower compared to their fixed counterparts.
+
+#### 4.2. Interpretation
+
+In Table 7 we report both the average marginal effect, as well as the marginal effect evaluated at the averages of the regressors. We only interpret the model with random coefficients, since the overall model fit is better and the parameter estimates are quite close for most of the variables.
+
+The variable that has the strongest effect on the number of accidents is the measure of average daily traffic. Since the variable ADT pc enters in logarithmic form it means that a 1% increase in average daily traffic on average leads to a 0.81% increase in the expected number of accidents. An increase of truck perc by 0.1 units, hence an increase of the truck ratio by 10 percentage points leads to an increase in the expected number of accidents by 12.08%. The mean effect "Avg" suggests that the average effect of a 10 percentage point increase in the ratio of trucks yields 1.56 more expected accidents per ramp in a time period of three years. The "Avg" estimates for this model are about 26% higher than those of the "representative" ramp given in "At Avg", which is due to the convex exponential mean function. The same phenomenon can therefore be observed for the other variables. The remaining variables are more interesting from an engineering perspective. The estimated coefficient of the variable ln(angle abs) implies that a 1% increase in the absolute total deflection angle leads to a 0.27% increase in the expected number of accidents. Next, a ramp on which a curve gets steeper on average has an exp (0.24) = 1.27 times higher expected number of accidents than a ramp on which no curve is getting steeper. In absolute terms you expect on average 3.06 more accidents over a period of three years when a curve on a ramp gets steeper. The distribution of the random coefficient implies that in 35% of the cases the effect of a curve getting steeper actually reduces the number of accidents, but for the majority of cases this has a positive effect.
+
+The estimates of the remaining variables are rather counterintuitive. The estimate of 0.4352 for the coefficient of the variable T length decel180 suggests that exp (0.43) = 1.54 times more accidents occur on ramps with a deceleration lane larger than 180 m in contrast to ramps with a deceleration lane that is smaller than 180 m. However, 20% of the parameter distribution is less than 0 and thus of the expected sign. Similarly, the expected number of accidents on ramps with lane widths exceeding 3.9 m is 1.5 times higher than on ramps with lane widths of less than 3.9 m. Finally, the estimate of the threshold variable T pos steepest1 suggests that we can expect the number of accidents to be 1.25 times higher, if the first curve is not the steepest on the ramp. In this case, about 33% of the distribution is smaller than zero. One reason for these three counterintuitive results might be that an unsafe looking ramp causes the driver to be more aware. Another explanation is an omitted variable bias, since it is likely that there are stricter speed restrictions (or warning sings) on these unsafe ramps, which in would turn decrease the number of accidents. However, part of the possible problem of omitted variable bias is handled by allowing for random parameters.
+
+## **5. Conclusion**
+
+The aim of this paper was to find an appropriate statistical model that helps to explain accident frequencies on Autobahn connectors in Germany. The negative binomial regression model with random coefficients turned out to be the most appropriate tool. Our dataset contains detailed information on accidents on 197 connectors, data on traffic flow of passenger cars and trucks, and a set of nearly 30 geometry variables. Although the three types of ramps, egressramps (n =95), tangent-ramps (n =69) and loop-ramps (n =33), have quite distinct characteristics, dummy variables indicating ramp types are not significant and separate models cannot be estimated due to the small number of observations in the sub-populations.
+
+The most important variable explaining accident frequencies is the average daily traffic. The fraction of trucks is also an important factor. Beyond that, measures of the curvature, like the radius of the steepest curve or a dummy indicating that a curve gets steeper, turned out to be relevant. The variables measuring the length of the deceleration lane, the width of the lanes and the position of the steepest curve only have an effect when exceeding certain thresholds.
+
+The final question is whether and how our findings can be used to improve the safety of existing Autobahn connectors and to give recommendations in the construction of new ones. The accident factors identified in this study cannot be used for simple short term improvements, which is not surprising, as the easiest and cheapest solution one can think of is putting up additional warning signs and speed restrictions. Since we had no data available on these, and it is likely that these measures were already taken on relatively dangerous connectors, we have to leave the recommendation of simple solutions to future research that includes such information. However, if connectors are built from scratch, our results might be helpful. The finding that curves getting steeper yield higher accident frequencies is definitely a result that future planning should not disregard. The radius effect might also be interesting for the design of ramps. This can be simplified as: the steeper a curve, the more accidents can be observed. The significant positive parameter of the variable absolute total deflection angle can be interpreted as: the simpler a ramp is constructed, the less accidents can be expected.
+
+In future research we need to deal with the data limitations encountered. Information on speed limitations, vertical grades on the ramps or exit approaches, warning signs and pavement friction is likely to add significant explanatory power to the model. Furthermore, one may try to expand the dataset and consider temporal and dynamic effects, possibly in a panel framework. Finally, the small number of observations is another limitation of the current research, as it was not possible to estimate models for the different ramp types separately.
+
+### <span id="page-7-0"></span>**Acknowledgments**
+
+The authors would like to thank Jean-Pierre Urbain, Frowin Schulz and three anonymous referees for valuable comments. The authors would also like to thank the Landesbetrieb Straßenbau Nordrhein-Westfalen and the Autobahnpolizei Düsseldorf for providing the raw data.
+
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+- Lord, D., Washington, S., Ivan, J., 2005. Poisson, poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory. Accident Analysis and Prevention 37, 35–46.
+- Miaou, S., Lum, H., 1993. Modeling vehicle accidents and highway geometric design relationships. Accident Analysis and Prevention 25, 689–709.
+- Pickering, D., Hall, R., Grimmer, M., 1986. Accidents on rural t-junctions. Tech. rep., Research Report 65. Transportation and Research Laboratory, Department for Transport, Crowthrone, Berkshire, United Kingdom.
+- Richter, D., Heindel, M., 2004. Straßen- und Tiefbau. Mit lernfeldorientierten Projekten. Teubner.
+- Schwarz, G., 1978. Estimating the dimension of a model. Annals of Statistics 6, 461–464.
+- Shankar, V., Albin, R., Milton, J., Mannering, F., 1998. Evaluating median cross-over likelihoods with clustered accident counts: an empirical inquiry using the random effects negative binomial model. Transportation Research Record, 1635.
+- Shankar, V., Mannering, F., Barfield, W., 1995. Effect of roadway geometrics and environmental factors on rural freeway accident frequencies. Accident Analysis and Prevention 27, 371–389.
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+- Train, K., (1999). Halton sequences for mixed logit. Working paper. University of California, Department of Economics, Berkeley.
+- Treat, J., Tumbas, N., McDonald, S., Shinar, D., Hume, R., Mayer, R., Stanisfer, R., Castellan, N., 1977. Tri-level study of the causes of traffic accidents. Report No. DOT-HS-034–3-535–77 (TAC).
+- Vuong, Q., 1989. Likelihood ratio tests for model selection and non-nested hypothesis. Econometrica 57, 307–334.
+- Washington, S., Karlaftis, M.G., Mannering, F.L., 2003. Statistical and Econometric Methods for Transportation Data Analysis. CRC, Chapman and Hall.

Zotero/001_artiklid/Road Safety Indicators/gitelmandesigningcompositeindicatorroad2010.md

@@ -0,0 +1,595 @@
+---
+category: literaturenote
+citekey: gitelmandesigningcompositeindicatorroad2010
+title: Designing a composite indicator for road safety
+authors: "Gitelman, Victoria; Doveh, Etti; Hakkert, Shalom"
+year: 2010
+date: 2010-00-00 2010
+doi: 10.1016/j.ssci.2010.01.011
+publication: Safety Science
+url: "https://doi.org/10.1016/j.ssci.2010.01.011"
+zotero_key: B4W7HUXZ
+zotero_storage: 9DKWFUXN
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "Gitelman, Victoria"
+status: converted
+---
+![](_page_0_Picture_1.jpeg)
+
+## Contents lists available at [ScienceDirect](http://www.sciencedirect.com/science/journal/09257535)
+
+# Safety Science
+
+journal homepage: [www.elsevier.com/locate/ssci](http://www.elsevier.com/locate/ssci)
+
+![](_page_0_Picture_5.jpeg)
+
+# Designing a composite indicator for road safety
+
+Victoria Gitelman a,\*, Etti Doveh <sup>b</sup> , Shalom Hakkert <sup>a</sup>
+
+- <sup>a</sup> Transportation Research Institute, Technion City, Haifa 32000, Israel
+- <sup>b</sup> The Technion Statistical Laboratory, Technion City, Haifa 32000, Israel
+
+### article info
+
+#### Article history: Received 1 September 2009 Received in revised form 12 January 2010 Accepted 14 January 2010
+
+Keywords: Road safety Performance Composite indicator Statistical weighting
+
+### abstract
+
+This study set out to develop a composite road safety indicator for benchmarking countries' road safety performance, which would combine the main layers of the road safety pyramid which describes the complex nature of road safety activities, performance and outcomes. Four groups of basic safety indicators were considered, which refer to: policy performance (road safety programmes), final road safety outcomes (fatality rates, scope of traffic injury), intermediate outcomes (wearing rates of seat belts, crashworthiness and composition of vehicle fleet, alcohol-impaired driving), and background characteristics of countries (motorization level, population density). The analysis used the data collected for 27 European countries. Weights based on statistical models were used to combine the basic indicators into a composite one. Principal Component Analysis and Common Factor Analysis weighting were examined. The composite indicators, estimated by several methods, enabled us to rank and group the countries according to their safety performance.
+
+The analysis revealed that the countries' ranking based on the composite indicators is not necessarily similar to the traditional ranking of countries based on fatality rates only. Furthermore, it was observed that the indicators belonging to the final outcomes and intermediate outcomes are not uniform in their behaviour. Indicators which were found to be more consistent and influential and termed a 'core set of basic indicators' are recommended for future uses. The general conclusion is that the design of a composite road safety indicator in which relevant information from the different components of the road safety pyramid has been captured and weighted is realistic and meaningful. Such an indicator gives a more enriched picture of road safety than a ranking based only on fatality rates, which is the common practice at present. Grouping countries in this process is promising and seems to be preferable to simply ranking countries.
+
+> -2010 Elsevier Ltd. All rights reserved.
+
+# 1. Introduction
+
+The number of indicators suggested for use in the field of road safety has been growing rapidly, especially over the last decade ([ETSC, 2001; Wegman et al., 2005; Al Haji, 2005; Hakkert et al.,](#page-12-0) [2007; Hermans et al., 2008\)](#page-12-0). The purposes of road safety indicators are to enable meaningful national or sub-national (e.g. regional, local, etc.) comparisons and monitoring over time, of road safety developments. Recognising the complex character of the road safety phenomenon, today more and more indicators are intended to measure the factors contributing to accidents, to identify conditions which are associated with increased accident/injury risks, and to detail the structure of traffic injury patterns. In contrast, the traditional approach mainly considered the safety outcomes in terms of fatalities per population, vehicle fleet or exposure.
+
+Moreover, road safety is steadily developing as a major policy area [\(Peden et al., 2004](#page-12-0)), where safety performance indicators could and should serve as supportive tools for policymakers. In comparing the safety achievements of countries there is a need to reduce the dimensions of the problem and to be able to work with a composite indicator which can describe all the relevant components in a concise and comprehensive way. Examples of such indicators are known in other domains such as: the Human Development Index which reflects life expectancy, education level and living standards in each country, and is used by the United Nations for the estimation of progress and annual country comparisons; the Environmental Sustainability Index which is used by the World Economic Forum; the Overall Health System Index used by the World Health Organisation (WHO), and others ([Al Haji,](#page-12-0) [2005; Nardo et al., 2005\)](#page-12-0).
+
+A number of studies were recently carried out that were aimed at the development of a composite road safety index. [Al Haji \(2005\)](#page-12-0) suggested a Road Safety Development Index (RSDI) and used it for a comparison of road safety progress in ten Asian countries plus Sweden. The RSDI development started with the definition of eight
+
+<sup>\*</sup> Corresponding author. Tel.: +972 4 8295132; fax: +972 4 8225716. E-mail addresses: [trivica@tx.technion.ac.il](mailto:trivica@tx.technion.ac.il) (V. Gitelman), [ierde01@ie.technion.](mailto:ierde01@ie.technion.ac.il) [ac.il](mailto:ierde01@ie.technion.ac.il) (E. Doveh), [hakkert@tx.technion.ac.il](mailto:hakkert@tx.technion.ac.il) (S. Hakkert).
+
+dimensions of the road safety domain, which are traffic risk, personal risk, vehicle safety, road situation, road user behaviour, socio-economic background, road safety organisation and enforcement. For each dimension, one or several quantitative indicators were suggested and their applicability was analysed based on available data. Finally, each country was characterized by eleven separate indicators which were combined into one composite indicator. To construct a composite index, [Al Haji \(2005\)](#page-12-0) applied three ways of weighting, which were the simple equal average, the use of theoretical weights, and the Principal Component Analysis. The results of the different methods were consistent and enabled a robust classification of countries into three groups of high, medium or low safety development.
+
+[Hermans et al. \(2008\)](#page-12-0) studied the issue of assigning weights to individual indicators, to provide a combined road safety index. The researchers considered the seven safety domains which were defined by the SafetyNet project [\(Hakkert et al., 2007](#page-12-0)): alcohol and drugs, speed, protective systems, visibility (daytime running lights), vehicles, infrastructure, and trauma care. They suggested one indicator for each domain. Based on the data available in the international databases, from the WHO, and from the SARTRE project, the indicators were estimated for 21 European countries. Five weighting techniques as suggested by [Nardo et al. \(2005\)](#page-12-0) were used to combine the separate indicators into one index: factor analysis, analytical hierarchy process, budget allocation, data envelopment analysis, and equal weighting. The rankings resulting from these weighting methods were further compared with the countries' rankings according to the personal risk (the number of traffic fatalities per million inhabitants). It was found that different weighting methods agreed most on the ranking of countries with a low road safety ranking. Moreover, of the five methods, the data envelopment analysis method resulted in a ranking which best approaches the countries' ranking based on the personal risk.
+
+Both studies have clearly demonstrated the possibilities for creating composite road safety indices. However, they both considered a relatively small number of basic indicators, for some of which the quality of the data for the quantitative measures selected can be questioned.
+
+In this study, we aimed to create and explore a comprehensive composite road safety indicator, based on the recent concepts of the road safety domain developed by the SUNflower ([Wegman](#page-12-0) [et al., 2005\)](#page-12-0) and SafetyNet ([Hakkert et al., 2007](#page-12-0)) projects. In the SafetyNet project safety performance indicators were developed, but no attempt was made to combine the results from different indicators into one composite value, in order to compare countries. Somewhat earlier the SUNflower project tried to develop a methodology to compare countries on their safety level. This resulted in the footprint methodology. It was felt that, on the basis of these prior methods and the available data, a new composite indicator could be developed, what has been carried out in the present study.
+
+In this process, the types of benchmarking discussed in the literature were considered, and data for the European countries were used that were collected in the SafetyNet project and which were available from international databases. This study was a component of a comprehensive project aimed at developing a knowledge-based framework for the benchmarking of road safety performances and developments for national and sub-national jurisdictions [\(Wegman et al., 2008\)](#page-12-0).
+
+### 2. The model
+
+### 2.1. The road safety pyramid
+
+The SUNflower approach ([Koornstra et al., 2002; Wegman et al.,](#page-12-0) [2005](#page-12-0)) described the road safety domain as a pyramid consisting of several layers, from bottom to top: safety measures and programmes (as the road safety policy performance); safety performance indicators (as intermediate outcomes); the numbers of accident fatalities/injuries (as the final outcomes) and the social costs of accidents/injuries at the very top. An additional 'Structure and culture' layer has been added at the bottom of the pyramid to include the background conditions of the system or the policy context [\(Koornstra et al., 2002\)](#page-12-0).
+
+The layer of safety performance indicators (SPIs) was originally explored by [ETSC \(2001\).](#page-12-0) The reason for the SPIs development was the assumption that accidents and injuries are only the tip of the iceberg, because they occur as the 'worst case' result of unsafe operational conditions in the road traffic system. Thus, SPIs can be defined as measures that are causally related to accidents or injuries and are used in addition to the figures about accidents or injuries, in order to indicate safety performance or understand the processes that lead to accidents [\(ETSC, 2001\)](#page-12-0).
+
+The SafetyNet project [\(Hakkert et al., 2007\)](#page-12-0) provided a further methodological basis for the SPIs' development. Based on the potential of different road safety areas for increasing road safety as well as on the experiences and data available, seven problem areas were designated as central to road safety activities in Europe. They are: (1) alcohol and drug-use; (2) speeds; (3) protective systems; (4) daytime running lights; (5) vehicles (passive safety); (6) roads and (7) trauma management.
+
+For each one of these areas, SPIs were developed and, then, using the data provided by national representatives of the European countries, SPIs were estimated and country comparisons were performed – see [Vis and Van Gent \(2007\)](#page-12-0).
+
+### 2.2. Basic indicators
+
+This study set out to develop a composite road safety indicator for benchmarking purposes, which would combine the main layers of the road safety pyramid.
+
+The layers considered were the road safety policy performance (safety measures and programmes), accident fatalities/injuries (as the final outcomes) and safety performance indicators (as intermediate outcomes). These layers will be further described by A-, Band C-groups of indicators, respectively. A fourth group of indicators (D) was added trying to present some background variables for each country as a first attempt to identify components of the lowest level of the pyramid ('structure and culture').
+
+To develop a composite indicator, basic indicators should first be defined, for each layer of the pyramid that needs to be considered. As stated earlier, the present study builds upon the theory and evidence developed and collected in two earlier related projects: the SUNflower [\(Wegman et al., 2005](#page-12-0)) and SafetyNet ([Hakkert](#page-12-0) [et al., 2007](#page-12-0)) studies. In these studies a theory was developed linking the characteristics of four basic layers related to safety, especially concerning the final outcomes' and intermediate outcomes' layers. In the SafetyNet project a large amount of evidence was collected and described linking the indicators of intermediate outcomes to safety. On the other hand, the final selection of basic indicators was limited by the data currently available for the European countries from international databases and from the Safety-Net project.
+
+As for the policy indicators, results have been reported in the literature that countries with comprehensive safety programs and quantitative targets usually performed better than others. The main principles of successful road safety management are well summarized by [OECD \(2002\), ETSC \(2006\), Elvik \(2008\).](#page-12-0) Based on these principles, for the A-group of indicators a number of characteristics were suggested which would reflect the quality of national road safety programmes. The five indicators introduced for the Agroup related to the level of national safety targets, the approach applied for selection of interventions, the scope of economic evaluation which preceded the programme's composition, the way of monitoring and the level of responsibility for the programme's performance. For each indicator, the categories of values were defined as presented in Table 1.
+
+For each country, the value of each indicator should be selected based on the published national road safety programmes, other background papers and available follow-up reports, including those prepared by the European Transport Safety Council (ETSC), Organisation for Economic Co-operation and Development (OECD) or other international working groups. The values applied in the current study should be treated as preliminary as those are mostly based on two sources: country reports from [OECD/ECMT \(2008\)](#page-12-0) and surveys provided by [OECD/ITF \(2008\),](#page-12-0) and on some other frequently cited road safety publications.
+
+Giving the values according to Table 1, the national safety programme was marked as having an ''ambitious" target when it was in line with the European policy of 50% reduction in fatalities by 2010 or when it implied an average annual reduction of fatalities by 5% or more; such a mark (value ''a") was given for many countries. On the other hand, some countries (e.g. Italy) stated that they have no national targets (value ''c"); the remainder of countries received value ''b".
+
+Considering the selection of safety interventions for the national programme, the best mark (value ''a") was given for the programmes where a comprehensive categorization of road safety problems and estimation of their magnitude was performed as it was done, for example, for Sweden by [Elvik and Amundsen](#page-12-0) [\(2000\)](#page-12-0) and for Switzerland by [VESIPO \(2002\).](#page-12-0) Value ''b" of this indicator reflects the emphasis on evidence-based measures selected by the programme, where the ''c" value indicates a case where detailed analysis of accident statistics is performed but no estimation of safety effects associated with the measures is provided.
+
+Considering the economic evaluation, the best mark (value ''a") is given for the programme, when a background study estimated the safety benefits expected. For example, in Switzerland, the development of a road traffic safety policy was based on a comprehensive study which assessed the efficiency of 77 road safety measures [\(VESIPO, 2002](#page-12-0)); [Elvik \(2001\)](#page-12-0) demonstrated cost-effective analyses of road safety policies for Norway and Sweden, which enveloped 132 and 139 road safety measures, respectively. Usually, a general economic evaluation is performed where the numbers of fatalities and injuries to be saved are compared with the investments required for the programme's performance (value ''b").
+
+For the monitoring indicator, value ''a" is assigned when the monitoring analysis reports are available, e.g. [Broughton and](#page-12-0) [Buckle \(2006\)](#page-12-0) for the UK. As to the stakeholders' indicator, the level of adoption and responsibility for the programme's performance can be learnt from the OECD country reports where the governmental responsibility (value ''a"), the responsibility of national road safety authority (value ''b"), shared responsibility of several bodies (value ''c") or no clear responsibility (value ''d") are indicated.
+
+In spite of the thorough effort to provide the data, it should be realised that it is difficult to obtain quantitative and unbiased estimates on the actual implementation of road safety policies and programs.
+
+The B-group of indicators deals with the final outcomes of the system, i.e. the numbers of road accident fatalities and injuries, which should be presented in a form suitable for comparisons. The present study focused on four issues: personal risk, traffic risk, the scope of traffic injury and the scope of the problem of vulnerable road users. For each issue one or several indicators were defined – [Table 2.](#page-3-0)
+
+Concerning this group of indicators, we can note that personal risk and traffic risk indicators are common in international comparisons; the indicators of traffic injury, in addition to fatalities, receive more attention over the last years both in international comparisons and in setting national safety targets (e.g. [OECD/ITF,](#page-12-0) [2008\)](#page-12-0). As to the share of pedestrians/two-wheelers out of the total fatalities, those are compared among the countries where higher than average values frequently lead to more concerted safety efforts and interventions related to the subject (e.g. pedestrian safety issue in the national safety programme in the UK).
+
+The C-group of indicators captures the intermediate outcomes, containing the safety performance indicators which characterize the safety quality of the road traffic system. Having analysed the data available in the seven pre-defined SPI areas ([Vis and Van Gent,](#page-12-0) [2007\)](#page-12-0) as well as the summaries on safety performance indicators (PIN Flashes) recently published by the ETSC, it was decided to limit the present project to only those safety areas for which the estimates are available for a significant number of EU Member States. The remaining safety areas are: alcohol-impaired driving, use of protective systems in cars, the crashworthiness of the passenger car fleet, and the vehicle fleet composition. For each area one or two indicators have been defined – [Table 3.](#page-3-0)
+
+Table 1 Definition of basic indicators for the A-group: characteristics of national safety programmes.
+
+| Indicators                    | Possible values                                                                                                                                                                   |
+|-------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
+| A1 Safety targets             | a. Ambitious                                                                                                                                                                      |
+|                               | b. Available but not ambitious                                                                                                                                                    |
+|                               | c. Not available                                                                                                                                                                  |
+| A2 Selection of interventions | a. Sound analysis and diagnosis of road safety problems preceded the programme's development, and evidence-based                                                                  |
+|                               | interventions were selected                                                                                                                                                       |
+|                               | b. Some analysis was performed, and evidence-based interventions were selected                                                                                                    |
+|                               | c. Detailed analysis of road safety problems was performed, however, the selection of interventions was arbitrary                                                                 |
+|                               | d. The diagnosis of road safety problems was poor and the selection of interventions was arbitrary                                                                                |
+| A3 Economic evaluation        | a. Detailed economic evaluation preceded the programme's composition                                                                                                              |
+|                               | b. Some economic evaluation was performed                                                                                                                                         |
+|                               | c. Economic evaluation was not performed                                                                                                                                          |
+| A4 Monitoring the programme's | a. Systematic monitoring takes place                                                                                                                                              |
+| performance                   | b. A need for monitoring is stated but monitoring reports are not found                                                                                                           |
+|                               | c. No evidence of monitoring activities                                                                                                                                           |
+| A5 Programme's stakeholders   | a. Commitment was stated on the governmental level, and the programme is supervised by a central authority which is<br>empowered to coordinate the activities of all other bodies |
+|                               | b. No commitment from the government, however, a central authority was commissioned for the programme's performance                                                               |
+|                               | c. A number of authorities share the responsibility for the programme's performance                                                                                               |
+|                               | d. No authority has a clear responsibility for the programme's performance                                                                                                        |
+
+<span id="page-3-0"></span>Table 2 Definition of basic indicators for the B-group: final outcomes.
+
+| Issues considered                             | Indicators defineda                                             |
+|-----------------------------------------------|-----------------------------------------------------------------|
+| Personal risk                                 | B1 Fatalities per million inhabitants                           |
+| Traffic risk                                  | B2 Fatalities per million passenger cars                        |
+|                                               | B3 Fatalities per 10 billion passenger-km travelled             |
+| Scope of traffic injury                       | B4 Injury accidents per fatalityb                               |
+| Scope of the problem of vulnerable road users | B5 Share of pedestrian fatalities out of the total fatalities   |
+|                                               | B6 Share of bicyclist fatalities out of the total fatalities    |
+|                                               | B7 Share of motorcyclist fatalities out of the total fatalities |
+
+<sup>a</sup> Note: Obviously, various definitions are possible. B2 can for instance be defined per total vehicle fleet instead of passenger cars, B3 per vehicle kilometer travelled instead of passenger kilometer, etc. The selection was based on the estimates available to the EU Member States.
+
+Table 3 Definition of basic indicators for the C-group: intermediate outcomes, SPIs.
+
+| Safety areas considered                              | Indicators defined                                                                                    |
+|------------------------------------------------------|-------------------------------------------------------------------------------------------------------|
+| Alcohol-impaired driving                             | C1 Share of total for fatalities in drink-driving accidents                                           |
+| Use of protective systems in cars                    | C2 Daytime wearing rates of seat belts in the front seats (aggregated for driver and front passenger) |
+|                                                      | C3 Daytime wearing rates of seat belts in the rear seats                                              |
+| Vehicles: crashworthiness of the passenger car fleet | C4 Average EuroNCAP score of passenger car fleet                                                      |
+|                                                      | C5 Median age of the passenger car fleet                                                              |
+| Vehicle fleet composition                            | C6 Share of motorcycles in the vehicle fleet                                                          |
+|                                                      | C7 Share of heavy goods vehicles (HGV) in the vehicle fleet                                           |
+
+Finally, two background indicators were added (the D-group) which characterize the motorization level and the population density of the country – Table 4. Both indicators are common in international and other comparisons as context variables reflecting the development and structural differences among the countries or other entities compared [\(Wegman et al., 2008](#page-12-0)).
+
+The choice of indicators used was influenced by the immediate availability of data and, therefore, their definitions have a preliminary character, supporting the main purpose of the study, to demonstrate along which lines composite indicators can be designed.
+
+# 2.3. Data collection
+
+In total, 21 basic safety indicators were defined for consideration. The estimates of the indicators and/or data for their calculation were taken from a wide range of international databases and recent publications of international working groups, including:
+
+For group A – [OECD/ITF \(2008\), OECD/ECMT \(2008\)](#page-12-0); For group B – [EC \(2007\), ERSO \(2008\);](#page-12-0) For C1 – [ETSC \(2007a\);](#page-12-0) for C2, C3 – [ETSC \(2007b\);](#page-12-0) for C4 – [Vis](#page-12-0) [and Van Gent \(2007\)](#page-12-0); for C5 – [UNECE \(2008\)](#page-12-0); for C6, C7 – [EC](#page-12-0) [\(2007\)](#page-12-0) and OECD country reports (2008).
+
+The basic indicators were estimated for 27 countries: 25 Member States of the European Union plus Norway and Switzerland – [Table 5](#page-4-0). (The majority of indicators are not yet available for the new Member States Bulgaria and Romania.)
+
+### 2.4. Method of analysis
+
+The purpose of this analysis is to create a composite road safety indicator and to explore the behaviour of basic indicators. The
+
+Table 4 Definition of basic indicators for the D-group: background characteristics.
+
+| Characteristic<br>considered | Indicators defined                               |
+|------------------------------|--------------------------------------------------|
+| Motorization level           | D1 Number of passenger cars per 1000 inhabitants |
+| Population density           | D2 Population per 1 km2 of country's territory   |
+
+composite indicator will enable ranking countries in accordance with their safety performance or, at least, to define several groups of countries with different levels of safety performance.
+
+As can be seen in [Table 5](#page-4-0), only six countries had values for the whole set of basic indicators A–D. Therefore, prior to the analysis, missing data imputations were performed. The SAS 9.2 MI procedure was applied using the MCMC method for imputation. This imputation assumes multivariate normality of variables. We used SAS macro % bctrans to find a Box–Cox transformation in order to achieve marginal normality of each of the continuous variables ([LaLonde, 2005\)](#page-12-0). Due to the relatively small number of observations with respect to the number of basic indicators, the imputations were carried out separately for the groups of indicators. The final data set, with initial and imputed values of basic indicators, is presented in Appendix A.
+
+To combine the basic indicators into a composite one, weights based on statistical models were applied. We examined both Principal Component Analysis (PCA) and Common Factor Analysis (FA) weighting [\(Tabachnick and Fidell, 2006\)](#page-12-0). Both methods group collinear indices to form a composite indicator that captures as much common information among sub-indicators as possible. The idea under PCA/FA is to account for the highest possible variation in the set of indicators using the smallest possible number of factors ([Nardo et al., 2005\)](#page-12-0). If there is no correlation between indicators these methods can not be used to obtain the weights.
+
+The first step in the FA is to check the correlation structure of the data, and the second step is to identify a certain number of latent factors, smaller than the number of indicators, representing the data. In the PCA, we retain those factors that account for the largest amount of variance. This implies that in both methods the number of factors fitted to the data were data-dependent and not dictated by an external reason.
+
+We used Kaiser–Meyer–Olkin (KMO) statistics to predict and demonstrate if the data are likely to factor well, based on their correlations and partial correlations. There is a KMO statistic for each individual variable, and an overall KMO statistic. It is customary that the KMO overall should be 0.60 or higher, to proceed with the factor analysis. If this condition is not satisfied, one should drop the indicator variables with the lowest individual KMO statistic values, until the KMO overall rises above 0.60.
+
+<sup>b</sup> Considering the reporting problems and definition's differences among the countries, a preferable indicator would be the 'number of hospitalized injuries per one fatality', which is unavailable as yet.
+
+<span id="page-4-0"></span>Table 5Basic indicators estimated for 27 European countries (n/a <sup>=</sup> not available).
+
+| Cou<br>ntry              | Cod      | e B<br>1                                                                        | B2                                                                                 | B3                                                                     | B4                                                                       | B5                                                                                      | B6                                                                                     | B7                                                                                                            | D1                                                                                                       | D2                                                                    | C1                                                                            | C2                                                                                       | C3                                                               | C4                                                           | C5                                                                    | C6                                                                   | C7                                                 | A1                        | A2                                                    | A3                                     | A4                 | A5                           |
+|--------------------------|----------|---------------------------------------------------------------------------------|------------------------------------------------------------------------------------|------------------------------------------------------------------------|--------------------------------------------------------------------------|-----------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------|-----------------------------------------------------------------------|-------------------------------------------------------------------------------|------------------------------------------------------------------------------------------|------------------------------------------------------------------|--------------------------------------------------------------|-----------------------------------------------------------------------|----------------------------------------------------------------------|----------------------------------------------------|---------------------------|-------------------------------------------------------|----------------------------------------|--------------------|------------------------------|
+|                          |          | Fata<br>litie<br>s<br>mil<br>lion<br>per<br>inh<br>abit<br>ant<br>s<br>200<br>6 | Fata<br>litie<br>s<br>per<br>mil<br>lion<br>pas<br>sen<br>ger<br>s-2<br>006<br>car | Fata<br>litie<br>s<br>per<br>10 b<br>illio<br>n<br>pkm<br><br>200<br>6 | Inju<br>ry<br>Acc<br>ide<br>nts<br>per<br>fata<br>litie<br>s<br>200<br>6 | Ped<br>ian<br>estr<br>fata<br>litie<br>s<br>as %<br>of<br>l<br>tota<br>6 (%<br>)<br>200 | Bicy<br>clis<br>t<br>fata<br>litie<br>s<br>as %<br>of<br>l<br>tota<br>6 (%<br>)<br>200 | Mo<br>ycli<br>torc<br>st +<br>ped<br>mo<br>fata<br>litie<br>s<br>of t<br>l<br>as %<br>ota<br>6 (%<br>)<br>200 | Num<br>ber<br>of<br>pas<br>sen<br>ger<br>cars<br>per<br>100<br>0<br>inh<br>abit<br>ant<br>s,<br>200<br>6 | Pop<br>ulat<br>ion<br>m2<br>1 k<br>per<br>of a<br>rea<br><br>200<br>6 | Sha<br>f<br>re o<br>drin<br>k<br>driv<br>ing<br>iden<br>ts<br>acc<br>200<br>5 | We<br>arin<br>g<br>-Fro<br>rate<br>nt<br>ts<br>sea<br>d<br>ate<br>agg<br>reg<br>200<br>5 | We<br>arin<br>g<br>rate<br><br>Rea<br>r<br>ts<br>sea<br>200<br>5 | Ave<br>rag<br>e<br>Eur<br>oNC<br>AP<br>sco<br>re<br>200<br>3 | Me<br>dia<br>n<br>of<br>age<br>pas<br>sen<br>ger<br>s-2<br>003<br>car | %<br>Mo<br>ycle<br>torc<br>s<br>in fl<br>eet<br><br>6 (%<br>)<br>200 | %<br>HG<br>V<br>in<br>flee<br>t<br>200<br>6<br>(%) | Safe<br>ty<br>targ<br>ets | Sele<br>ctio<br>f<br>n o<br>inte<br>ntio<br>rve<br>ns | Eco<br>ic<br>nom<br>luat<br>ion<br>eva | Mo<br>nito<br>ring | Sta<br>ke<br>hol<br>der<br>s |
+| Aus<br>tria              | AT       | 88                                                                              | 175                                                                                | 100                                                                    | 54.<br>6                                                                 | 15.<br>1                                                                                | 6.6                                                                                    | 18.<br>4                                                                                                      | 507                                                                                                      | 98.<br>9                                                              | 6.0<br>%                                                                      | 83                                                                                       | 52                                                               | n/a                                                          | 7.5                                                                   | 12.<br>4                                                             | 7.0                                                | a                         | c                                                     | b                                      | b                  | a                            |
+| Belg<br>ium              | BE       | 101                                                                             | 216                                                                                | 96                                                                     | 38.<br>5                                                                 | 11.<br>4                                                                                | 8.6                                                                                    | 15.<br>5                                                                                                      | 470                                                                                                      | 347<br>.0                                                             | 4.4<br>%                                                                      | 71                                                                                       | n/a                                                              | 21.<br>3                                                     | 6.7                                                                   | 6.0                                                                  | 11.<br>1                                           | b                         | b                                                     | b                                      | b                  | b                            |
+| lan<br>Swi<br>tzer       | d C<br>H | 50                                                                              | 95                                                                                 | n/a                                                                    | 58.<br>1                                                                 | 20.<br>5                                                                                | 9.5                                                                                    | 21.<br>6                                                                                                      | 519                                                                                                      | 181<br>.8                                                             | 19.<br>3%                                                                     | 82                                                                                       | 53                                                               | n/a                                                          | 7.3                                                                   | 12.<br>5                                                             | 6.4                                                | a                         | a                                                     | a                                      | b                  | a                            |
+| Cyp<br>rus               | CY       | 111                                                                             | 236                                                                                | 167                                                                    | 31.<br>1                                                                 | 22.<br>1                                                                                | 2.3                                                                                    | 29.<br>1                                                                                                      | 479                                                                                                      | 83.<br>8                                                              | 22.<br>5%                                                                     | 80                                                                                       | n/a                                                              | n/a                                                          | 9.3                                                                   | 7.6                                                                  | 21.<br>7                                           | n/a                       | n/a                                                   | n/a                                    | n/a                | n/a                          |
+| Cze<br>ch                | CZ       | 104                                                                             | 264                                                                                | 146                                                                    | 20.<br>8                                                                 | 19.<br>0                                                                                | 10.<br>3                                                                               | 10.<br>9                                                                                                      | 399                                                                                                      | 130<br>.4                                                             | 5.5<br>%                                                                      | 72                                                                                       | 13                                                               | 20.<br>7                                                     | 11                                                                    | 15.<br>1                                                             | 9.0                                                | b                         | c                                                     | b                                      | b                  | b                            |
+| Rep<br>ubl<br>ic         |          |                                                                                 |                                                                                    |                                                                        |                                                                          |                                                                                         |                                                                                        |                                                                                                               |                                                                                                          |                                                                       |                                                                               |                                                                                          |                                                                  |                                                              |                                                                       |                                                                      |                                                    |                           |                                                       |                                        |                    |                              |
+| Ger<br>ma<br>ny          | DE       | 62                                                                              | 110                                                                                | 57                                                                     | 64.<br>4                                                                 | 14.<br>0                                                                                | 9.5                                                                                    | 17.<br>7                                                                                                      | 566                                                                                                      | 230<br>.6                                                             | 5.1<br>%                                                                      | 96                                                                                       | 89                                                               | 20.<br>1                                                     | 6                                                                     | 10.<br>5                                                             | 5.1                                                | a                         | b                                                     | b                                      | a                  | b                            |
+| rk<br>Den<br>ma          | DK       | 56                                                                              | 154                                                                                | 56                                                                     | 17.<br>7                                                                 | 19.<br>6                                                                                | 10.<br>1                                                                               | 14.<br>7                                                                                                      | 371                                                                                                      | 126<br>.4                                                             | 23.<br>0%                                                                     | 85                                                                                       | 63                                                               | n/a                                                          | 7.3                                                                   | 6.7                                                                  | 18.<br>7                                           | a                         | b                                                     | b                                      | b                  | b                            |
+| nia<br>Esto              | EE       | 152                                                                             | 389                                                                                | 175                                                                    | 12.<br>7                                                                 | 27.<br>2                                                                                | 4.1                                                                                    | 4.1                                                                                                           | 413                                                                                                      | 29.<br>7                                                              | 28.<br>4%                                                                     | 74                                                                                       | 30                                                               | n/a                                                          | 12.<br>7                                                              | 1.9                                                                  | 14.<br>0                                           | b                         | c                                                     | b                                      | b                  | a                            |
+| Gre<br>ece               | EL       | 149                                                                             | 375                                                                                | 174                                                                    | 9.8                                                                      | 16.<br>1                                                                                | 1.3                                                                                    | 30.<br>0                                                                                                      | 407                                                                                                      | 84.<br>6                                                              | 10.<br>7%                                                                     | n/a                                                                                      | n/a                                                              | 20.<br>7                                                     | 8                                                                     | 17.<br>2                                                             | 17.<br>4                                           | a                         | b                                                     | b                                      | b                  | b                            |
+| Spa<br>in                | ES       | 93                                                                              | 201                                                                                | 117                                                                    | 24.<br>3                                                                 | 15.<br>3                                                                                | 1.8                                                                                    | 17.<br>6                                                                                                      | 464                                                                                                      | 87.<br>9                                                              | n/a                                                                           | 74                                                                                       | 51                                                               | n/a                                                          | 7.6                                                                   | 14.<br>6                                                             | 16.<br>7                                           | a                         | c                                                     | b                                      | b                  | b                            |
+| Fin<br>land              | FI       | 64                                                                              | 136                                                                                | 53                                                                     | 20.<br>1                                                                 | 11.<br>9                                                                                | 11.<br>3                                                                               | 9.5                                                                                                           | 475                                                                                                      | 15.<br>6                                                              | 23.<br>5%                                                                     | 88                                                                                       | 78                                                               | n/a                                                          | 9.1                                                                   | 10.<br>5                                                             | 11.<br>6                                           | a                         | b                                                     | b                                      | b                  | b                            |
+| Fra<br>nce               | FR       | 77                                                                              | 153                                                                                | 64                                                                     | 17.<br>1                                                                 | 11.<br>4                                                                                | 3.8                                                                                    | 23.<br>5                                                                                                      | 504                                                                                                      | 113<br>.1                                                             | 28.<br>8%                                                                     | 97                                                                                       | 70                                                               | n/a                                                          | 8.3                                                                   | 6.4                                                                  | 13.<br>7                                           | a                         | a                                                     | b                                      | a                  | a                            |
+| Hun<br>gar<br>y          | HU       | 129                                                                             | 446                                                                                | 271                                                                    | 16.<br>1                                                                 | 22.<br>7                                                                                | 11.<br>7                                                                               | 10.<br>1                                                                                                      | 293                                                                                                      | 108<br>.2                                                             | 8.8<br>%                                                                      | 67                                                                                       | 34                                                               | 20.<br>6                                                     | 8                                                                     | 3.7                                                                  | 12.<br>5                                           | a                         | c                                                     | b                                      | b                  | b                            |
+| Irel<br>and              | IE       | 86                                                                              | 211                                                                                | 130                                                                    | 18.<br>6                                                                 | 19.<br>0                                                                                | 3.0                                                                                    | 16.<br>3                                                                                                      | 418                                                                                                      | 61.<br>4                                                              | n/a                                                                           | 86                                                                                       | 46                                                               | n/a                                                          | 5.1                                                                   | 1.6                                                                  | 14.<br>7                                           | b                         | b                                                     | b                                      | a                  | b                            |
+| Ital<br>y                | IT       | 96                                                                              | 162                                                                                | 74                                                                     | 42.<br>0                                                                 | 12.<br>6                                                                                | 4.8                                                                                    | 23.<br>8                                                                                                      | 597                                                                                                      | 196<br>.3                                                             | n/a                                                                           | 71                                                                                       | n/a                                                              | n/a                                                          | 7.9                                                                   | 20.<br>5                                                             | 8.7                                                | c                         | d                                                     | c                                      | c                  | d                            |
+| Lith<br>ia<br>uan        | LT       | 224                                                                             | 498                                                                                | 191                                                                    | 8.9                                                                      | 34.<br>0                                                                                | n/a                                                                                    | n/a                                                                                                           | 470                                                                                                      | 51.<br>9                                                              | 11.<br>8%                                                                     | 60                                                                                       | n/a                                                              | n/a                                                          | 14.<br>5                                                              | 1.4                                                                  | 7.7                                                | b                         | c                                                     | b                                      | b                  | b                            |
+| Lux<br>bou<br>em<br>rg   | LU       | 76                                                                              | 116                                                                                | 54                                                                     | 21.<br>2                                                                 | 9.7                                                                                     | 1.6                                                                                    | 0.0                                                                                                           | 661                                                                                                      | 183<br>.1                                                             | 0.0<br>%                                                                      | 80                                                                                       | 60                                                               | n/a                                                          | 4.4                                                                   | 10.<br>0                                                             | 8.0                                                | n/a                       | n/a                                                   | n/a                                    | n/a                | n/a                          |
+| Latv<br>ia               | LV       | 178                                                                             | 520                                                                                | 256                                                                    | 10.<br>6                                                                 | 38.<br>0                                                                                | 6.0                                                                                    | 4.0                                                                                                           | 360                                                                                                      | 35.<br>3                                                              | 21.<br>7%                                                                     | 77                                                                                       | n/a                                                              | 21.<br>3                                                     | 10                                                                    | 3.7                                                                  | 12.<br>2                                           | b                         | c                                                     | b                                      | b                  | b                            |
+| Ma<br>lta                | MT       | 25                                                                              | 46                                                                                 | 49                                                                     | 84.<br>1                                                                 | 35.<br>3                                                                                | 0.0                                                                                    | 17.<br>6                                                                                                      | 535                                                                                                      | 136<br>0.0                                                            | n/a                                                                           | 96                                                                                       | 28                                                               | 18.<br>6                                                     | 9                                                                     | 4.4                                                                  | 16.<br>4                                           | a                         | c                                                     | b                                      | b                  | b                            |
+| her<br>lan<br>ds<br>Net  | NL       | 45                                                                              | 102                                                                                | 48                                                                     | 33.<br>6                                                                 | 9.4                                                                                     | 18.<br>3                                                                               | 18.<br>4                                                                                                      | 442                                                                                                      | 394<br>.2                                                             | 15.<br>3%                                                                     | 90                                                                                       | 64                                                               | 20.<br>2                                                     | 6                                                                     | 6.5                                                                  | 11.<br>3                                           | a                         | a                                                     | b                                      | a                  | a                            |
+| Nor<br>way               | NO       | 52                                                                              | 116                                                                                | n/a                                                                    | 32.<br>7                                                                 | 14.<br>5                                                                                | 3.3                                                                                    | 15.<br>3                                                                                                      | 445                                                                                                      | 14.<br>4                                                              | n/a                                                                           | 91                                                                                       | 83                                                               | 21                                                           | 8                                                                     | 9.4                                                                  | 17.<br>0                                           | b                         | a                                                     | a                                      | b                  | b                            |
+| Pol<br>and               | PL       | 137                                                                             | 408                                                                                | 235                                                                    | 8.9                                                                      | 32.<br>3                                                                                | 11.<br>1                                                                               | 3.9                                                                                                           | 351                                                                                                      | 121<br>.9                                                             | 9.8<br>%                                                                      | 78                                                                                       | n/a                                                              | n/a                                                          | 11.<br>8                                                              | 4.7                                                                  | 14.<br>4                                           | b                         | c                                                     | b                                      | b                  | b                            |
+| al<br>Por<br>tug         | PT       | 92                                                                              | 228                                                                                | 131                                                                    | 36.<br>8                                                                 | 16.<br>0                                                                                | 4.1                                                                                    | 24.<br>1                                                                                                      | 405                                                                                                      | 115<br>.3                                                             | n/a                                                                           | 86                                                                                       | 45                                                               | n/a                                                          | 9.7                                                                   | 9.0                                                                  | 21.<br>3                                           | b                         | c                                                     | b                                      | b                  | b                            |
+| Swe<br>den               | SE       | 49                                                                              | 107                                                                                | 45                                                                     | 40.<br>7                                                                 | 12.<br>4                                                                                | 5.8                                                                                    | 15.<br>7                                                                                                      | 461                                                                                                      | 20.<br>3                                                              | 34.<br>0%                                                                     | 92                                                                                       | 73                                                               | 22.<br>6                                                     | 7                                                                     | 9.6                                                                  | 9.2                                                | a                         | a                                                     | a                                      | a                  | a                            |
+| Slov<br>eni<br>a         | SI       | 131                                                                             | 270                                                                                | 113                                                                    | 44.<br>4                                                                 | 13.<br>7                                                                                | 5.3                                                                                    | 20.<br>5                                                                                                      | 488                                                                                                      | 99.<br>0                                                              | 32.<br>2%                                                                     | 87                                                                                       | 30                                                               | n/a                                                          | 5.0                                                                   | 4.8                                                                  | 6.3                                                | b                         | c                                                     | b                                      | b                  | b                            |
+| Slov<br>akia             | SK       | 107                                                                             | 439                                                                                | 215                                                                    | 13.<br>8                                                                 | 9.3                                                                                     | 5.5                                                                                    | 7.4                                                                                                           | 247                                                                                                      | 110<br>.5                                                             | 12.<br>0%                                                                     | n/a                                                                                      | n/a                                                              | n/a                                                          | n/a                                                                   | 3.7                                                                  | 11.<br>9                                           | b                         | c                                                     | b                                      | b                  | b                            |
+| Gre<br>at<br>Brit<br>ain | UK       | 54                                                                              | 116                                                                                | 48                                                                     | 58.<br>9                                                                 | 21.<br>0                                                                                | 4.6                                                                                    | 17.<br>5                                                                                                      | 471                                                                                                      | 249<br>.3                                                             | 5%<br>17.                                                                     | 90                                                                                       | 84                                                               | 20.<br>6                                                     | 5                                                                     | 3.7                                                                  | 10.<br>7                                           | a                         | b                                                     | b                                      | a                  | a                            |
+
+In both methods (PCA/FA), the combination of factors into a composite indicator is done by their weighted sum, where the weights are taken in accordance with the variance explained by each factor. At this point, different estimation procedures are possible. For both PCA and FA, we used orthogonal rotation of factors and, hence, 'the variance explained by each factor' was applied for estimating the weights.
+
+Both PCA and FA are suitable for the creation of a composite indicator. Accounting for the data behaviour, five trials of creating a composite indicator were performed. They are:
+
+- (1) PCA-all A PCA in which all variables (basic indicators) were analysed together.
+- (2) PCA-groups A PCA in which each group of basic indicators (A, B, C, D) was first analysed separately to create the group factors. The group factors were then analysed together to provide the final composite indicator.
+- (3) FA-4factors A common factor analysis with all variables considered and four factors' solution accepted.
+- (4) FA-2factors-noC4 A common factor analysis with two factors' solution, where C4 (average EuroNCAP score) is excluded from the analysis, due to statistical reasons.
+- (5) FA-2factors A common factor analysis with two factors' solution, where C4 is retained in the analysis.
+
+Concerning the FA analyses, a preliminary examination of all variables together revealed a low value of the overall KMO statistics (0.45), and the lowest values of the KMO statistics for such variables as B6 (0.131), B7 (0.309), C7 (0.136). Once the indicators B6, B7, C7 were excluded, the overall KMO statistics increased to 0.63, enabling to proceed with the FA. Therefore, the three trials of creating composite indicator by means of FA considered 18 variables (basic indicators), without B6 (share of bicyclist fatalities), B7 (share of motorcyclist fatalities) and C7 (percentage of HGV in fleet).
+
+To determine the number of factors required, the variance explained criterion was applied. At this point, two approaches are possible. Some researchers use the rule of keeping enough factors to account for a certain share (e.g. 90% or 80%) of the variation. Conversely, if the researcher's goal emphasizes parsimony (explaining variance with as few factors as possible), the criterion could be as low as 50%. In our case, the variation was taken to be the sum of the Eigenvalues of the reduced correlation matrix. It was found, for example, that four factors explain more than 80% of the variation.
+
+Further, examining the solution for four factors demonstrated that the C4 variable (average EuroNCAP score) is nearly identical to one of the factors, where in such cases it is customary to exclude such a variable from the analysis. The exclusion of C4 enabled fitting two factors to the rest of the variables (indicators), but with a significantly lower value of the total explained variance than in the four factors' analysis (71% versus 84%). A further consideration revealed that keeping C4 inside the set and limiting the number of factors to two yielded a comparable value of the explained variance (about 69%). Hence, we decided to explore the results of all three trials as mentioned above.
+
+Each of the five analyses produced a rotated factor pattern showing which variables (basic indicators) are more heavily loaded by each one of the factors built, i.e. the correlations between the variables and the factors. Considering the 'safety-desirable' behaviour of major variables which composed the factors and their coefficients, it was stated whether higher or lower values of each factor are associated with better safety performance. An insight into similarities and dissimilarities in the behaviour of basic indicators was also provided. In addition, each trial produced the tools for the estimation of each country's score, including: scoring coefficients, factors' weights, means and variances of the variables to estimate the standardized values. Appendix B provides an example of a rotated factor pattern and of tools for the estimation of country scores produced by the 'FA-4factors' analysis.
+
+Once the factors are created, the following procedure is applied to calculate a composite indicator, for each country:
+
+- a. Standardize the data, for each country, i.e. subtract mean and divide by standard deviation, for each variable.
+- b. Multiply these standardized variables by their respective standardized scoring coefficients.
+- c. Sum up these products over all the relevant variables. The sum is the value of the new variable Factor 1.
+- d. Repeat steps a–c for Factors 2, 3, etc. (if relevant). This creates the data set scores.
+- e. The composite indicator is a weighted sum of the Factors (called WF – weighted factor).
+
+Using the WF and a WARD clustering procedure, in each trial a classification tree was produced, i.e. the countries were classified into similar groups (clusters). Inside the group the WF values are close, but there are distances between the groups.
+
+### 3. Results and discussion
+
+Detailed results of each of the five analyses can be found in [Wegman et al. \(2008\).](#page-12-0) Section 3.1 gives a summary of the results of each trial. Furthermore, in Section 3.2, the composite indicators and clusters of countries are compared among the trials, providing considerations of their meanings and practical implications for the development of composite safety indicator.
+
+### 3.1. Results of separate trials
+
+# 3.1.1. PCA-all
+
+In the 'PCA-all' analysis, five factors were fitted to the data (explaining 76.3% of the total variation), where
+
+Factor 1 – Mainly reflects the road safety outcomes (the Bgroup), car fleet's age and seatbelt use;
+
+Factor 2 – The policy performance indicators (the A-group) but also includes a negative correlation with C1 (share of drinkdriving accidents);
+
+Factor 3 – Reflects the share of bicyclist fatalities, EuroNCAP scores for cars and population density;
+
+Factor 4 – The share of motorcycles in the fleet and the share of motorcyclist fatalities;
+
+Factor 5 – The share of HGV in the fleet, the number of injury accidents per fatality and the motorization level of a country.
+
+Similar behaviour was noted for variable groups such as: B1-B2- B3 (number of fatalities per population, vehicles, passenger kilometers travelled), A1–A4 (safety targets, monitoring the programme performance), A2-A3-A5 (other characteristics of safety programmes) and C2–C3 (safety belt wearing rates in front and rear seats).
+
+[Fig. 1](#page-6-0) presents the countries' subdivision into six clusters based on the WF values, where the country positions are plotted using the combined indicator (WF) and Factor 1 values. In this model, better safety position is associated with lower WF and Factor 1 values. According to this classification, the countries with the best safety level are Sweden, Great Britain and France; the second group includes Luxembourg, Norway, Germany and Ireland; the third group consists of Slovenia, Finland and the Netherlands, and so on.
+
+### <span id="page-6-0"></span>3.1.2. PCA-groups
+
+The first step in the 'PCA-groups' analysis was to fit one combined factor for each group of indicators separately, namely for the A-, B-, C- and D- groups of basic indicators. The four combined factors obtained are then subjected to another PCA, where the final combined safety index is generated.
+
+For the A-group indicators ('policy performance'), one factor was fitted to all basic (A1–A5) indicators in the first step of this analysis (explaining 64.4% of the total variation).
+
+For the B-group indicators ('final outcomes'), two factors were chosen, explaining 74.5% of the total variation, where variables B1-B2-B3-B4-B5 (number of fatalities per population, vehicles, passenger kilometers travelled, injury accidents per fatality, and share of pedestrian fatalities) were mainly loaded by Factor 1 and B6–B7 (shares of bicyclist and motorcyclist fatalities) – by Factor 2. The results demonstrated similarities in the behaviour of B1- B2-B3-B5 indicators and very different behaviours of B4, B6, B7.
+
+Exploring the C-group indicators ('intermediate outcomes'), low communalities with other indicators were observed for C6, C7 indicators (the percentages of motorcycles and HGV in the vehicle fleet, respectively), which, consequently, were excluded from the analysis. For the retained indicators, two factors were chosen, explaining 80.1% of the total variation, where variables C2–C3 (seat belt wearing rates) and C5 (median age of passenger cars) were mainly loaded by Factor 1, while C1 (share of drink-driving accidents) and C4 (average EuroNCAP score) were mainly loaded by Factor 2.
+
+For the D-group indicators ('background characteristics'), one factor was chosen, which reflected both basic variables (explaining 63.2% of the total variation).
+
+In the second step of this analysis two factors were chosen (explaining 86.3% of the total variation), where the combined factors of A- and C-groups were mainly loaded by Factor 1, and the combined factors of B- and D-groups – by Factor 2. Based on the factors' scoring coefficients and components, in this analysis, lower values of A- and B-group factors and higher values of C-group factors are 'safety-preferable', leading to lower values of Factor 1 and higher values of Factor 2 as associated with a better safety position.
+
+Plotting the positions of countries on the dimensions of these two combined factors, one general 'cloud' can be noted, with several outliers (e.g. Italy, Malta) – Fig. 2. Inside the 'cloud', the countries with better safety-related positions are: France, Great Britain, Sweden, Switzerland, the Netherlands, Germany and Norway. Besides, in this analysis a lack of similarity in the behaviour of the group factors was recognized.
+
+![](_page_6_Figure_10.jpeg)
+
+Fig. 1. Countries plotted using the composite indicator (WF) and Factor 1 values (PCA-all analysis).
+
+### 3.1.3. FA with four factors
+
+In the 'FA-4factors' analysis (see a rotated factor pattern in Appendix B) the basic indicators B1–B3 (number of fatalities per population, vehicles, passenger kilometers travelled), B5 (share of pedestrian fatalities), C5 (median age of passenger cars), C2–C3 (safety belt wearing rates in front and rear seats), B4 (injury accidents per fatality), and D1 (number of passenger cars per population) were mainly loaded by Factor 1, whereas Factor 2 reflected mostly the behaviour of policy performance indicators A1, A2, A4, A5 and C6 (percentage of motorcycles in vehicle fleet). Factor 3 mainly loaded the C4 variable only (average EuroNCAP score), whereas Factor 4 reflected mostly the behaviour of D2 (population density), A3 (quality of economic basis of safety programmes) and C1 (share of drink-driving accidents). The four factors explained 84% of the total variance.
+
+The countries were subdivided into five groups ([Fig. 3](#page-7-0)), where the countries with the best safety performance (first group) are Sweden, Norway, Switzerland, Great Britain, France, the Netherlands and Germany; the second group includes Finland, Denmark, Malta, Austria, Luxembourg and Ireland; and so on. Malta, Luxembourg and, especially, Italy, are 'outliers' of their groups, having much lower values of Factor 1 in comparison with the countries with a similar level of the combined safety indicator. (In this model, similar to the 'PCA-all', better safety position is associated with lower WF and Factor 1 values.)
+
+### 3.1.4. FA with two factors
+
+In the FA with two factors, two alternatives were considered: excluding and including the C4 indicator (average EuroNCAP score). Those were termed 'FA-2factors-noC4' and 'FA-2factors', respectively, and provided 71% and 69% of the explained variance.
+
+In both trials, Factor 1 reflected mostly the behaviour of B1–B5 indicators (final outcomes), D1–D2 (background characteristics), C5 (median age of passenger cars), C6 (percentage of motorcycles in vehicle fleet) and C4 (if included in the analysis); whereas Factor 2 reflected mostly the behaviour of policy performance indicators A1–A5, C2–C3 (safety belt use) and C1 (share of drink-driving accidents).
+
+In both cases, similar behaviour was observed for basic indicators: B1-B2-B3-B5-C5 (final outcomes and median age of cars), A1-A2-A3-A4-A5 (policy performance), C2–C3 (use of seat belts) and D1–D2 (background characteristics). Moreover, C4 indicator is relatively close to the group of 'final outcomes' plus 'median age of cars', whereas C1 (share of drink-driving accidents) behaves
+
+![](_page_6_Figure_19.jpeg)
+
+Fig. 2. Countries' positions on the dimensions of the combined factors (PCA-group analysis).
+
+<span id="page-7-0"></span>![](_page_7_Figure_2.jpeg)
+
+Fig. 3. Countries plotted using the composite indicator (WF) and Factor 1 values (FA-4factors analysis).
+
+differently from all the other indicators. Besides, B4 (injury accidents per fatality) and C6 (percentage of motorcycles in fleet) are relatively close to the D1–D2-group.
+
+In both cases the groups of countries with similar values of combined indicators were as shown in Fig. 4, where the countries with the best safety level (first group) are Malta, the Netherlands, Sweden, Great Britain, Germany, Switzerland, France and Norway; the second group includes Finland, Denmark, Austria, Luxembourg and Ireland; and so on. Similar to the results of the 'FA-4factors' analysis, Malta, Italy and Luxembourg behave as 'outliers' of their groups, and better safety position of a country is associated with lower values of WF and Factor 1.
+
+### 3.2. Discussion: comparisons among the trials
+
+The discussion is focused on two major issues. The first is an analysis of the consistency of the results of the various trials and identification of final groups of countries with similar safety performance – Sections 3.2.1 and [3.2.2](#page-8-0). The second issue relates to the summing up of the behaviour of the basic indicators in the various trials, to recognize the existence of a stable group of indicators
+
+![](_page_7_Figure_8.jpeg)
+
+Fig. 4. Countries plotted using the composite indicator (WF) and Factor 1 values (FA-2factors analysis).
+
+– Section [3.2.3.](#page-9-0) Both issues are essential for further development of a composite road safety indicator.
+
+### 3.2.1. Comparisons of countries' rankings
+
+The composite indicators obtained for each country with each analysis (WF values) were compared graphically in [Fig. 5](#page-8-0). The values obtained for each country were plotted against the countries' ranking according to their final scores from the 'PCA-all'.
+
+It can be seen that:
+
+- The results of the 'PCA-groups' analysis are very different from all other results.
+- The results of the 'FA-2factors' and the 'FA-2factors-noC4' analyses are very close.
+- In general, a certain similarity exists between the results of 'PCA-all', 'FA-4factors', 'FA-2factors' and 'FA-2factors-noC4' analyses.
+
+The different character of the results obtained with the 'PCAgroups' method probably stems from the different approach taken in this case, where the indicators were initially analysed in the predefined groups, not accounting for the inter-group correlations. Such a consideration enables a deeper insight into the behaviour of indicators in each group, in comparison to other analyses, but can provide a different final picture when a combined indicator is created.
+
+Accounting for their character, it was interesting to compare the intermediate results of the 'PCA-groups' analysis, i.e. the factors built for the A-, B-, C-groups of indicators, with the results of other analyses. Due to scaling reasons, prior to this step, we passed from the WF values to country ranks, where a country with the best value of the combined indicator receives rank '1', the next country – rank '2' and so on.
+
+For example, [Fig. 6](#page-8-0) presents a comparison of country ranks according to the 'PCA-all' analysis and the group factor analyses: FB (final B-group factor), FC (final C-group factor) and FB1 – Factor 1 fitted in B-group analysis, which reflects five B-indicators together (fatalities per population, vehicles, passenger km-travelled as well as injury accidents per fatality and share of pedestrian fatalities). The basic countries' ranking is built using FB1 results, which actually represents a substitute to the traditional approach of countries' comparison in terms of fatality rates (per population, vehicles, etc.). To note, a similar comparison was performed by [Hermans et al. \(2008\),](#page-12-0) who used the countries' ranking based on personal risk as a basis for judging the results of other rankings. The FB1 ranks in [Fig. 6](#page-8-0) are accompanied by ±5 rank deviation bars (vertical grey lines).
+
+It can be seen from [Fig. 6](#page-8-0) that:
+
+- For the majority of countries, the total FB ranks are close to the FB1 ranks, which confirms the leading role of FB1 indicators (fatalities per population, vehicles, passenger kilometers travelled, etc.) in countries' estimation by 'final safety outcomes'.
+- Both 'PCA-all' ranks and FC ranks create deviations from the countries' ranks based on final outcomes only. The countries with the widest deviations in ranks and, therefore, with the most unstable answers in this context are Malta and Italy. Essential deviations from the FB1 ranking are also observed for France, Luxembourg, Slovenia, Ireland, Estonia and Latvia.
+- At the same time, we can note a number of countries for which the ranks are relatively consistent across the different considerations. These are: Sweden, Great Britain, Norway, Portugal, Spain, Slovakia, Greece, Hungary, Poland and Lithuania.
+
+<span id="page-8-0"></span>![](_page_8_Figure_2.jpeg)
+
+Fig. 5. Final composite safety indicators (WF values) as a result of five analyses.
+
+![](_page_8_Figure_4.jpeg)
+
+Fig. 6. Countries' ranks resulting from the FB1 ranks versus PCA-all, FC and FB ranks.
+
+Finally, to compare the countries' ranks based on the combined indicators, we decided to present the results of four analyses, i.e. 'PCA-all', 'FA-4factors', 'FA-2factors', and 'FA-2factors-noC4' (where the results of the 'PCA-groups' analysis are left out due to their different nature) – [Fig. 7](#page-9-0). As a basic ranking we chose the one that provided the minimum sum of squared deviations from other rankings, i.e. the 'FA-2factors-noC4' ranking.
+
+[Fig. 7](#page-9-0) shows that:
+
+- Similar to countries' ranking based on the combined indicators WF (see Fig. 5), the results of 'FA-4factors', 'FA-2factors' and 'FA-2factors-noC4' analyses are reasonably close, whereas 'PCA-all' ranks are associated with large deviations.
+- Essential differences between all rankings are observed for Malta.
+- Relatively large deviations between some rankings are observed for the Netherlands, Switzerland, Norway, Luxembourg, Ireland, Slovenia, the Czech Republic, Italy and Estonia.
+
+In general, the level of consistency between the different rankings seems average, whereas the most similar results were provided by a similar type of analysis (e.g. the FA variations).
+
+## 3.2.2. Identification of groups of countries
+
+Due to various reasons (e.g. data quality, method of analysis, random variations in data), the country rankings from different analyses will probably never be identical. Therefore, a more reasonable comparison of the results of several analyses could be made by forming groups of countries with similar safety performance. Such a comparison is possible in our case, because each analysis produced clusters of countries with very similar values of the composite indicator.
+
+Using the results of countries' clustering observed in separate trials, the countries' classifications into five groups were compared. [Table 6](#page-9-0) summarizes the findings. The left part of [Table 6](#page-9-0) illustrates the country groupings obtained from the four analyses with more consistent results, i.e. 'FA-4factors', 'FA-2factors', 'FA-2factorsnoC4' and 'PCA-all', whereas the right part of the table illustrates the country groupings obtained from the initial and final steps of the 'PCA-groups' analysis. The two central columns give the final classifications of the countries.
+
+[Table 6](#page-9-0) clearly shows that the countries' classifications in the left part are much more consistent than those in the right part of the table. Based on the left part of the table (results of four analyses), five groups of countries with different levels of safety performance can be defined as follows:
+
+- 1. Countries with the highest level of safety performance: Sweden, Norway, France, Great Britain, Germany.
+- 2. Countries with a relatively high level of safety performance: Switzerland, the Netherlands, Finland, Denmark, Ireland, Austria, Luxembourg, Malta.
+- 3. Countries with a medium level of safety performance: Cyprus, Slovenia, Portugal, Belgium, Spain.
+
+<span id="page-9-0"></span>![](_page_9_Figure_2.jpeg)
+
+Fig. 7. Final countries' ranks resulting from four analyses.
+
+Table 6 Groups of countries with similar safety performance, based on the results of various analyses.
+
+- 4. Countries with a relatively low level of safety performance: Estonia, Slovakia, Greece, Czech Republic.
+- 5. Countries with a low level of safety performance: Latvia, Hungary, Poland, Lithuania, Italy.
+
+# 3.2.3. Behaviour of basic indicators
+
+In the analyses performed, similarities in behaviour were observed for the following groups of indicators:
+
+B1-B2-B3-B5-C5 (final safety outcomes – the fatality rates per population, per vehicles, per passenger kilometers travelled and share of pedestrian fatalities, and the median age of passenger cars),
+
+A1-A2-A3-A4-A5 (indicators of the quality of national safety programmes),
+
+C2–C3 (wearing rates of safety belts in front and rear seats) and D1–D2 (background characteristics).
+
+Moreover, the C4 indicator (average EuroNCAP score) was relatively close to the group containing final outcomes, where B4 (injury accidents per fatality) and C6 (percentage of motorcycles in fleet) were relatively close to the D1–D2 group. On the other hand, C1 (share of drink-driving accidents) behaved differently from all the other indicators, whereas indicators B6 (share of bicyclists fatalities), B7 (share of motorcyclist fatalities) and C7 (percentage of HGV in fleet) were excluded from several analyses due to low correlation with other variables.
+
+We should mention here that the values of the indicators relating to safety policy have a rather arbitrary and subjective element, which could partly explain the homogeneity of their behaviour. As <span id="page-10-0"></span>far as possible, the indicators were based on quantifiable facts, collected from published country reports. However, at this stage it is difficult to objectively quantify elements of a safety policy, and further research is required.
+
+Using the scoring coefficients and factors' weights produced by each of the five analyses (see example in App. B), final weights of the basic indicators can be estimated and compared among the trials. Such weights may illustrate the contribution of various indicators to the composite safety indicator. Table 7 presents these final weights, which for a comparison are given in a normalized form (a sum in column is equal to 1). It can be seen that among the basic indicators considered (except for B6, B7 and C7, which were excluded from several analyses):
+
+- The largest differences between the trials are observed for B2 (fatalities per vehicles) and both background characteristics.
+- On average, higher weights were observed for B2, C1–C5 (intermediate outcomes), D2 (population density) and A2–A5 (policy indicators), where the lowest weights are associated with B4 (injury accidents per fatality) and B5 (share of pedestrian fatalities).
+- More consistent weights between the various trials are found for C1–C5 and A1–A5 groups of indicators.
+
+However, as to the contribution to the composite indicator, the interpretation of the weights is not straightforward, since for the estimation of composite indicator for each country the original
+
+Table 7 Final weights of the basic indicators based on the results of five analyses.
+
+| Basic indicator | PCA-all   | PCA-groups | FA-4factors | FA-2factors-noC4 | FA-2factors | Average value | Standard deviation |
+|-----------------|-----------|------------|-------------|------------------|-------------|---------------|--------------------|
+| B1              | 0.091     | <br>0.039  | <br>0.039   | 0.081            | 0.013       | 0.021         | 0.063              |
+| B2              | 0.122     | 0.049<br>  | 0.897       | 0.531            | 0.555       | 0.411         | 0.376              |
+| B3              | 0.166     | <br>0.047  | 0.107       | 0.133            | <br>0.008   | 0.070         | 0.093              |
+| B4              | <br>0.022 | 0.042      | <br>0.035   | <br>0.061        | 0.008       | <br>0.013     | 0.040              |
+| B5              | 0.089     | <br>0.042  | 0.003       | 0.039            | <br>0.033   | 0.011         | 0.054              |
+| B6              | 0.239     | 0.026<br>  | n/a         | n/a              | n/a         | 0.107         | 0.187              |
+| B7              | 0.209     | 0.049      | n/a         | n/a              | n/a         | 0.129         | 0.113              |
+| C1              | <br>0.191 | <br>0.211  | <br>0.047   | <br>0.003        | <br>0.123   | <br>0.115     | 0.090              |
+| C2              | 0.243<br> | 0.157<br>  | 0.417<br>   | 0.197<br>        | 0.111<br>   | 0.225<br>     | 0.118              |
+| C3              | <br>0.256 | <br>0.139  | <br>0.250   | <br>0.221        | <br>0.159   | <br>0.205     | 0.053              |
+| C4              | <br>0.155 | <br>0.073  | <br>0.155   | n/a              | <br>0.063   | <br>0.111     | 0.051              |
+| C5              | 0.216     | 0.023      | 0.160       | 0.171            | 0.013       | 0.117         | 0.093              |
+| C6              | 0.257     | n/a        | 0.011<br>   | 0.005<br>        | 0.075       | 0.079         | 0.125              |
+| C7              | 0.120     | n/a        | n/a         | n/a              | n/a         | 0.120         | n/a                |
+| D1              | <br>0.181 | 0.479      | 0.035       | <br>0.012        | 0.082       | 0.080         | 0.244              |
+| D2              | 0.116     | 0.479      | 0.002       | 0.046<br>        | 0.062       | 0.123         | 0.208              |
+| A1              | 0.016     | 0.135      | 0.147       | 0.099            | 0.062       | 0.092         | 0.054              |
+| A2              | 0.021     | 0.154      | 0.244       | 0.195            | 0.196       | 0.162         | 0.085              |
+| A3              | 0.004     | 0.131      | 0.194       | 0.075            | 0.130       | 0.107         | 0.071              |
+| A4              | 0.270     | 0.140      | 0.008<br>   | 0.067            | 0.107       | 0.115         | 0.103              |
+| A5              | 0.113     | 0.153      | 0.173       | 0.152            | 0.195       | 0.157         | 0.031              |
+
+Table A1 The final set of basic safety indicators for the 27 countries.
+
+| Country | A1 | A2 | A3 | A4 | A5 | B1    | B2    | B3    | B4   | B5   | B6   | B7   | C1   | C2 | C3 | C4   | C5   | C6   | C7   | D1  | D2   |
+|---------|----|----|----|----|----|-------|-------|-------|------|------|------|------|------|----|----|------|------|------|------|-----|------|
+| AT      | 1  | 3  | 2  | 2  | 1  | 88.1  | 174.6 | 99.7  | 54.6 | 0.15 | 0.07 | 0.18 | 0.06 | 83 | 52 | 20.5 | 7.5  | 0.12 | 0.07 | 507 | 99   |
+| BE      | 2  | 2  | 2  | 2  | 2  | 101.3 | 216.1 | 96.2  | 38.5 | 0.11 | 0.09 | 0.16 | 0.04 | 71 | 24 | 21.3 | 6.7  | 0.06 | 0.11 | 470 | 347  |
+| CY      | 1  | 2  | 2  | 2  | 1  | 111.3 | 236.2 | 167.5 | 31.1 | 0.22 | 0.02 | 0.29 | 0.23 | 80 | 36 | 20.7 | 9.3  | 0.08 | 0.22 | 479 | 84   |
+| CZ      | 2  | 3  | 2  | 2  | 2  | 103.5 | 263.5 | 145.8 | 20.8 | 0.19 | 0.10 | 0.11 | 0.06 | 72 | 13 | 20.7 | 11.0 | 0.15 | 0.09 | 399 | 130  |
+| DK      | 1  | 2  | 2  | 2  | 2  | 56.3  | 153.6 | 55.8  | 17.7 | 0.20 | 0.10 | 0.15 | 0.23 | 85 | 63 | 20.7 | 7.3  | 0.07 | 0.19 | 371 | 126  |
+| EE      | 2  | 3  | 2  | 2  | 1  | 151.8 | 389.4 | 175.3 | 12.7 | 0.27 | 0.04 | 0.04 | 0.28 | 74 | 30 | 21.7 | 12.7 | 0.02 | 0.14 | 413 | 30   |
+| FI      | 1  | 2  | 2  | 2  | 2  | 63.8  | 136.1 | 53.0  | 20.1 | 0.12 | 0.11 | 0.09 | 0.23 | 88 | 78 | 20.5 | 9.1  | 0.10 | 0.12 | 475 | 16   |
+| FR      | 1  | 1  | 2  | 1  | 1  | 76.8  | 153.1 | 63.9  | 17.1 | 0.11 | 0.04 | 0.23 | 0.29 | 97 | 70 | 20.7 | 8.3  | 0.06 | 0.14 | 504 | 113  |
+| DE      | 1  | 2  | 2  | 1  | 2  | 61.8  | 109.9 | 57.3  | 64.4 | 0.14 | 0.10 | 0.18 | 0.05 | 96 | 89 | 20.1 | 6.0  | 0.10 | 0.05 | 566 | 231  |
+| UK      | 1  | 2  | 2  | 1  | 1  | 54.4  | 115.7 | 47.6  | 58.9 | 0.21 | 0.05 | 0.18 | 0.17 | 90 | 84 | 20.6 | 5.0  | 0.04 | 0.11 | 471 | 249  |
+| EL      | 1  | 2  | 2  | 2  | 2  | 148.6 | 374.6 | 174.4 | 9.8  | 0.16 | 0.01 | 0.30 | 0.11 | 79 | 28 | 20.7 | 8.0  | 0.17 | 0.17 | 407 | 85   |
+| HU      | 1  | 3  | 2  | 2  | 2  | 129.0 | 446.0 | 271.2 | 16.1 | 0.23 | 0.12 | 0.10 | 0.09 | 67 | 34 | 20.6 | 8.0  | 0.04 | 0.13 | 293 | 108  |
+| IE      | 2  | 2  | 2  | 1  | 2  | 86.3  | 211.1 | 129.6 | 18.6 | 0.19 | 0.03 | 0.16 | 0.15 | 86 | 46 | 20.6 | 5.1  | 0.02 | 0.15 | 418 | 61   |
+| IT      | 3  | 4  | 3  | 3  | 4  | 96.2  | 162.1 | 73.8  | 42.0 | 0.13 | 0.05 | 0.24 | 0.02 | 71 | 21 | 21.0 | 7.9  | 0.20 | 0.09 | 597 | 196  |
+| LV      | 2  | 3  | 2  | 2  | 2  | 177.9 | 520.3 | 256.5 | 10.6 | 0.38 | 0.06 | 0.04 | 0.22 | 77 | 23 | 21.3 | 10.0 | 0.04 | 0.12 | 360 | 35   |
+| LT      | 2  | 3  | 2  | 2  | 2  | 223.6 | 498.1 | 190.6 | 8.9  | 0.34 | 0.05 | 0.12 | 0.12 | 60 | 13 | 22.6 | 14.5 | 0.01 | 0.08 | 470 | 52   |
+| LU      | 1  | 4  | 2  | 2  | 2  | 76.2  | 115.8 | 54.1  | 21.2 | 0.10 | 0.02 | 0    | 0    | 80 | 60 | 20.8 | 4.4  | 0.10 | 0.08 | 661 | 183  |
+| MT      | 1  | 3  | 2  | 2  | 2  | 24.6  | 46.4  | 48.8  | 84.1 | 0.35 | 0    | 0.18 | 0.25 | 96 | 28 | 18.6 | 9.0  | 0.04 | 0.16 | 535 | 1360 |
+| NL      | 1  | 1  | 2  | 1  | 1  | 44.7  | 101.9 | 48.4  | 33.6 | 0.09 | 0.18 | 0.18 | 0.15 | 90 | 64 | 20.2 | 6.0  | 0.06 | 0.11 | 442 | 394  |
+| NO      | 2  | 1  | 1  | 2  | 2  | 52.2  | 116.0 | 62.8  | 32.7 | 0.14 | 0.03 | 0.15 | 0.31 | 91 | 83 | 21.0 | 8.0  | 0.09 | 0.17 | 445 | 14   |
+| PL      | 2  | 3  | 2  | 2  | 2  | 137.5 | 407.6 | 234.9 | 8.9  | 0.32 | 0.11 | 0.04 | 0.10 | 78 | 23 | 20.6 | 11.8 | 0.05 | 0.14 | 351 | 122  |
+| PT      | 2  | 3  | 2  | 2  | 2  | 91.6  | 228.3 | 130.8 | 36.8 | 0.16 | 0.04 | 0.24 | 0.11 | 86 | 45 | 20.7 | 9.7  | 0.09 | 0.21 | 405 | 115  |
+| SK      | 2  | 3  | 2  | 2  | 2  | 107.4 | 439.1 | 215.0 | 13.8 | 0.09 | 0.06 | 0.07 | 0.12 | 76 | 24 | 21.0 | 7.0  | 0.04 | 0.12 | 247 | 111  |
+| SI      | 2  | 3  | 2  | 2  | 2  | 130.6 | 270.0 | 112.7 | 44.4 | 0.14 | 0.05 | 0.21 | 0.32 | 87 | 30 | 21.1 | 5.0  | 0.05 | 0.06 | 488 | 99   |
+| ES      | 1  | 3  | 2  | 2  | 2  | 93.0  | 200.7 | 117.2 | 24.3 | 0.15 | 0.02 | 0.18 | 0.12 | 74 | 51 | 20.6 | 7.6  | 0.15 | 0.17 | 464 | 88   |
+| SE      | 1  | 1  | 1  | 1  | 1  | 49.0  | 106.5 | 44.7  | 40.7 | 0.12 | 0.06 | 0.16 | 0.34 | 92 | 73 | 22.6 | 7.0  | 0.10 | 0.09 | 461 | 20   |
+| CH      | 1  | 1  | 1  | 2  | 1  | 49.6  | 95.0  | 42.1  | 58.1 | 0.21 | 0.09 | 0.22 | 0.19 | 82 | 53 | 20.5 | 7.3  | 0.12 | 0.06 | 519 | 182  |
+
+Note: Prior to the calculations, the nominal values of the A-group indicators were converted into ordinal scale values. In our calculations we used the usual Pearson correlation for all the measures. This correlation treats all variable as scale variables. Using the ordinal measures as scales is equivalent in our case to the idea of using rank correlation. <span id="page-11-0"></span>indicators should be standardized, i.e. mean centred and divided by their standard deviation (see Section [2.4](#page-3-0)), which may influence the sign and the value of the contribution.
+
+Based on all the analyses performed in the study, basic safety indicators with consistent behaviour and a clearer contribution to the final composite safety indicator can be suggested. Such indicators are: B1-B2-B3 (fatality rates), A1-A2-A3-A4-A5 (quality of national safety programmes), C2–C3 (wearing rates of safety belts) and C5 (median age of cars). These indicators can serve as a core set of basic indicators for the characteristic of a country's safety performance.
+
+#### 4. Conclusions
+
+In this study, we examined Principal Component Analysis and Common Factor Analysis weighting to create a composite safety indicator, based on four groups of basic road safety indicators of countries. The basic indicators considered referred to the three types of road safety benchmarking: policy performance indicators, final road safety outcomes and intermediate outcomes, and also included background characteristics of the countries (motorization level, population density). The analysis used the data collected for 27 European countries. Five trials of creating a composite indicator were performed, where each trial produced a composite road safety indicator for each country, and groups of countries with similar values of the composite indicator.
+
+The purpose of our analysis was to explore the ways for creating a composite road safety indicator and the behaviour of basic indicators involved. It has been demonstrated that both tasks can be realized by the statistical weighting methods applied. The composite indicators, estimated by several methods, enabled us to rank the countries according to their safety performance.
+
+Similar to other studies ([Hermans et al., 2008](#page-12-0)) differences were observed in the countries' rankings obtained by the different methods used. It appears that a more reasonable comparison can be made by using groups of countries with similar levels of safety performance, where the countries are grouped based on the values of composite indicators received. In particular, among the 27 European countries considered, five groups with different safety performance were recognized, although, of course, a particular country could move from one group to another (neighbouring) group, depending on the method used. With the methodology used and with the available data, the countries with the highest level of safety performance are: Sweden, Norway, France, Great Britain and Germany. This group remained fairly consistent among the different methods used.
+
+The analysis revealed that the results of countries' rankings based on the composite indicators are not necessarily identical to the traditional ranking they receive based on fatality rates only. Moreover, it was observed that the indicators belonging to the final outcomes (fatality and injury rates) and intermediate outcomes (wearing rates of seat belts, crashworthiness and composition of vehicle fleet, share of drink-driving) are not uniform in their behaviour in the analyses. Indicators which were found to be more consistent and influential and termed the 'core set of basic indicators' are recommended for future use.
+
+The overall conclusion is that it is realistic and meaningful to design a composite road safety indicator in which relevant information from the different components of the road safety pyramid has been captured and weighted. Such an indicator gives a more
+
+Table B2 Standardized scoring coefficients.
+
+| Basic indicator (variables) | Factor1   | Factor2   | Factor3   | Factor4   |
+|-----------------------------|-----------|-----------|-----------|-----------|
+| B3                          | 0.283     | 0.039     | <br>0.474 | <br>0.046 |
+| B2                          | 0.832     | <br>0.191 | <br>0.348 | 0.202     |
+| B1                          | 0.433<br> | 0.071<br> | 0.970     | 0.030     |
+| B5                          | 0.017     | <br>0.050 | 0.055     | <br>0.011 |
+| C5                          | 0.091     | 0.060     | 0.046     | <br>0.103 |
+| C2                          | 0.085<br> | 0.045     | 0.332<br> | 0.203<br> |
+| C3                          | 0.061<br> | 0.163<br> | 0.087     | 0.090<br> |
+| B4                          | <br>0.049 | <br>0.051 | 0.041     | 0.102     |
+| D1                          | <br>0.107 | 0.028     | 0.124     | 0.133     |
+| A4                          | 0.041<br> | 0.371     | 0.240<br> | 0.282<br> |
+| A5                          | <br>0.027 | 0.330     | <br>0.136 | <br>0.056 |
+| A2                          | <br>0.122 | 0.143     | 0.263     | 0.168     |
+| C6                          | 0.063<br> | 0.223     | 0.089<br> | 0.146<br> |
+| A1                          | 0.088<br> | 0.039     | 0.344     | 0.013     |
+| C4                          | <br>0.148 | 0.010     | 0.219     | <br>0.160 |
+| D2                          | <br>0.109 | <br>0.180 | 0.143     | 0.413     |
+| A3                          | 0.133     | 0.042     | 0.281<br> | 0.243     |
+| C1                          | 0.030     | <br>0.044 | 0.149     | <br>0.241 |
+|                             |           |           |           |           |
+
+Table B3 Factors' weights.
+
+| w1    | w2    | w3    | w4    |
+|-------|-------|-------|-------|
+| 0.388 | 0.273 | 0.178 | 0.161 |
+
+Table B1 Rotated factor pattern.
+
+|    | Basic indicator and its ''safety-desired" behaviour | Factor1   | Factor2   | Factor3   | Factor4   |
+|----|-----------------------------------------------------|-----------|-----------|-----------|-----------|
+| B3 | ;                                                   | 0.931     | 0.162     | 0.164     | 0.099     |
+| B2 | ;                                                   | 0.901     | 0.158     | 0.343     | 0.072     |
+| B1 | ;                                                   | 0.686     | 0.247     | 0.594     | 0.114     |
+| B5 | ;                                                   | 0.604     | <br>0.039 | 0.454     | <br>0.064 |
+| C5 | ;                                                   | 0.527     | 0.208     | 0.463     | <br>0.235 |
+| C2 | "                                                   | 0.501<br> | 0.490<br> | 0.433<br> | 0.288<br> |
+| C3 | "                                                   | 0.588<br> | 0.472<br> | 0.412<br> | 0.255<br> |
+| B4 | ;                                                   | <br>0.704 | <br>0.170 | <br>0.094 | 0.140     |
+| D1 | "                                                   | <br>0.821 | 0.139     | 0.195     | 0.174     |
+| A4 | ;                                                   | 0.187     | 0.850     | 0.139     | 0.019<br> |
+| A5 | ;                                                   | 0.028     | 0.819     | <br>0.008 | 0.196     |
+| A2 | ;                                                   | 0.318     | 0.656     | 0.221     | 0.414     |
+| C6 | ;                                                   | 0.456<br> | 0.587     | 0.307<br> | 0.055<br> |
+| A1 | ;                                                   | 0.160     | 0.560     | 0.446     | 0.108     |
+| C4 | "                                                   | 0.096     | <br>0.002 | 0.773     | <br>0.325 |
+| D2 | ;                                                   | <br>0.361 | <br>0.193 | <br>0.165 | 0.715     |
+| A3 | ;                                                   | 0.096     | 0.482     | 0.013<br> | 0.659     |
+| C1 | ;                                                   | <br>0.024 | <br>0.401 | 0.131     | <br>0.739 |
+
+<span id="page-12-0"></span>Table B4 Means and standard deviations of variables.
+
+|                            | B1             | B2             | B3             | B4             | B5             | C1             | C2            | C3           | C4          | C5          | C6             |
+|----------------------------|----------------|----------------|----------------|----------------|----------------|----------------|---------------|--------------|-------------|-------------|----------------|
+| Mean<br>Standard deviation | 98.6<br>44.1   | 240.1<br>135.3 | 120.0<br>71.1  | 29.1<br>16.9   | 0.180<br>0.077 | 0.158<br>0.098 | 81.2<br>9.1   | 46.6<br>23.5 | 20.9<br>0.6 | 8.08<br>2.4 | 0.082<br>0.050 |
+|                            | N_A1           | N_A2           | N_A3           | N_A4           | N_A5           | D1             | D2            |              |             |             |                |
+| Mean<br>Standard deviation | 1.530<br>0.566 | 2.381<br>0.871 | 1.937<br>0.405 | 1.795<br>0.489 | 1.784<br>0.638 | 449.3<br>88.0  | 126.6<br>95.6 |              |             |             |                |
+
+enriched picture of road safety than a ranking based only on data on fatality rates, which is normal practice today. Grouping countries in this process is promising and seems to be preferable to simply ranking countries. Before defining the composite road safety indicator and actually using the results for policy making, two improvements are recommended: firstly, to design the final set of basic safety performance indicators and, secondly, to develop procedures for collecting high-quality and comparable data for the indicators for all the countries compared.
+
+### Acknowledgements
+
+The authors would like to acknowledge the SUNflowerNext team (Wegman et al., 2008) for the inspiration, multiple fruitful discussions and assistance in data collection for the study's performance.
+
+### Appendix A
+
+See [Table A1.](#page-10-0)
+
+### Appendix B
+
+Results of the 'FA-4factors' analysis See [Tables B1–B4.](#page-11-0)
+
+## References
+
+- Al Haji, G., 2005. Towards a road safety development index (RSDI). Development of an international index to measure road safety performance. Linkoping studies in Science and Technology, Licentiate Thesis No. 1174. Department of Science and Technology, Linkoping University.
+- Broughton, J. Buckle, G, 2006. Monitoring progress towards the 2010 casualty reduction target – 2004 data. TRL Report 653. TRL Limited, Wokingham.
+- European Commission, 2007. Energy and Transport in Figures. Part 3: Transport. Directorate-General for Energy and Transport in co-operation with Eurostat. (Chapter: 3.6 Means of Transport; Chapter 3.7 Safety).
+- Elvik, R., 2001. Improving road safety in Norway and Sweden: analyzing the efficiency of policy priorities. Traffic Engineering and Control January, 9–16.
+- Elvik, R., 2008. Road safety management by objectives: a critical analysis of the Norwegian approach. Accident Analysis and Prevention 40, 1115–1122.
+- Elvik, R., Amundsen, A.H., 2000. Improving road safety in Sweden. Report 490. Institute of Transport Economics, Oslo.
+- European Road Safety Observatory, 2008. Annual statistical Report 2007. [<http://](http://www.erso.eu) [www.erso.eu>](http://www.erso.eu)
+- European Transport Safety Council, 2001. Transport Safety Performance Indicators, Brussels.
+
+- European Transport Safety Council, 2006. A Methodological Approach to National Road Safety Policies, Brussels.
+- European Transport Safety Council, 2007a. Reducing Deaths From Drink Driving. PIN Flash 5 Background data.
+- European Transport Safety Council, 2007b. Increasing Seat Belt Use. PIN Flash 4 Background data.
+- Hakkert, A.S., Gitelman, V., Vis, M.A. (Eds.), 2007. Road Safety Performance Indicators: Theory. Deliverable D3.6 of the EU FP6 Project SafetyNet.
+- Hermans, E., Van der Bossche, F., Wets, G., 2008. Combining road safety information in a performance index. Accident Analysis and Prevention 40, 1337–1344.
+- Koornstra, M., Lynam, D., Nilsson, G., Noordzij, P., Pettersson, H.-E., Wegman, F., Wouters, P., 2002. SUNflower; A Comparative Study of the Development of Road Safety in Sweden, the United Kingdom, and the Netherlands. SWOV Institute for Road Safety Research, Leidschendam, the Netherlands.
+- LaLonde, S.M., 2005. Transforming variables for normality and linearity When, How, Why and Why Not's. In: SAS Conference Proceedings NESUG 2005, 11–14 September, Portland, Maine.
+- Nardo, M., Saisana, M., Saltelli, A., Tarantola, S., 2005. Handbook on Constructing Composite Indicators: Methodology and User Guide. OECD Statistics Working Papers, STD/DOC(2005)3. Organisation for Economic Co-operation and Development.
+- Organisation for Economic Co-operation and Development, 2002. Safety on Roads What's the Vision, Paris.
+- Organisation for Economic Co-operation and Development/European Conference of Ministers of Transport, 2008. Country Reports on Road Safety Performance. OECD/ECMT working group on achieving ambitious road safety targets, Joint OECD/ECMT Transport Research Centre, Paris. [<http://www.](http://www.internationaltransportforum.org/jtrc/safety/targets/Performance/performance.html) [internationaltransportforum.org/jtrc/safety/targets/Performance/performance.](http://www.internationaltransportforum.org/jtrc/safety/targets/Performance/performance.html) [html>.](http://www.internationaltransportforum.org/jtrc/safety/targets/Performance/performance.html)
+- Organisation for Economic Co-operation and Development/International Transport Forum, 2008. Towards Zero – Ambitious Road Safety Targets and the Safe System Approach. Joint Transport Research Centre of OECD/ITF, Paris.
+- Peden, M., Scurfield, R., Sleet, D., Mohan, D., Hyder, A., Jarawan, E., Mathers, C. (Eds.), 2004. World Report on Road Traffic Injury Prevention. World Health Organisation, Geneva.
+- Tabachnick, B.G., Fidell, L.S., 2006. Using Multivariate Statistics. Pearson/Allyn & Bacon, Boston.
+- UNECE Database, 2008. [<http://w3.unece.org/pxweb/Dialog/varval.asp?ma=01\\_](http://w3.unece.org/pxweb/Dialog/varval.asp?ma=01_TRRoadtypVeh_r&ti=Road+vehicle+fleet+at+31+December+by+Type+of+vehicle%2C+Age+group%2C+Country+and+Year&path=./DATABASE/Stat/40-TRTRANS/02-TRRoadFleet/&lang=1) [TRRoadtypVeh\\_r&ti=Road+vehicle+fleet+at+31+December+by+Type+of+vehicle%](http://w3.unece.org/pxweb/Dialog/varval.asp?ma=01_TRRoadtypVeh_r&ti=Road+vehicle+fleet+at+31+December+by+Type+of+vehicle%2C+Age+group%2C+Country+and+Year&path=./DATABASE/Stat/40-TRTRANS/02-TRRoadFleet/&lang=1) [2C+Age+group%2C+Country+and+Year&path=./DATABASE/Stat/40-TRTRANS/02-](http://w3.unece.org/pxweb/Dialog/varval.asp?ma=01_TRRoadtypVeh_r&ti=Road+vehicle+fleet+at+31+December+by+Type+of+vehicle%2C+Age+group%2C+Country+and+Year&path=./DATABASE/Stat/40-TRTRANS/02-TRRoadFleet/&lang=1) [TRRoadFleet/&lang=1>.](http://w3.unece.org/pxweb/Dialog/varval.asp?ma=01_TRRoadtypVeh_r&ti=Road+vehicle+fleet+at+31+December+by+Type+of+vehicle%2C+Age+group%2C+Country+and+Year&path=./DATABASE/Stat/40-TRTRANS/02-TRRoadFleet/&lang=1)
+- VESIPO, 2002. Erarbeitung der Grundlagen fur die Strassenverkehrssicherheitspolitik des Bundes u.a. Basler & Hofman, Eckhardt, Perrin, Schonenberger, Fierz.
+- Vis, M.A., Van Gent, A.L. (Eds.), 2007. Road Safety Performance Indicators: Country Comparisons. Deliverable D3.7a of the EU FP6 Project SafetyNet.
+- Wegman, F., Eksler, V., Hayes, S., Lynam, D., Morsink, P., Oppe, S., 2005. SUNflower+6: A Comparative Study of the Development of Road Safety in the SUNflower+6 Countries: Final Report. SWOV Institute for Road Safety Research, Leidschendam, The Netherlands.
+- Wegman, F., Commandeur, J., Doveh, E., Eksler, V., Gitelman, V., Hakkert, S., Lynam, D., Oppe, S., 2008. SUNflowerNext: Towards a Composite Road Safety Performance Index. SWOV Institute for Road Safety Research, Leidschendam, the Netherlands.

Zotero/001_artiklid/Road Safety Indicators/goelcorrelatesfatalityriskvulnerable2018.md

@@ -0,0 +1,350 @@
+---
+category: literaturenote
+citekey: goelcorrelatesfatalityriskvulnerable2018
+title: Correlates of fatality risk of vulnerable road users in Delhi
+authors: "Goel, Rahul; Jain, Parth; Tiwari, Geetam"
+year: 2018
+date: 2018-00-00 2018
+doi: 10.1016/j.aap.2017.11.023
+publication: "Accident Analysis & Prevention"
+url: "https://doi.org/10.1016/j.aap.2017.11.023"
+zotero_key: EZZJUVJ5
+zotero_storage: 8ZZ9QJ53
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "Goel, Rahul"
+status: converted
+---
+![](_page_0_Picture_1.jpeg)
+
+Contents lists available at [ScienceDirect](http://www.sciencedirect.com/science/journal/00014575)
+
+# Accident Analysis and Prevention
+
+journal homepage: [www.elsevier.com/locate/aap](https://www.elsevier.com/locate/aap)
+
+![](_page_0_Picture_5.jpeg)
+
+# Correlates of fatality risk of vulnerable road users in Delhi
+
+Rahul Goel[a,](#page-0-0)[⁎](#page-0-1) , Parth Jain[b](#page-0-2) , Geetam Tiwari[c](#page-0-3)
+
+- <span id="page-0-0"></span><sup>a</sup> MRC Epidemiology Unit, University of Cambridge, United Kingdom, UK
+- <span id="page-0-2"></span><sup>b</sup> Civil Engineering, Shiv Nadar University, Gautam Budh Nagar District, India
+- <span id="page-0-3"></span>c Transportation Research and Injury Prevention Programme (TRIPP), Indian Institute of Technology Delhi, New Delhi, India
+
+![](_page_0_Picture_11.jpeg)
+
+## ARTICLE INFO
+
+Keywords: Delhi Vulnerable road users Road deaths India Population Density Grade separators
+
+# ABSTRACT
+
+Pedestrians, cyclists, and users of motorised two-wheelers account for more than 85% of all the road fatality victims in Delhi. The three categories are often referred to as vulnerable road users (VRUs). Using Bayesian hierarchical approach with a Poisson-lognormal regression model, we present spatial analysis of road fatalities of VRUs with wards as areal units. The model accounts for spatially uncorrelated as well as correlated error. The explanatory variables include demographic factors, traffic characteristics, as well as built environment features. We found that fatality risk has a negative association with socio-economic status (literacy rate), population density, and number of roundabouts, and has a positive association with percentage of population as workers, number of bus stops, number of flyovers (grade separators), and vehicle kilometers travelled. The negative effect of roundabouts, though statistically insignificant, is in accordance with their speed calming effects for which they have been used to replace signalised junctions in various parts of the world. Fatality risk is 80% higher at the density of 50 persons per hectare (pph) than at overall city-wide density of 250 pph. The presence of a flyover increases the relative risk by 15% compared to no flyover. Future studies should investigate the causal mechanism through which denser neighborhoods become safer. Given the risk posed by flyovers, their use as congestion mitigation measure should be discontinued within urban areas.
+
+# 1. Introduction
+
+Indian cities have witnessed an exponential growth of vehicles during the previous two decades or so, contributed largely by motorised two-wheelers (MTW) [\(Pucher et al., 2007](#page-7-0); [MoRTH, 2012\)](#page-7-1). Coincident to this, burden from road traffic injuries in India has also been rising, and the number of deaths have more than doubled from 1991 through 2011 ([Mohan et al., 2015\)](#page-7-2). According to the official sources, there were more than 140,000 road deaths in year 2013-14 ([NCRB, 2015](#page-7-3)). When expressed as the number of road deaths per 100,000 persons, fatality risk in India is 2–4 times higher than high-income settings such as the UK, Germany, France and Canada [\(MoRTH, 2012](#page-7-1)).
+
+A majority of the victims are men in age-group 15–59 years ([Gururaj, 2008; Mohan et al., 2009; Hsiao et al., 2013\)](#page-7-4). Pedestrians, cyclists, and MTW riders have the largest share. The three road-user categories, with no rigid barrier protecting them against traumatic forces, are often termed as vulnerable road users (VRU) [\(Peden et al.,](#page-7-5) [2004\)](#page-7-5). Globally, VRUs account for around 46% of all road deaths ([WHO, 2015\)](#page-7-6), while in India this share is much higher.
+
+According to Million Death Study, a national-level mortality survey in India, VRUs accounted for 68% of all road deaths during the period 2001–2003 [\(Hsiao et al., 2013](#page-7-7)). A study conducted in six Indian cities with population ranging between 1–2 million reported that the proportion of VRU fatalities for years 2008 through 2011 varied from 84% to 93% ([Mohan et al., 2016](#page-7-8)). This proportion is much lower in high– income countries and is as low as 22% in the Americas [\(WHO, 2015](#page-7-6)). There are multiple factors contributing to these differences, such as road design, provision of safe infrastructure for pedestrians and cyclists, traffic management, and the enforcement of speed and alcohol limits. Apart from these, the major underlying difference is how people travel in these settings.
+
+According to Census 2011, close to one-third of the workers (30%) in Indian cities walk to work, 17% cycle, a quarter (25%) use some form of public transport (bus, autorickshaw or train), more than one-fifth (22%) use MTW and only 5% use cars [\(Census-India, 2016\)](#page-6-0). As a result, 69% of the workers can be categorised as VRUs during their commute trips. If we consider walking involved in either ends of a public transport trip, the proportion of work trips involving VRU reach up to 94%.
+
+When trips of all purposes are considered, data from various cities in India show that the share of non-motorised modes is even higher ([Arora](#page-6-1) [et al., 2014](#page-6-1); [RITES, 2008](#page-7-9); [Goel, 2017\)](#page-7-10). As a result, a large proportion of road users are exposed to high injury risk through collisions with high-
+
+E-mail addresses: [rahulatiitd@gmail.com,](mailto:rahulatiitd@gmail.com) [rg574@medschl.cam.ac.uk](mailto:rg574@medschl.cam.ac.uk) (R. Goel).
+
+0001-4575/ © 2017 Elsevier Ltd. All rights reserved.
+
+<span id="page-0-1"></span><sup>⁎</sup> Corresponding author.
+
+powered motorised vehicles such as cars, buses, and trucks. This is in complete contrast with high-income settings where a large proportion of trips are carried out in cars. For instance, 86% of the work trips in the US (2009; [McKenzie and Rapino, 2011](#page-7-11)), 64% in the UK ([2011; Gower,](#page-7-12) [2013\)](#page-7-12) and 62% in the Netherlands (2007; [MOT, 2009\)](#page-7-13) were carried out using cars. As a result, in case of a crash, the road users in these settings have much higher protection.
+
+Road transport in India also differs in the form of motorisation from their western counterparts. Increasing motorisation is not resulting in reduction of VRUs on roads, as MTW remains a preferred mode of private transport. While MTW in India account for more than two-thirds of private motorised fleet [\(MoRTH, 2012\)](#page-7-1), their share in western settings such as the USA, UK, Germany and France, is only 3–10% ([EEA,](#page-7-14) [2003;](#page-7-14) [USDOT, 2015](#page-7-15)).
+
+A large number of crash-level epidemiological studies have been carried out in India to understand the causal mechanism of crashes or the injury severity [\(Garg and Hyder, 2006](#page-7-16)). However, epidemiology of crashes using ecological models is lacking. In this study, we present a spatial analysis of VRU fatalities in Delhi to assess their geographic variation with respect to built environment, demographic factors, and traffic characteristics. We restricted our analysis to fatal crashes as number of injury crashes reported by police are highly underreported in India ([Gururaj, 2008; Mohan et al., 2009; Mohan et al., 2015\)](#page-7-4). Delhi being the capital of India and the seat of federal government has an active police department and is a dense urban area. Therefore, underreporting of traffic deaths in a setting like Delhi is highly unlikely.
+
+#### 2. Literature review
+
+Crash rates have been established to have a positive association with the speed of vehicles [\(Nilsson, 1981; Cameron and Elvik, 2010](#page-7-17)). In addition to the probability of a crash, speed of vehicles is also a determinant of severity level of injuries ([OECD/ECMT, 2006; Aarts and](#page-7-18) [Van Schagen, 2006](#page-7-18)). How fast vehicles travel on road is a function of built environment ([Ewing and Dumbaugh, 2009\)](#page-7-19) and road design features ([Török, 2011; Fitzpatrick et al., 2001\)](#page-7-20), among other factors such as speed limit ([Fitzpatrick et al., 2001](#page-7-21)), or traffic conditions ([Török,](#page-7-20) [2011\)](#page-7-20). Given these links of crashes with speed and that of speed with built environment, many studies have found association between crash rates and built environment ([Ewing et al., 2003](#page-7-22)).
+
+There are other factors which result in higher number of crashes such as through increasing the exposure to risk, increasing the chances of a crash, or increasing the severity of injury. Higher exposure to risk is a function of economic and demographic factors and mode of travel. Higher crash occurrence is associated with lack of law enforcement by police and lack of safe infrastructure for pedestrians and cyclists, and higher severity level can result from lack of forgiving vehicle front to protect pedestrians in a collision, use of seat belts by cars occupants and helmets by MTW riders and cyclists ([Peden et al., 2004](#page-7-5)).
+
+A large number of studies have carried out area-level crash modelling to quantify the association of road traffic injuries with built environment and traffic characteristics as well as population characteristics. Such models, after accounting for confounding variables, estimate the independent effects of different built environment variables, such as, type of junctions, intersection density, type of roads, speed limit, road widths, and road curvature. With this knowledge, built environment can be modified in ways which can increase the safety of road users. The sensitivity of safety to those modifications is given by the coefficients of the regression models.
+
+Most of the area-level modelling studies have been carried out in settings from highly motorised developed countries—US, Canada, UK, and Australia. For instance, studies from cities/states in the US include San Francisco, California ([LaScala et al., 2000; Wier et al., 2009](#page-7-23)), Tucson, Arizona [\(Ladron de Guevara et al., 2004](#page-7-24)), Pennsylvania ([Aguero-Valverde and Jovanis, 2006](#page-6-2)), Hawaii [\(Kim et al., 2006](#page-7-25)), Charlotte, North Carolina [\(Pulugurtha et al., 2013\)](#page-7-26), California ([Chakravarthy et al., 2010](#page-6-3)), San Antonio, Texas [\(Dumbaugh et al.,](#page-7-27) [2013\)](#page-7-27), New York city ([DiMaggio, 2015](#page-7-28)), Manhattan ([Narayanamoorthy](#page-7-29) [et al., 2013\)](#page-7-29), New Jersey [\(Demiroluk and Ozbay, 2014](#page-7-30)), and Hillsborough and Pinellas counties of Florida [\(Siddiqui et al., 2012; Xu et al.,](#page-7-31) [2017\)](#page-7-31), from those in Canada include Toronto [\(Hadayeghi et al., 2003](#page-7-32)), Greater Vancouver region [\(Lovegrove and Sayed, 2006](#page-7-33)) and British Columbia [\(MacNab, 2004](#page-7-34)), those in UK, London [\(Quddus, 2008](#page-7-35)), England [\(Graham and Glaister, 2003; Noland and Quddus, 2004\)](#page-7-36), and England and Wales [\(Jones et al., 2008](#page-7-37)), and in Australia, Melbourne ([Amoh-Gyimah et al., 2016\)](#page-6-4). Among low-and middle-income countries (LMICs), the only study reported is by [Wang et al. \(2016\)](#page-7-38) in which they modeled pedestrian crashes in Shanghai city.
+
+The areal unit of analyses used by various studies also varied and included counties [\(Aguero-Valverde and Jovanis, 2006; Demiroluk and](#page-6-2) [Ozbay, 2014\)](#page-6-2), census tracts ([LaScala et al., 2000; Chakravarthy et al.,](#page-7-23) [2010; Narayanamoorthy et al., 2013; DiMaggio, 2015](#page-7-23)), census statistical area levels [\(Amoh-Gyimah et al., 2016\)](#page-6-4), wards ([Graham and](#page-7-36) [Glaister, 2003; Noland and Quddus, 2004; Quddus, 2008\)](#page-7-36), traffic analysis zones (TAZ) [\(Hadayeghi et al., 2003; Pulugurtha et al., 2013;](#page-7-32) [Siddiqui et al., 2012; Wang et al., 2016; Xu et al., 2017\)](#page-7-32), city blocks ([Dumbaugh et al., 2013\)](#page-7-27) or grids [\(Kim et al., 2006](#page-7-25)).
+
+The modeling has been carried out using non-spatial models (Hadayeghi [et al., 2003; Graham and Glaister, 2003; Noland and](#page-7-32) [Quddus, 2004; Kim et al., 2006; Pulugurtha et al., 2013; Lovegrove and](#page-7-32) [Sayed, 2006; Wier et al., 2009; Chakravarthy et al., 2010; Dumbaugh](#page-7-32) [et al., 2013\)](#page-7-32), spatial models [\(LaScala et al., 2000; MacNab, 2004;](#page-7-23) [Narayanamoorthy et al., 2013; Demiroluk and Ozbay, 2014; DiMaggio,](#page-7-23) [2015; Wang et al., 2016](#page-7-23)), as well as both [\(Quddus, 2008; Aguero-](#page-7-35)[Valverde and Jovanis, 2006; Siddiqui et al., 2012; Amoh-Gyimah et al.,](#page-7-35) [2016; Xu et al., 2017](#page-7-35)). Spatial models have accounted for spatial correlation using traditional econometric models, such as spatial autoregressive models ([Quddus, 2008; LaScala et al., 2000\)](#page-7-35) or spatial error models [\(Quddus, 2008](#page-7-35)) or using more recently developed hierarchical Bayesian modelling which include specifications of error terms for uncorrelated heterogeneity as well as spatial heterogeneity [\(MacNab,](#page-7-34) [2004; Aguero-Valverde and Jovanis, 2006; Quddus, 2008; Siddiqui](#page-7-34) [et al., 2012; Wang et al., 2016; Amoh-Gyimah et al., 2016; Xu et al.,](#page-7-34) [2017\)](#page-7-34).
+
+It is noteworthy that even though a major share of global road traffic injury burden is contributed by LMICs, their representation in such studies is almost absent. In Indian cities, most roads do not have posted speed limits, and when they do, police rarely enforces those. As a result, speed chosen by drivers is likely to be much more associated with traffic conditions, road design features and other built environment factors. This underscores the importance of built environment as risk factor for crashes in Indian cities. Other factors which set Indian cities apart from their high-income counterparts are lack of safe infrastructure for non-motorised modes, heterogeneous mix of traffic, low level of car-based travel and a high share of MTW. The contrasting contexts of on-road traffic mix, built environment, demographics, and level of traffic enforcement between India and high-income countries warrant an area-level crash study in an Indian city.
+
+## 3. Case study city—Delhi
+
+Delhi is the capital city of India and one of the most heavily motorised large cities in India. Among the cities with population more than 10 million, it has the highest ownership of cars, with more than one in every 5 households owning a car ([Guttikunda et al., 2014\)](#page-7-39). Delhi along with its contiguous cities have grown rapidly over the last two decades. The population of the region more than doubled from 10 million in 1991–22 million in 2011, with Delhi contributing 16.7 million to the latter. Over the same period, the number of registered vehicles have increased by more than 300%. Public transport (PT) is served through a combination of road– and rail–based modes. These include buses, intermediate public transportation such as cycle rickshaws, electric rickshaws, auto rickshaws or tuktuks, and mini buses, and rail-based systems including metro rail and commuter rail [\(Goel and Guttikunda,](#page-7-40) [2015; Goel and Tiwari, 2016\)](#page-7-40).
+
+According to Census 2011, among all the work trips in Delhi, up to a quarter of trips are walked (26%), one-tenth are cycled (11%), onethird use some form of public transport (32%), 17% use MTW and 13% use cars ([Census-India, 2016](#page-6-0)). A large number of grade-separated intersections have been built in Delhi as a measure to reduce congestion as well as to reduce vehicular idling. Cycle lanes have been built as a part of 5.8-km long bus rapid transit corridor, while almost no other road in Delhi has cycle lanes. Though small isolated sections of cycle lanes have been built in various parts of the city. There is no helmet use among bicycle users in Delhi.
+
+#### 4. Data
+
+In this study we model road deaths corresponding to the 3-year period: 2010–2012. The year 2011 corresponds to the latest Census. The inclusion of fatalities for three years brings stability in the fatality counts for disaggregated spatial units within the city. We used casespecific fatal crashes reported in First Information Reports (FIRs) compiled by Delhi Traffic Police for the years 2010 through 2012. FIRs are the first set of information documented by police department as reported by those involved in the crash or anyone who knows about the crash or by a police official [\(Mohan et al., 2015\)](#page-7-2).
+
+The case-specific details consist of date, time, location, police station of the crash location, striking vehicle type, and victim road-user type. Age and gender of crash victims were available for year 2010 only. The three-year period includes a total of 5972 fatalities, which amounts to 1991 fatalities per year, and 11.9 fatalities per 100,000 persons, assuming 2011 census population as average of the 3-year period. In comparison, New York has a fatality rate of 3 per 100,000 persons ([NYDMV, 2014\)](#page-7-41), Greater London, 1.6, [\(TFL, 2014](#page-7-42)), and Amsterdam, 2 ([Iamsterdam, 2014](#page-7-43)). The three VRU categories, pedestrians (45.5%), cyclists (5.9%), and motorised two-wheeler (MTW) riders (34.5%), contribute 86% (5138) of all the fatalities.
+
+The location of the crashes mentioned in the FIR data consisted of the name of the road where the crash occurred along with a landmark. Using this information, geographical coordinates of the crash locations were identified using Google Maps as well as Wikimapia [\(http://](http://wikimapia.org/country/India/Delhi/) [wikimapia.org/country/India/Delhi/](http://wikimapia.org/country/India/Delhi/)). The latter has information regarding informal landmarks known among local population and collected through crowdsourcing, which are often missing in Google Maps. In addition, we referred to jurisdiction map of police stations. Landmarks of some of the crash locations were reported using serial number of pillars of elevated metro corridors, and were also not available on Wikimapia. For these, we visited those road sections and geo-located those pillars using GPS.
+
+We use wards as areal units which are administrative units in the city for the purpose of municipal corporations. In 2011, Delhi was divided in to 282 wards with an average size of 4.9 km<sup>2</sup> with more than half (54%) of all the wards having an area of less than 2 km<sup>2</sup> . The average number of VRU fatalities across the wards is 18 varying from a minimum of zero to maximum of 183. We used ward-specific demographic and socio-economic statistics from Primary Census Abstract (PCA) reported by Census 2011.
+
+From PCA, we used population, literacy rate, and percent of population who are workers. The population of wards also vary from ∼14,000 to ∼146,000 with an average of ∼58,000. Literacy rate is defined as the percentage of population above 6 years who are literate. Workers have been classified based on the length of employment during the past one year—main worker: 6 months or more, marginal worker: less than 6 months, and non-worker: no employment. For our analysis, we only used the main worker category.
+
+In the absence of city-wide traffic counts, modelled vehicle kilometers travelled (VKT) were used from Travel Demand Forecast Study (TDFS) commissioned by Transport Department of Delhi ([RITES, 2008](#page-7-9)). The study carried out traffic assignment model for 2007 which consisted of volume of vehicles in each link (road segments), expressed as Passenger Car Units. TDFS also included validation of assignment model with the observed traffic counts at various locations. We used model output for 2007 and estimated ward-specific VKT using the sum total of product of length of each link and its corresponding volume. While the traffic deaths in our model refer to 2010–2012 period, we assume that 2007 traffic volume is sufficient for assessing relative variation across the wards. Even if the growth in traffic volume occurred, we assume that growth rate was consistent across the wards.
+
+The model of road deaths presented in this study also accounts for exposure for each ward. We calculated exposure as the sum of population of the ward and the total number of daily person trips destined to the ward. This was then multiplied by 3 since the fatality counts correspond to a three-year period. Thus, exposure accounts for population residing in the ward as well those visiting the ward during the course of a day. For instance, in case of a ward with offices and other commercial land use, while the residing population could be small, it will still attract a large number of people during the day. For estimating the number of external trips to wards we used TDFS study.
+
+From TDFS, origin-destination (OD) matrices of person trips estimated for year 2011 were available for motorised modes and classified among four categories—car, MTW, intermediate public transport (IPT) which includes auto rickshaws (or tuk-tuks), and public transport (PT) including bus and train. We used OD matrices for year 2011 as these need to be consistent with the population which corresponds to 2011. We used sum total of all modes to estimate total trips destined to each zone. The OD units in TDFS are traffic analysis zones (TAZs) which were formed using wards. In cases where ward size was much bigger, TAZs were formed by dividing the ward into two or more units. By overlaying the TAZ over wards in a GIS platform, TAZs were mapped to their corresponding wards. Using this correspondence, ward-specific VKT and exposure were calculated using zonal data. The total number of external trips to each ward are shown in [Table 1](#page-2-0) as Person trips destined to ward.
+
+For built environment variables we included grade separators (overpass/flyovers), roundabouts, bus stops, and built-up population density. Built up area was identified using Google Earth for 2013 ([Goel](#page-7-40) [and Guttikunda, 2015\)](#page-7-40), using which ward-specific population density were estimated. The average built-up population density of wards is 490 persons per hectare (pph), with 60% of the wards within 500 pph and 85% within 800 pph. Other built environment variables were also identified using Google Earth for year 2012. In case of grade-separated intersections, we used the corresponding intersection as a point location to represent grade separator. Most flyovers in Delhi connect two
+
+<span id="page-2-0"></span>Table 1 Descriptive statistics.
+
+|                                         | Mean   | Standard<br>Deviation | Min    | Median | Max     |
+|-----------------------------------------|--------|-----------------------|--------|--------|---------|
+| Population                              | 58,046 | 19,205                | 14,217 | 54,404 | 145,715 |
+| Population Density<br>(persons per km2) | 49,359 | 38,216                | 1808   | 40,796 | 279,200 |
+| Person trips destined to<br>ward        | 38,786 | 31,192                | 5287   | 30,450 | 300,213 |
+| VKT                                     | 2581   | 3396                  | 20     | 1631   | 36,326  |
+| # Bus stops                             | 12     | 13                    | 0      | 9      | 67      |
+| # Flyovers                              | 0      | 1                     | 0      | 0      | 7       |
+| # Roundabouts                           | 0      | 1                     | 0      | 0      | 12      |
+| Area                                    | 4.9    | 10.7                  | 0.3    | 1.9    | 80.0    |
+| # VRU fatalities                        | 18     | 20                    | 0      | 13     | 183     |
+| % Population main<br>workers            | 32.3   | 4.0                   | 23.7   | 32.3   | 46.1    |
+| % Population (> 6 years)<br>literate    | 86.6   | 5.5                   | 72.0   | 87.5   | 97.1    |
+
+parallel legs of a major intersection to facilitate the uninterrupted movement of through moving traffic. Few flyovers span across more than one intersection and are often referred to as elevated roads. For those flyovers, we denoted locations at their beginnings and at their ends. [Table 1](#page-2-0) presents descriptive statistics of all the variables.
+
+## 5. Method
+
+The objective of this study is to explore the effect of built environment and demographic and socioeconomic characteristics of the population on the fatality risk of VRUs. For this, we used the Bayesian hierarchical modelling framework as proposed by Besag, York and Mollié (BYM) [\(Besag et al., 1991](#page-6-5)). The model has been implemented widely such as for cancer mapping by [Cramb et al. \(2011\)](#page-6-6) and injury modelling by [Quddus \(2008\)](#page-7-35) and [DiMaggio \(2015\)](#page-7-28). The model is described as follows:
+
+<span id="page-3-1"></span><span id="page-3-0"></span>
+$$y_i = Poisson(\theta_i) \tag{1}$$
+
+$$\log(\theta_i) = \log(e_i) + \beta_0 + \beta_i X_i + \delta_i + \nu_i$$
+(2)
+
+where, yi are the observed VRU fatality counts in each ward i, θ<sup>i</sup> are the expected count of fatalities, Xi represents a vector of explanatory variables, or covariates for each ward, ei is the exposure, β<sup>0</sup> is the intercept, β is a vector of fixed effect parameters, δ*<sup>i</sup>* is the uncorrelated heterogeneity or unstructured error, and ν<sup>i</sup> is the spatially correlated heterogeneity. The random error components represent the effects of unmeasured/unknown risk factors. Here, δ*<sup>i</sup>* represents overdispersion and accounts for variation in the expected fatality risk of wards after controlling for the independent variables, and ν<sup>i</sup> represents spatial patterns affecting fatality risk and not accounted for by the independent variables.
+
+The first level of the hierarchical modeling framework presented in the Eq. [\(1\)](#page-3-0) represents ward-level observed crash counts (yi) generated from a Poisson distribution with an expected θ<sup>i</sup> count of
+
+The second level, presented in Eq. [\(2\)](#page-3-1), includes the linear relationship between log of expected counts and independent variables. Here, exposure (ei) is an offset (a covariate with coefficient value 1) and, therefore, effectively acts as a denominator for left-hand side of the equation. This in turn expresses the dependent variables as risk (log (λi) =log( / ) *θ e i i* ). Therefore, this modelling framework accounts for exposed population explicitly, rather than treating it as a covariate. Note that exposure is the sum total of population and the number of external trips destined to the ward.
+
+The Bayesian modelling was done using R-INLA [\(Rue et al., 2009\)](#page-7-44) which is an R package and employs Integrated Nested Laplace Approximations to estimate the posterior distributions. R-INLA has been recently developed as a computationally efficient alternative to Monte Carlo Markov Chain (MCMC). Unlike MCMC methods which rely on simulation methods to trace posterior distribution, INLA estimates parameters using a closed-form deterministic method and is much faster. It has been applied in injury modeling by [DiMaggio \(2015\).](#page-7-28)
+
+R-INLA includes a latent model for uncorrelated random effects (δ*i*), in which these effects are modelled as δ (0, 1/ *<sup>i</sup>* ∼ *N τ*δ), where *τ*<sup>δ</sup> refers to the precision of the Normal distribution and is inverse of the variance. log(*τ*δ) is assigned a prior of log-gamma distribution with mean and precision of 1 and 0.0005, respectively. Using log(*τ*δ) instead of simply *τ*<sup>δ</sup> provides some advantages as log(*τ*δ) is not constrained to be positive. Fixed effects, including the intercept, have a Gaussian prior with fixed mean and precision (*N* (0,0.001)).
+
+For spatial dependence we use the intrinsic conditional autoregressive (CAR) specification as proposed by [Besag et al. \(1991\).](#page-6-5) According to this specification, the spatial random effects ν<sup>i</sup> are distributed as:
+
+$$\nu_i \left| \nu_j, \; \tau_\nu \sim N \left( \frac{1}{n_i} \sum_{i \sim j} \; \; \nu_j, \; \frac{1}{\tau_\nu n_i} \right) i \neq j \right.$$
+
+where, j refers to the indices of all wards which are neighbours of a given ward i, and ni is the total number of neighbours of ward i. To determine the number of neighbours and to identify the pairs of wards as neighbours, a contiguous neighbor-adjacency matrix was created using the poly2 nb function in the spdep R package [\(Bivand et al., 2011](#page-6-7)). To define neighbours, we used queen adjacency method according to which two wards are neighbours if they share a common boundary or a point.
+
+The above specification implies that spatial component of error at any ward (νi) has a normal distribution. That distribution is centered around the mean of the spatial error components of all its neighbouring wards and the variation around the mean is inversely proportional to the number of its neighbours. As the number of neighbouring wards increase, the spread of the distribution around the mean value also reduces.
+
+Similar to log(*τ*δ), log(τν) is also assigned a prior of log-gamma distribution with mean and precision of 1 and 0.0005. The parameters describing the priors are often referred to as hyper-parameters, which in the current specifications are *τ*<sup>δ</sup> and τν, for uncorrelated and spatially correlated error terms, respectively. Their respective distributions are called hyperprior distributions. Fixed effects, on the other hand, have no hyperparameters. Note that all the priors are defined with very large variances (inverse of variance varies from 0 for intercept, to 0.0005 for hyperparameters, to 0.001 for other fixed effects), and therefore, these priors are uninformative, signifying lack of our prior understanding of these effects.
+
+Note that while *τ*<sup>δ</sup> is an indicator of uncorrelated heterogeneity across all wards, τν represents the variation of the conditional autoregressive specification, therefore the two cannot be interpreted in the similar manner. Using R-INLA output, we obtained the posterior distributions of spatial error components of each of the ward. To estimate variance of spatial components, we simulated 1000 random values of spatial components of each of the ward using their corresponding posterior distributions. For each of those 1000 runs, we estimated variance of spatial error across all wards, and the mean of 1000 variance values was estimated as the variance of spatial error component.
+
+To compare the performance of Bayesian models, Deviance information criterion (DIC) is estimated which is a Bayesian version of Akaike information criterion (AIC). DIC is calculated as:
+
+$$DIC = D(\hat{\theta}_{Bayes}) + 2p_{DIC}$$
+
+where, the first term in right-hand side is the deviance calculated for the posterior mean of the estimated parameters, and second term is the effective number of parameters in the model. Compared to maximum likelihood method, in Bayesian hierarchical modeling, deviance is evaluated at mean of posterior distributions rather than maximum likelihood estimate of parameters and the number of effective parameters tend to be less [\(Gelman et al., 2014,](#page-7-45) p. 172). Similar to AIC, lower value of DIC implies higher predictive accuracy.
+
+# 5.1. Selection of variables
+
+Before progressing to development of the regression model, we investigate the Pearson correlation between various variables in order to avoid multicollinearity between the independent variables. VKT has high positive correlation with number of bus stops and high negative correlation with population density. Population density and number of bus stops are also highly negatively correlated. We found that adding the three variables together did not significantly affect the standard deviations of their coefficients compared to when they are added individually. In addition, magnitude of the coefficients also changed by a maximum of 25% in case of population density. At the same time, DIC
+
+<span id="page-4-0"></span>Table 2 Results of intercept-only and full model using Bayesian Hierarchical modelling.
+
+| Variable               | Intercept-only model |         |         | Full model     |         |        |
+|------------------------|----------------------|---------|---------|----------------|---------|--------|
+|                        | mean (sd)            | P2.5    | P97.5   | mean (sd)      | P2.5    | P97.5  |
+| Intercept              | −10.108 (0.042)      | −10.192 | −10.024 | −8.049 (1.480) | −10.988 | −5.170 |
+| % Literate             |                      |         |         | −0.024 (0.009) | −0.042  | −0.006 |
+| % Main workers         |                      |         |         | 0.039 (0.016)  | 0.008   | 0.071  |
+| ln(Population density) |                      |         |         | −0.355 (0.090) | −0.532  | −0.177 |
+| ln(VKT)                |                      |         |         | 0.317 (0.064)  | 0.192   | 0.445  |
+| # Bus stops            |                      |         |         | 0.012 (0.004)  | 0.004   | 0.021  |
+| # Flyovers             |                      |         |         | 0.137 (0.056)  | 0.028   | 0.247  |
+| # Roundabouts          |                      |         |         | −0.042 (0.038) | −0.117  | 0.034  |
+| τδ (iid component)     | 3.069 (1.103)        | 1.503   | 5.772   | 3.434 (0.651)  | 2.304   | 4.85   |
+| τv (spatial component) | 0.467 (0.136)        | 0.251   | 0.779   | 9.706 (11.461) | 1.548   | 38.67  |
+| DIC                    | 1737.91              |         |         | 1705.71        |         |        |
+
+reduced significantly by 5 units compared to the model with only VKT among the three variables. Therefore, in the final model, all the three variables were retained.
+
+#### 6. Results
+
+We obtained results for an intercept-only as well as a full model, as shown in [Table 2.](#page-4-0) The table shows mean and 2.5th and 97.5th percentiles of the posterior distributions of all coefficients as well as error components, and also presented are the DIC values. The percentiles represent the 95% confidence interval (CI). We found that for the frailty or intercept-only model, 66% of the variance is due to spatial component, while the rest is due to unstructured heterogeneity of ward. Full model explained 89% of the variation of spatial error, however, it explained less than 20% of the variation in uncorrelated heterogeneity. In the intercept-only model, exponential of intercept term, exp(β0), represents the background fatality risk across the wards and exponential of sum of two error components, exp(δ ν ) + , *i i* represents the relative risk of each ward, and the latter is presented in [Fig. 1.](#page-5-0)
+
+On the basis of 95% CI of posterior distributions, all the coefficients are significantly different from zero, except number of roundabouts. Percentage of literate population, number of roundabouts and population density have a negative association with fatality risk and percentage of population as workers, number of bus stops, number of flyovers, and VKT have positive association. Here, a positive association indicates that with an increase in a variable, the fatality risk increases.
+
+#### 7. Discussion
+
+# 7.1. Socio-economics and demographics
+
+An increase in literacy rate, which is an indicator of socio-economic status (SES) of the ward, is associated with lower risk of fatalities. This is possible because population with low SES are more likely to be VRUs as they walk, cycle, use PT or ride MTW for their daily travel. In Delhi, only one-fifth of all households own a car [\(Census-India, 2012](#page-6-8)). With low level of car ownership, whether an individual is VRU or not is highly sensitive to their income level. Million Death Study [\(Hsiao et al.,](#page-7-7) [2013](#page-7-7)) also reported pedestrian deaths to be positively associated with living in poorer neighborhoods. A large number of studies have shown similar results linking higher risk of fatalities, or number of road crashes in general, with lower SES ([Aguero-Valverde and Jovanis, 2006;](#page-6-2) [Wier et al., 2009; DiMaggio, 2015; Xu et al., 2017\)](#page-6-2).
+
+The percentage of population as main workers is positively associated with the fatality risk. According to Census 2011, 65% of the main workers in Delhi are in the age group 30–59, and 86% of them are males. Therefore, workers represent a specific demographic group, which is predominantly male in the age group 30–59. This is also reflected in the age and sex distribution of injuries. For the three-year fatality data (2010–2012) reported in the current study, sex of victims was reported for year 2010, according to which males accounted for 91% of all fatality victims, while their share in overall population is 54% [\(Census-India, 2012](#page-6-8)). The disproportionate share of men in the age group 15–59 years was also reported by the Million Death Study ([Hsiao](#page-7-7) [et al., 2013\)](#page-7-7). This explains a positive association of main workers with fatality risk.
+
+It is interesting to note that even though Pearson correlation between percentage of main workers and percentage of literate population is positive, the coefficients of the two variables are opposite in signs. This means that SES (indicated by literacy) and demographics (indicated by workers) have their independent effects which are opposite in directions.
+
+#### 7.2. Traffic volume and roundabouts
+
+Positive effect of VKT is expected and has been consistently reported by all studies which considered it as one of the covariates [\(Amoh-](#page-6-4)[Gyimah et al., 2016; Demiroluk and Ozbay, 2014; DiMaggio, 2015;](#page-6-4) [Quddus, 2008; Xu et al., 2017; Aguero-Valverde and Jovanis, 2006;](#page-6-4) [Huang et al., 2010; Wier et al., 2009\)](#page-6-4). According to the posterior distribution of coefficient of number of roundabouts, up to 85th percentile value is a negative. One of the benefits of Bayesian method over frequentist method is that while the latter reports coefficients as single values, the former reports them as distributions of values. Thus it can be said that, given the data, there is more evidence in favour of a negative association of roundabouts with fatality risk than a positive or no effect.
+
+The negative association of roundabouts with fatality risk is also expected from international experience. Roundabouts have been adopted globally as a traffic calming measure because of their effectiveness to reduce road crashes. According to a meta-analysis of 28 studies in non-US locations, conversion of intersections to roundabouts resulted in 50–70% reduction of the fatal crashes [\(Elvik, 2003](#page-7-46)). In Holland, before-and-after studies of the construction of about 200 roundabouts showed a significant drop of 89% of pedestrian fatalities ([Schoon and van Minnen, 1994\)](#page-7-47).
+
+# 7.3. Flyovers and bus stops
+
+Apart from roundabouts, flyovers and bus stops are two other variables representing road infrastructure, and we will discuss the two together because of their related features. Flyovers have a strong positive association with fatality risk, with one flyover increasing the relative risk by 15% compared to no flyover. Bus stops are also positively related to fatality risk. These effects are independent of the volume of traffic. The coefficients of the two variables may not be isolated effects of the two infrastructure elements and could also be indicating the effect of other built environment features which occur simultaneously.
+
+Flyovers in Delhi have been built along major arterial roads (for
+
+Fig. 1. Relative risk of VRU fatality risk in wards across Delhi.
+
+<span id="page-5-0"></span>![](_page_5_Figure_3.jpeg)
+
+instance the two ring roads) as well as highways. Bus stops in Delhi are also located on most major roads, of which arterials and highways are subsets. Most residential and commercial areas do not have enough carriageway width for movement of the bus. Therefore, both bus stops and flyovers are likely to represent road types with heavy vehicular movement. The roads with flyovers also have 40–50% higher average speed than other major roads [\(Mohan et al., 2017](#page-7-48)).
+
+A study conducted in Delhi ([Khatoon et al., 2013\)](#page-7-49) studied traffic characteristics before and after the replacement of signalised junction with a flyover. The study reported that the average speed travelled by trucks and buses as well as the variability of the speed of all vehicle types increased after the construction of flyover. Another study from Delhi also found presence of flyovers as a significant factor affecting the number of pedestrian crashes ([Rankavat and Tiwari, 2015](#page-7-50)). Thus there is a strong evidence suggesting that construction of flyovers results in high increase in the risk of injuries.
+
+One of the major confounding variables which has been excluded in this analysis is the volume of trucks, which may bring endogeneity in the model results. A network of national highways pass through the city in multiple directions making it a natural route for long–distance trucks as well as a hub for goods exchange. A large proportion of goods movement occurs in Delhi through road-based freight modes. High volume of trucks is also a major source of pollution in Delhi ([Goel and](#page-7-40) [Guttikunda, 2015](#page-7-40)). It is possible that the model may have introduced an upward bias in the effect of number of flyovers and number of bus stops. However, given the magnitude of association for both bus stops and flyovers as well as high statistical significance indicated by their posterior distributions, the addition of any other risk factor is unlikely to change the direction of association.
+
+Population density is log transformed therefore its coefficient
+
+cannot be interpreted in the similar manner as other independent variables. Since the relative risk is an exponent of product of the variable and its coefficient (exp (βiXi)), the relative risk (RR) of population density can be expressed as power functions, as[1](#page-5-1)
+
+= <sup>−</sup> *RR Populationdensity* ( ) 0.355
+
+In order to understand the effect of density, we expressed the relative risk with respect to the overall average population density (total population/total built-up area) of 250 pph. [Fig. 2](#page-6-9) indicates that relative risk of fatalities is more than 1.8 times higher at density of 50 pph compared to city-level average. The non-linear curve shows that at higher density levels, the effect of density flattens off and the most reduction in relative risk is up to a density of 850 pph. There are various factors which could result in this association of density with risk and we discuss those in the following text.
+
+High density locations are more likely to have higher number of pedestrians. In the absence of dedicated facilities for pedestrians and cyclists, the two slow-moving road users occupy the curb-side lane of the roads. This effectively slows down the traffic and makes roads safer. With an increase in the volume of pedestrian, their risk reduces, and this phenomenon is referred to as safety-in-numbers [\(Jacobsen, 2003;](#page-7-51) [Elvik and Bjørnskau, 2017\)](#page-7-51). Thus the negative association of relative risk with density may likely be an indicator of safety-in-numbers.
+
+High density also attracts higher number of IPT, such as cycle rickshaws, auto rickshaws, and e-rickshaws. These modes are demand responsive and are operated by private operators. Therefore, their volumes are proportional to density or the demand. Since buses do not
+
+<span id="page-5-1"></span><sup>1</sup> <sup>e</sup>β.ln(X) = X<sup>β</sup>
+
+<span id="page-6-9"></span>![](_page_6_Figure_2.jpeg)
+
+Fig. 2. Relative risk at different density levels compared to city-level average (250 pph).
+
+operate through streets in residential areas, IPT is also used for last-mile connectivity of a bus or metro trip [\(Goel and Tiwari, 2016\)](#page-7-52). In the absence of dedicated parking bays or stops, these vehicles idle along the curb-side lane for passenger boarding and alighting, leading to further congestion. On-street parking/idling effectively narrows the roads, and driver tend to be more cautious while driving through those sections ([Gattis, 2000](#page-7-53)).
+
+In Delhi, as well as in most Indian cities, most informal neighborhoods or commercial areas have high built-up density and narrow roads. Informality implies that most growth in built-up is in-situ (as opposed to Greenfield development). Also, the street design is not according to municipal bye-laws which ensure wide-enough streets. Formally designed high-income neighborhoods often have wider streets, but due to on-street car parking by the residents, road widths are effectively reduced.
+
+As a result, most through movement of motorised traffic occurs on major roads, and those driving through the narrow streets tend to drive slow. In addition to slower and low volume of traffic, trucks and buses are almost absent in these locations. While trucks are restricted by police, buses do not ply due to lack of space. This can also be seen through a negative correlation of population density with both, number of bus stops as well as VKT, which in turn are proxies of major roads. Therefore, high density should also be interpreted as a proxy of residential/commercial land-use and street design, and these correlates of high density act as speed calming measures.
+
+The relationship of crash risk with population density has been inconsistent across the studies. While [Graham and Glaister \(2003\)](#page-7-36) and [Noland and Quddus \(2004\)](#page-7-54) reported a negative association between density and crash risk, [Lovegrove and Sayed \(2006\),](#page-7-33) [Huang et al.](#page-7-55) [\(2010\),](#page-7-55) [Dumbaugh and Li \(2010\),](#page-7-56) [Chakravarthy et al. \(2010\),](#page-6-3) [Siddiqui](#page-7-31) [et al. \(2012\)](#page-7-31), and [Narayanamoorthy et al. \(2013\)](#page-7-29) reported a positive association between the two. Both the studies showing negative relationship were based on country-wide analysis in the UK using wards as areal units, and all the studies showing positive relationship were based in either US or Canada— Florida, San Antonio, California, Manhattan, and Vancouver.
+
+The cities in the US have higher car ownership and lower population density than the UK ([Giuliano and Narayan, 2003](#page-7-57)). Compared to both US and UK, Delhi's density is an order of magnitude higher and car ownership a magnitude of order lower. In a setting with high car ownership, higher density may imply higher number of cars against a smaller number of pedestrians. In contrast, in a setting such as Delhi, it implies much higher number of pedestrians in conflict with comparatively smaller number of motorised modes. Thus, density can imply different mechanisms in place in different settings.
+
+## 8. Conclusion
+
+Pedestrians, cyclists and MTW users constitute the largest group of fatality victims in Delhi. In Delhi as well as in most Indian cities, overall traffic enforcement is weak, especially in terms of speed as well as alcohol limit. In addition, the infrastructure facilities for pedestrians are poor, for cyclists almost absent, and MTW use the same lanes as other motorised modes. The mixing of VRUs with vehicles of much larger weight and speed results in greater injury risk. In this context, improving safety through design of built environment can prove to be highly effective. Therefore, it is important to understand built environment factors which affect fatality risk. In this study we assessed the risk resulting from roundabouts, bus stops, flyovers and population density while controlling for traffic volumes and population characteristics.
+
+With higher emphasis on smooth traffic flow and higher speed, a large number of flyovers have been built within populated areas in Delhi as well as many Indian cities. We found that an addition of a flyover increases the fatality risk in a ward by up to 15%, and this effect is independent of traffic volume. While the construction of flyovers pose a challenge of lock-in, their effect on speed of vehicles can be controlled by using speed enforcement by the police or using passive measures such as installment of rumble strips. Given the high risk posed by addition of flyovers, their use as congestion mitigation measures within urban areas should be discontinued.
+
+In addition, cities in India need to consider the use of roundabouts as an alternative of traffic junctions to minimise the number of road crashes. Many cities in India are doing exactly the reverse by replacing roundabouts with traffic junctions. For traffic planners to willingly adopt roundabouts, it is important that their designs are based on latest international experience which result in increased safety as well as efficient traffic movement.
+
+There is a positive association with fatality risk and social deprivation, thus indicating socio-economic inequity of injury risk. Given a negative relationship of risk and population density, future studies should investigate the street design and built environment features of high density locations in Delhi to understand the causal mechanism behind this relationship. These factors can then be incorporated in future city designs.
+
+## References
+
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Zotero/001_artiklid/Road Safety Indicators/greibeaccidentpredictionmodelsurban2003.md

@@ -0,0 +1,565 @@
+---
+category: literaturenote
+citekey: greibeaccidentpredictionmodelsurban2003
+title: Accident prediction models for urban roads
+authors: "Greibe, Poul"
+year: 2003
+date: 2003-00-00 2003
+doi: 10.1016/s0001-4575(02)00005-2
+publication: "Accident Analysis & Prevention"
+url: "https://doi.org/10.1016/s0001-4575(02)00005-2"
+zotero_key: QVSGTIXD
+zotero_storage: JCVAIJBJ
+collections: transpordi_planeerimine
+folder: 001_artiklid/Road Safety Indicators
+firstAuthor: "Greibe, Poul"
+status: converted
+---
+![](_page_0_Picture_0.jpeg)
+
+Accident Analysis and Prevention 35 (2003) 273–285
+
+![](_page_0_Picture_2.jpeg)
+
+# Accident prediction models for urban roads
+
+# Poul Greibe
+
+*Danish Transport Research Institute, Knuth Winterfeldts Allé, DK-2800 Kgs. Lyngby, Denmark* Received 23 May 2001; received in revised form 16 November 2001; accepted 4 December 2001
+
+#### **Abstract**
+
+This paper describes some of the main findings from two separate studies on accident prediction models for urban junctions and urban road links described in [Uheldsmodel for bygader-Del1: Modeller for 3-og 4-benede kryds. Notat 22, The Danish Road Directorate, 1995; Uheldsmodel for bygader- Del2: Modeller for strækninger. Notat 59, The Danish Road Directorate, 1998] (Greibe and Hemdorff, 1995, 1998).
+
+The main objective for the studies was to establish simple, practicable accident models that can predict the expected number of accidents at urban junctions and road links as accurately as possible. The models can be used to identify factors affecting road safety and in relation to 'black spot' identification and network safety analysis undertaken by local road authorities.
+
+The accident prediction models are based on data from 1036 junctions and 142 km road links in urban areas. Generalised linear modelling techniques were used to relate accident frequencies to explanatory variables.
+
+The estimated accident prediction models for road links were capable of describing more than 60% of the systematic variation ('percentage-explained' value) while the models for junctions had lower values. This indicates that modelling accidents for road links is less complicated than for junctions, probably due to a more uniform accident pattern and a simpler traffic flow exposure or due to lack of adequate explanatory variables for junctions.
+
+Explanatory variables describing road design and road geometry proved to be significant for road link models but less important in junction models. The most powerful variable for all models was motor vehicle traffic flow. © 2002 Elsevier Science Ltd. All rights reserved.
+
+*Keywords:* Accident prediction models; Generalised linear modelling; Road accidents; Junction; Road links
+
+#### **1. Background**
+
+Traffic planners and engineers in Denmark have used accident prediction models since the early 1980s. The models used were based on data from state and county roads, which are generally located in rural areas. An increasing need for models that could also be used for urban roads stimulated research on accident prediction models for urban junctions and road links beginning in the early 1990s.
+
+The main objective of this study was to formulate practicable accident prediction models which would describe the expected number of accidents at junctions and road links in urban areas as accurately as possible. Furthermore, the models were to be used to identify factors affecting safety, e.g. geometry, land use, etc. Unlike the used models for rural roads, which were based only on traffic flows, this study was to include additional explanatory variables in the modelling.
+
+*E-mail address:* Poul@greibe.dk (P. Greibe).
+
+URL: <http://www.dtf.dk>
+
+#### **2. Description of data**
+
+In order to develop the models, detailed information on accident data, traffic flow and road design was required. Since the official Danish national road database only holds data on state and county roads (mainly rural), a close co-operation was established with a number Danish municipalities in order to collect data from urban roads.
+
+Accident data were collected from the official accident statistics database covering all police recorded accidents. The data included all possible data on the accident, including a small text description of the nature and location of each accident. All accidents were related to the specific road link or road junction by use of the road ID number. A 5 years accident period was used (1987–1991 for junctions and 1990–1994 for road links).
+
+Traffic flow counts were collected from the municipalities and converted to AADT counts. Unfortunately, the traffic counts did not always include heavy truck volumes and volumes of vulnerable road users, so these data fields were left blank.
+
+Data on junction and road link geometry were collected partly by visual inspections and video recordings, and partly by use of local road databases at the municipalities.
+
+The road network had to be divided into junctions and road links, since the objective was to make separate models for junctions and road links. Junctions with an incoming traffic flow on secondary arms of less than 250 and 500 AADT for 3- and 4-arm junctions, respectively were considered as part of the road link. These limits were chosen since most traffic count databases used had these as a minimum level for traffic flows. As a result of this definition, road links in this study may have a number of minor junctions or accesses along the road section. Variables describing the number of minor junctions and accesses are therefore included in the road link models.
+
+#### *2.1. Road link data*
+
+Data from 142 km urban road were collected and separated into 314 individual homogeneous road sections, giving an average road link length of approximately 450 m (S.D. = 285 m).
+
+Data on the following variables were collected for road links:
+
+- (a) traffic flow (motor vehicles, heavy vehicles and vulnerable road users);
+- (b) length of road section;
+- (c) speed limit;
+- (d) one/two-way traffic;
+- (e) number of lanes;
+- (f) road width;
+- (g) speed reducing measures;
+- (h) number of minor crossings/exits/side roads;
+
+- (i) cyclist facilities;
+- ( j) footway;
+- (k) central island;
+- (l) parking facilities;
+- (m) bus stop;
+- (n) land use.
+
+The traffic flow data were considered as a continuous variable while all other data were converted into class variables with two–six levels. See Appendix A for a complete list of variables.
+
+A total of 1058 police recorded accidents can be related to the 314 road links, 523 of which were personal injury accidents and 535 damage only accidents. The personal injury accidents resulted in 30 deaths and 554 injured persons.
+
+Even though the road links only have small access or exit roads, more than 40% of the accidents can be related to crossing manoeuvres.
+
+The accident distribution for road links can be found in Appendix A.
+
+#### *2.2. Junction data*
+
+The study included data from 1036 urban junctions. The number of each junction type is as follows: 85 (3-arm, signalised), 547 (3-arm, non-signalised), 250 (4-arm, signalised), 154 (4-arm, non-signalised).
+
+Other junction types, e.g. roundabouts, have not been treated since there was an insufficient number of them.
+
+Data on the following variables had been collected for junctions:
+
+(a) traffic flows (motor vehicles, heavy vehicles and vulnerable road users);
+
+![](_page_1_Figure_30.jpeg)
+
+Fig. 1. Illustration of correlation matrix for road link data. Thick lines indicate 'strong' correlation (ρ > 0.6) and thin or no lines indicate 'weaker' correlation among variables. For example, the number of lanes and the presence of a central island correlate strongly.
+
+- (b) number of lanes;
+- (c) traffic island;
+- (d) turning lane;
+- (e) bicycle facilities;
+- (f) signalised/non-signalised;
+- (g) number of arms.
+
+The traffic flow data were considered as a continuous variable while all other data were converted to class variables with two–seven levels. See Appendix A for a complete list of variables.
+
+A total of 2534 police recorded accidents can be related to the 1036 junctions. The majority of accidents occurred in 4-arm signalised junctions and more than 50% of the 3-arm non-signalised junctions had zero observed accidents.
+
+The accident distribution for junctions can be found in Appendix A.
+
+In general, data on traffic flows for vulnerable road users and heavy vehicles were difficult to obtain, since these are rarely counted. This unfortunately also applies to junctions and for road links.
+
+#### *2.3. Correlation among data*
+
+Analysis of the data collected from junctions and road links showed some correlation among the explanatory variables.
+
+Fig. 1 illustrates some general correlations within the data for road links based on the correlation matrix for the data-set. The motor vehicle traffic flow variable (AADT) correlated strongly (ρ > 0.6) with other explanatory variables, e.g. the presence of a central island, the number of lanes, road width, speed limit etc. The same conditions were found for data on junctions.
+
+Due to the strong correlation among variables in the data-sets, it was not expected to be possible to estimate the true safety effect from a single road geometry variable.
+
+#### **3. Model structure**
+
+The models relate the number of observed accidents to traffic flow and road design. Generalised linear modelling techniques were used to fit the model, and the distributions of accident counts were assumed to follow a Poisson distribution. The regression analyses were performed by use of the GENMOD procedure in SAS.
+
+Whether it is reasonable to assume that accident counts are Poisson distributed is a recurrent issue. The main advantage of the Poisson distribution is its simplicity, e.g. the variance is equal to its mean. However, difficulty arises concerning the phenomenon of "overdispersion" when the observed variance is actually greater than the mean. Overdispersion does not affect the coefficient estimates but does cause their standard errors to be underestimated (Miaou et al., 1992). Recent studies have proved that the negative binomial distribution might be more appropriate because it allows greater variance in the data and thereby deals with the overdispersion.
+
+In this study, the Poisson distribution was chosen over the negative binomial simply because it is easier to use and, as the study was planned and initiated in the early 1990s, the Poisson was the only practicable solution with the statistical software available at that time. However, the final estimations were performed by use of the GENMOD procedure, which does support a number of different distributions, but subsequent estimations proved, as in other studies (Kulmala, 1995), that the values of the model parameters were almost the same regardless of the distributional assumption. It was therefore decided to stick to the pure Poisson model. It should be mentioned that no corrections were made for any possible overdispersion.
+
+#### *3.1. Model structure*
+
+Different ways to relate accident frequencies to traffic flows have been investigated in a number of previous studies, e.g. Satterthwaite (1981), Hauer et al. (1988), Bélanger (1994), Brüde and Larson (1993), Golias (1992), Hall (1986), Taylor et al. (1996), Maher and Summersgill (1996).
+
+For road links the general opinion is that accident frequencies can be described by a flow function raised to a power. Often the flow function consists simply of the motor vehicle traffic flow along the link (AADT), but some studies (e.g. Summersgill et al., 1996) also include flows for pedestrians along or across the link.
+
+The flow function for junctions are more complex since there is a number of individual traffic flows, especially when turning flows and flows for pedestrians and cyclists are included. In most cases, as in this study, the only flow data available will be the incoming motor vehicle traffic from each arm of the junctions, leaving limited possibilities to use complicated flow functions.
+
+A number of TRL studies (e.g. Layfield et al., 1996) on junctions proved that models with more complicated flow functions based on data from individual traffic flow (including pedestrian flows) predict the accidents frequencies quite well. However, such models require data on turning flows, etc. which put a strain on practicality.
+
+Recent studies (Mountain et al., 1998) include variables that allow for changes in risk over time in order to take any possible trend into consideration. This would ensure that the models do not become rapidly outdated. They found a 6% annual decrease in risk per year for junctions. However, to estimate annual changes in risk, large time series are required.
+
+Previous Danish studies on accident prediction models (Wass et al., 1983; Kronbak and Greibe, 1994) have investigated models based on different flow functions of some with flows for cyclists and moped drivers as well. The general conclusion was that the models shown below are suitable for Danish conditions, and since these new models for urban roads were to be used along with existing models for rural roads, it was decided to use the same model structure here as well.
+
+The model structure for road links
+
+$$E(\mu) = aN^p \exp \sum \beta_j x_{ij}$$
+
+where *E*(µ) is the expected number of accidents (accidents per year per km), *N* the motor vehicle traffic flow (AADT), *x* variables describing road geometry or environment of the road *a*, *p*, βj are estimated parameters and for junctions
+
+$$E(\mu) = aN_{\text{pri}}^{p1}N_{\text{sec}}^{p2}\exp\sum\beta_{j}x_{ij}$$
+
+where *E*(µ) is the expected number of accidents (per year), *N*pri the incoming motor vehicle traffic flow (AADT) from the primary direction, *N*sec the incoming motor vehicle traffic flow (AADT) from the secondary direction, *x* variables describing road geometry, *a*, *p*1, *p*2, βj are estimated parameters.
+
+For non-signalised junctions, the primary direction represents the two arms where traffic has the right of way. For signalised junctions, the primary direction at the junction represents the two arms with the highest traffic volumes. It can not be rejected that the primary direction in signalised junctions represents two arms which are not opposite in the junction. This will be very seldom though.
+
+#### *3.2. Modelling procedure*
+
+At first, all variables were included in the model for the regression analysis. Insignificant variables were excluded one by one, starting with the least significant variables. Insignificant variables were identified based on likelihood ratio statistics and standard errors of the estimated parameter values. At the same time, the correlation matrix was studied and if two variables were correlated strongly with each other, one variable was excluded from the model on the condition that the model fit did not suffer significantly. If a variable turned out to be significant but did not contribute significantly to the decrease in deviance, the variable was excluded from the model.
+
+Some explanatory variables were simplified, e.g. if a model showed that the parameter values for speed limits of 60 and 70 km/h did not differ much, the two categories were combined. All variables were also tested solely along with the traffic volume in order to identify any 'hidden' effects that did not show when other variables were included.
+
+Separate models were estimated for: all accidents, all injury accidents, certain types of accidents (single accidents, rear-end accidents, crossing accidents, turning accidents, etc.). The purpose of modelling certain types of accidents was to examine the effect of road design factors on different accident types.
+
+Individual models for accidents involving two-wheelers were also examined. Some of these are presented in this paper.
+
+#### *3.3. Goodness-of-fit*
+
+The total variation in the accident count consists of a random part (presumed Poisson distributed) and a systematic part. The model's 'goodness-of-fit' was measured by how much of the systematic variation the model could explain and will be referred to as "percentage explained". The method is proposed by (Kulmala, 1995) as being suitable for Poisson models. The percentage explained value are estimated on the basis of the scaled deviance of the studied model, the zero model (a model with only one constant parameter) and the expected scaled deviance of a model describing the total systematic variation.
+
+Some problems arise in using this method when the average number of accidents is low (<0.5). Even though this study had a number of sites having zero accidents, we did not have mean values below 0.5. However, when modelling certain types of accidents, e.g. single accidents, mean values for some junction groups were below 0.5.
+
+In general, the results (as described below) showed 'percentage explained' values for the models in the area of 30–80%. The best models were produced for road links.
+
+#### **4. Results**
+
+#### *4.1. Junctions*
+
+Since there are considerable differences in the accident pattern and risk at different junction types, individual models were produced for four individual types of junctions, 3- and 4-arm, signalised and non-signalised, respectively.
+
+Individual models for each junction type were estimated with all explanatory variables included. There was difficulty in achieving stable and significant explanatory variables in the junction models. This might be due to the fact that the safety effect of the individual explanatory variables is relatively small, and the models allow only for small variations in the estimated coefficients without becoming insignificant.
+
+For all junction models, the variable for motor vehicle traffic proved to be the strongest variable, representing more than 90% of the systematic variation described by the entire model. Only few other explanatory variables were significant.
+
+As previously mentioned, strong correlation within the data-sets caused interpretation difficulties of the explanatory variables. The "true" safety effect of the explanatory variables could therefore not be estimated properly.
+
+To test whether the number of junctions in the data set was sufficient, models based on 40, 80, 120, 160 and 200 junctions were estimated. Serious estimation problems arose when the models were based on less than 80 junctions. The estimated parameter values did not change considerably when more than 100 junction were used. The standard error decreased as more junctions were added but the geometry variables were still not significant and it was estimated that
+
+Table 1 Estimated parameter values for 4-arm signalised junctions<sup>a</sup>
+
+| Parameter              |     | Estimated value         |
+|------------------------|-----|-------------------------|
+| a                      |     | 1.13 × 10−4 [0.41;4.04] |
+| p1                     |     | 0.56 [0.44;0.68]        |
+| p2                     |     | 0.47 [0.37;0.56]        |
+| β1: Number of lanes in | 2   | 1.29 [1.08;1.56]        |
+| primary direction      | >2  | 1                       |
+| β2: Number of lanes in | 2–3 | 0.83 [0.72;0.96]        |
+| secondary direction    | >3  | 1                       |
+
+<sup>a</sup> Values of 95% confidence limits are shown in brackets.
+
+the number of junctions would have to be increased by three times in order to see any effect. Since it was only practicable to increase the number of junctions by a few hundred, the idea of adding more junctions to the data was rejected, as this would not help to make geometry variables significant.
+
+An example of an accident prediction model for 4-arm signalised junctions with variables describing motor vehicle flow and other explanatory variables are presented in Table 1. The only significant variables, besides traffic flow were β<sup>1</sup> and β<sup>2</sup> describing the number of lanes.
+
+The model results shown in Table 1 has a percentage explained value of 60%, which is only 1% better than a similar model that excludes explanatory variables describing road geometry. Equivalent results were found for other junction types. By far the most powerful variable was that of motor vehicle volumes. In general, variables describing junction design improved the models by only 1–4%.
+
+The results for junctions indicate that simple models (only motor vehicle flow-functions) are almost as good as more complicated models. The reason for this must be the complicated internal correlations in junction design data or lack of good descriptive variables on road design.
+
+Models with explanatory variables describing traffic volumes for vulnerable road users were only 4–5% better than models without these variables. The reason for this might also be strong correlation between motor vehicle traffic flows and traffic flows for vulnerable road users, or the fact that less than 5% of accidents involving vulnerable road users are reported to the police.
+
+Results from the simple flow function models (only holding motor vehicle traffic flows) are presented in Table 2.
+
+The best models were estimated for 4-arm signalised junctions, probably because this junction type had the highest number of observed accidents.
+
+*4.1.1. Safety effect of signal control*
+
+To evaluate the influence of signal control (traffic light) on the total number of observed accidents, a model was created with a two-level variable with or without signal control. The effect is given by the estimated coefficients.
+
+The signal control variable was not significant in the model, which indicates that the expected total number of accidents is very similar for signalised and non-signalised junctions with the same flow function. In other words, non-signalised junctions are in general just as safe as signalised junctions with the same amount of incoming motor vehicles. This applies for an incoming motor vehicle traffic flow between 5,000–18,000 and 5,000–22,000 for 3- and 4-arm junctions, respectively.
+
+With respect to different accident types, the figures for single and rear-end accidents are significantly higher in signalised junctions than in non-signalised junctions. The number of crossing accidents is, however, lower in signalised junctions. The estimated safety effects are shown in Fig. 2.
+
+It was expected that signalised junctions would have more rear-end accidents and fewer accidents with crossing road users but also the number of single accidents are higher at signalised junction. The reason for this is unknown but one reason could be the fact that signalised junctions are more complex with more obstacles and other equipment that drivers can run into.
+
+Other effect studies on signal control (Elvik et al., 1997) finds by use of meta-analysis on a number of before–after studies a 15% reduction in accidents for 3-arm junction and 30% reduction for 4-arm junctions.
+
+These figures can not be confirmed in this study. However, considering only personal injury accidents (not shown in Fig. 2), a non-significant reduction of 9 and 12% were found for 3- and 4-arm junctions, respectively.
+
+## *4.1.2. Cyclist safety at junctions*
+
+As 32% of the accidents in junctions involve cyclists or moped riders, special models to predict these accidents were formulated. Unfortunately, only 4-arm signalised junctions had sufficient traffic flow data to permit regression analysis.
+
+The model below is estimated on a subgroup of junctions comprising only 41 4-arm signalised junctions. The results were
+
+$$E(\mu_{\text{cyc/mop}}) = 8.01 \times 10^{-8} N_{\text{tot}}^{0.91} C_{\text{tot}}^{0.86}$$
+
+Table 2 Estimated parameter values for junction models<sup>a</sup>
+
+| Junction type         | a                       | p1               | p2               | 'Percentage explained' |
+|-----------------------|-------------------------|------------------|------------------|------------------------|
+| 3-Arm, non-signalised | 1.04 × 10−5 [0.41;3.43] | 0.69 [0.57;0.82] | 0.60 [0.48;0.72] | 47                     |
+| 3-Arm, signalised     | 1.34 × 10−5 [0.07;23.4] | 0.88 [0.58;1.19] | 0.33 [0.14;0.50] | 32                     |
+| 4-Arm, non-signalised | 7.12 × 10−4 [1.16;43.7] | 0.30 [0.15;0.44] | 0.55 [0.34;0.76] | 29                     |
+| 4-Arm, signalised     | 1.08 × 10−4 [0.51;3.08] | 0.53 [0.42;0.64] | 0.52 [0.44;0.60] | 59                     |
+
+<sup>a</sup> Values of 95% confidence limits are shown in brackets.
+
+![](_page_5_Figure_2.jpeg)
+
+Fig. 2. Safety effect for the number of accidents at signalised junctions compared to non-signalised junctions. 1.00: no effect. (e.g. signalised 3-arm junctions have 2.85 times more rear-end accidents than non-signalised 3-arm junctions with the same traffic flows). Figures marked with an ∗ are not significant.
+
+where *E*(µcyc/mop) is the expected number of accident involving cyclists or moped riders per year, *N*tot the incoming motor vehicle traffic flow (total sum, AADT), *C*tot the incoming cyclist/moped traffic flow (total sum, AADT).
+
+Explanatory variables describing facilities for cyclist (cycle track/path) were not significant and stable in the model. The variable for traffic flows for cyclists and moped riders improved the 'percentage explained' value by 5% from 70 to 75%. It seems that although the explanatory variable for cyclist and moped traffic flows are statistically significant, they do not improve the models substantially. In view of the difficulty of obtaining flow data for cyclists and moped riders, it can be questioned whether it is worth using explanatory flow data variables for cyclists and moped riders in the models.
+
+#### *4.2. Road links*
+
+Road links with a speed limit of 30, 40 or 80 km/h were excluded from the data sets since these road sections were represented by a total of less than 20 km, and furthermore differed considerably from other road sections. Only sections with a speed limit of 50, 60 or 70 km/h are represented in the following models.
+
+As mentioned earlier, generalised linear modelling techniques were used to fit the models and the variation in accidents was assumed to follow a Poisson distribution.
+
+Separate models were estimated for:
+
+- (a) all accidents (injury and damage only accidents);
+- (b) injury accidents;
+- (c) certain types of accidents (single accidents, rear-end accidents, head-on accidents, accidents involving turning traffic, accidents involving pedestrians, accidents involving parked vehicles, etc.).
+
+The purpose of modelling certain types of accident, was to examine the effect of road design factors on different accident types. For reasons of space, only results for models based on all accidents (injury and damage only accidents) will be presented in the following sections.
+
+#### *4.2.1. Simple flow function model*
+
+First a simple model containing only variables for motor vehicle traffic flow was tested. The result was
+
+$$E(\mu) = 2.44 \times 10^{-3} N^{0.75}$$
+
+where *E*(µ) is the expected number of accidents (per km per year), and *N* the motor vehicle traffic flow measured as AADT.
+
+This model had a 'percentage explained' value of 30%. As found in other studies (Hemdorff, 1996; Summersgill and Layfield, 1996) the traffic volume is raised to a power of less than 1, in this case 0.75.
+
+#### *4.2.2. Models with explanatory variables*
+
+A model with other explanatory variables included was tried and the results are given below. Note that variables for vulnerable road user traffic flows were not included since data on this were insufficient.
+
+The model below describes the total number of accidents (injury and damage only accidents). Only variables that proved to be significant are included. The model (simplified) has the following structure:
+
+$$E(\mu) = aN^{p}\beta_{1,i}\beta_{2,i}\beta_{3,i}\beta_{4,i}\beta_{5,i}\beta_{6,i}$$
+
+where *E*(µ) is the expected number of accidents (per km per year), *N* the motor traffic flow (AADT), β1−<sup>6</sup> class variables-represents certain road design or road layout parameters, *a*, *p*, βn,i are estimated parameters.
+
+The estimated parameters are shown in Table 3.
+
+As an example, the estimated accident frequency for a road link with an AADT of 4000, speed limit of 50 km/h, road width of 5.0–7.5 m, 5–40 exits per km, 0–5 minor crossings per km, limited parking, situated in a residential neighbourhood would be
+
+$$\begin{split} E(\mu) &= 6.09 \times 10^{-4} \times 4000^{0.80} \times 2.25 \times 0.83 \times 1.00 \\ &\times 0.75 \times 1.00 \times 1.58 \\ &= 1.03 \text{ accidents per km per year} \end{split}$$
+
+Table 3 Estimated parameter values<sup>a</sup>
+
+An interpretation of the variable values, e.g. β<sup>4</sup> (number of minor side roads), indicates that the accident risk rises as the number of minor side roads per km increases. A road link with >10 side roads per km (value 1.25) has a 1.7 times higher accident risk than a road link with 0–5 side roads per km (value 0.75). Furthermore, road sections in shopping districts have approximately 2.4 times higher risk than roads in areas with scattered housing.
+
+The 'percentage explained' value for the model above is 69%, which is considerable higher than a model without the other explanatory variables (30%).
+
+Similar models have been estimated for different accident types. In general, variables describing traffic flow, land use, number of minor crossings, parking facilities and speed limits proved to be the most important variables in the models.
+
+Since the models did not include exposure data on vulnerable road users, it must be expected that other variables, e.g. land use and speed limit, to a certain extend explain the level of exposure for vulnerable road users. This relates to the fact that land use and speed limit turn out to be among the most descriptive variables in the data-set.
+
+#### *4.2.3. Cyclist safety on road links*
+
+A simple flow model describing the number of accidents involving cyclists and moped riders as a function of the traffic flows for motor vehicles, cyclists and mopeds were tested. The results are given below
+
+$$E(\mu_{\rm cyc/mop}) = 4.44 \times 10^{-5} N_{\rm car}^{0.68} N_{\rm cyc/mop}^{0.49}$$
+
+where *E*(µcyc/mop) is the expected number of accident involving cyclists and moped riders (per km per year), *N*car
+
+| Parameter                             |                                                                                       | Estimated value                                               |
+|---------------------------------------|---------------------------------------------------------------------------------------|---------------------------------------------------------------|
+| a                                     |                                                                                       | 6.09 × 10−4 [1.90;19.5]                                       |
+| p                                     |                                                                                       | 0.80 [0.68;0.92]                                              |
+| β1: Speed limit                       | 50 km/h<br>60 km/h<br>70 km/h                                                         | 2.25 [1.66;3.05]<br>2.85 [2.07;3.90]<br>1                     |
+| β2: Road width                        | 5.0–7.5 m<br>8.0–8.5 m<br>9.0–15.0 m                                                  | 0.83 [0.70;0.99]<br>0.68 [0.57;0.81]<br>0.80 [0.67;0.95]      |
+| β3: Number of exits per km            | 0 and >40<br>5–40                                                                     | 1<br>1                                                        |
+| β4: Number of minor side roads per km | 0<br>0–5<br>5–10<br>>10                                                               | 0.72 [0.58;0.89]<br>0.75 [0.64;0.88]<br>1<br>1.25 [1.05;1.48] |
+| β5: Parking                           | Prohibited<br>Rarely<br>Bays at kerb                                                  | 1.19 [1.48;2.11]<br>1<br>1.77 [1.48;2.11]                     |
+| β6: Land use                          | Shops<br>Blocks of flats<br>Industrial/residential/neighbourhood<br>Scattered housing | 2.44 [1.81;3.28]<br>1.56 [1.21;2.03]<br>1.58 [1.32;1.89]<br>1 |
+
+<sup>a</sup> Values of 95% confidence limits are shown in brackets.
+
+![](_page_7_Figure_2.jpeg)
+
+Fig. 3. Percentage of systematic variation explained by individual variables in the road link model.
+
+the motor vehicle traffic flow (AADT), *N*cyc/mop the traffic flow (AADT) for cyclists and moped riders.
+
+The model was estimated on a data sub-set comprising only 26 road sections.
+
+#### *4.2.4. Percentage explained by variables in road link models*
+
+A model with all variables included gives a 'percentage explained' value of 72%. Fig. 3 illustrates how much the individual variables contribute to the overall 'goodness-of-fit'.
+
+As mentioned earlier, the 'percentage explained' value indicates the level of systematic variation explained by the model. The AADT variable is the most powerful variable (describing approximately 30%), followed by variables for land use, number of side roads, etc.
+
+Even though all variables are represented in the models, 30% of the systematic variation remains unexplained. A likely explanatory variable that could increase the 'percentage explained' value might be the actual speed of the motor vehicles. We know from other studies that speed is one of the most significant factors in traffic safety. Another likely explanatory variable that could increase the 'percentage explained' value could be better exposure data for vulnerable road users and better exposure data for vehicles entering the road link. As mentioned earlier a high proportion of accidents at road links involved vehicles entering the link from side roads or accesses and/or accidents with vulnerable road users.
+
+The figure also illustrates that it is possible to explain more than 50% of the systematic variation by use of the four–five most important variables, and that additional explanatory variables do not improve the models very much.
+
+#### *4.2.5. Explanatory variables and their safety effect*
+
+One of the objectives of this study was to evaluate the safety effect of different explanatory variables, e.g. road layout, etc. Despite the strong correlation among the variables in the data-set, which may lead to incorrect conclusions, the effects derived by the models are given in the following sections. The list below is based on Table 3 and results on different types of accidents, which are not presented elsewhere in the article. Only variables that proved to be significant are shown.
+
+*4.2.5.1. AADT.* The motor vehicle traffic flow is the most important variable in the models. The results showed that accident frequencies are related to the AADT raised to power of 0.8–1.0. However, for some accident types, e.g. rear-end and single accidents, the parameter value were 1.23 and 0.52, respectively. These deviations correspond with results found by (Summersgill and Layfield, 1996).
+
+*4.2.5.2. Speed limits.* The modelling showed that road links with high speed limits tend to have lower accident risk. This does not mean that high speeds in general are safer, rather the results for this variable illustrate the correlation
+
+Table 4 Description of road types
+
+| Road type | Land use                                     | Minor side road per km | Speed limit (km/h) |
+|-----------|----------------------------------------------|------------------------|--------------------|
+| A–D       | Shopping/city centre                         | 0–10                   | 50–60              |
+| E         | Blocks of flats/residential housing/industry | 0–10                   | 50–60              |
+| F         | Blocks of flats/residential housing/industry | 0–10                   | 70                 |
+| G         | Blocks/residential housings/industry         | >10                    | 50–60              |
+| H         | Scattered                                    | –                      | 50–60              |
+| I         | Scattered                                    | –                      | 70                 |
+
+problems within the data set. High speed roads tend to have few vulnerable road users and to be situated in sparsely built-up areas.
+
+*4.2.5.3. Number of lanes.* Road links with only one lane (no marked centre line) have more accidents involving motor vehicles going in the same direction than road links with two or more lanes.
+
+*4.2.5.4. Road width.* Apparently, road links with a road width (from kerb to kerb) of 8–8.5 m have the lowest accident risks for most accident types.
+
+*4.2.5.5. Speed reducing measures.* Road links with speed reducing measures have a higher risk of single accidents. Even though it is well-known that speed reducing measures usually improve safety, the explanatory variable describing
+
+![](_page_8_Figure_9.jpeg)
+
+Fig. 4. Accidents per km per year as a function of the AADT for six urban road types.
+
+the presence of speed reducing measures in the models was not significant in most cases. It should be noted that only a few km of road with speed reducing measures were represented in the data material.
+
+*4.2.5.6. Number of accesses.* The relation between accident risk and the number of accesses (exits from private properties, parking places, etc.) seems to be an inverted 'U-shape'. Roads with no accesses and roads with a large number of accesses have the lowest accident risk, while roads with a medium number of accesses have the highest accident risk.
+
+*4.2.5.7. Number of minor side roads.* The explanatory variable for the number of minor side roads proved to be very important in the models. In general, the more side roads, the higher the accident risk.
+
+*4.2.5.8. Parking conditions.* Road links with parked motor vehicles along the roadside (at kerb) or in marked parking bays have the highest accident risk, particularly for accidents involving pedestrians, accidents involving motor vehicles from access roads or minor side roads, and for accidents involving parked vehicles. Other studies, (Elvik et al., 1997) also find that marked parking bays increases risk.
+
+*4.2.5.9. Land use.* The road environment (type and function of buildings along the road) has a considerable influence on the accident risk. Shopping streets and city centre roads have significantly higher accident risk than, for example, residential roads in less densely built-up areas. In general, the lower the building density, the lower the accident risk. Since exposure data for vulnerable road users were not included in the models, it must be presumed that the variable 'land use' to some extent also represents the level of pedestrian and cyclist activity.
+
+*4.2.5.10. Urban road types.* Based on the collected data, six urban road link types have been defined, and accident prediction models have been estimated for each road type. For practical reasons only six road types were defined, based on the most important variables found from the models. The road type definitions are therefore based on information on land use, number of minor side roads and on the speed limit.
+
+The six road types are shown in Table 4.
+
+Fig. 4 illustrates the expected average accident frequency for the six urban road types based on accident prediction models.
+
+The six road types were produced by starting from 23 road types, and then grouping the roads step by step until all individual road types had significant parameter estimates, while at the same time attempting to keep an overall logical and functional classification of the road type. From a statistical viewpoint road type F and H could possibly be grouped as one road type, but since these roads are very different in geometry, etc. it would not be consistent with the overall logic to put these roads in the same group.
+
+#### **5. Conclusion and discussion**
+
+The purpose of the study was to formulate accident prediction models which would describe the expected number of accidents at junctions and on road links in urban areas as accurately and practicably as possible. Furthermore, the objective was to identify factors affecting safety at junctions and on road links by use of the explanatory variables in the models.
+
+Based on data from 1024 junctions and 142 km of road links, a number of models were estimated in two separate studies.
+
+In general, the most powerful variables in the models were those describing the motor vehicle traffic flow, particularly for junctions. Additional explanatory variables in the junction models did not improve the 'percentage explained' value considerably. For road links, however, additional explanatory variables describing the road environment, number of minor side roads, parking facilities and speed limit proved to be significant and important variables for predicting the number of accidents.
+
+The models produced had a 'percentage explained' value in the area of 40–80%, with junction models seems to be at the lower end. This indicates that modelling accidents is less complex for road links than for junctions.
+
+The safety effect from signal control in 3- and 4-arm junctions was examined and the results showed that nonsignalised junctions in general are just as safe as signalised junction with the same traffic flows. The accident distribution differs though: for example, signalised junctions have fewer crossing accidents but more rear-end accidents.
+
+A high proportion of accidents in urban areas involve cyclists or moped riders. Models estimating this accident group were tested including explanatory variables describing exposure data for cyclists and moped riders. Models with exposure data for cyclists and moped riders were only slightly better than models without.
+
+A major problem was strong internal correlation within the data. Variables describing traffic flow tend to correlate strongly with other variables like road width, number of lanes, etc. Hence, the safety effects from a single explanatory variable were difficult to estimate since it may be affected by other variables in the model. Variables describing traffic flows for vulnerable road users (cyclist and mopeds) were also included in some of the models. They were significant but did not contribute considerably to the 'percentage explained' values, mainly due to strong correlation with motor vehicle traffic flow variables.
+
+Another well-known problem in safety analysis is the relatively small number of observed accidents in the data, which may cause problems in the statistical studies. In the study on junctions for example, less than 50% of the 3-armed non-signalised junctions had any police reported accidents, which limited modelling possibilities. Efforts were made to estimate accidents involving cyclists or moped riders, but since less than 10% of these accidents are reported by the police, the reliability of the data is limited, which complicates the modelling.
+
+In general, the safety effect from factors like road geometry, road environment, etc. can be estimated in various ways. The most reliable way is by use of controlled 'before–after' studies. However, 'before–after' studies require a large number of sites and long study periods. An alternative is to make multidimensional cross-tabulation of accident rates by different safety factors, a so-called 'with-or-without' study, e.g. accident rates for junctions with or without signal control. However, it is only possible to cross-tabulate for a limited number of variables/factors and these variables cannot be continuous. Furthermore, comparing accident rates at different sites can be complicated since differences in geometry, etc. can rarely be explained by a few variables.
+
+The use of models has some advantages over the abovementioned study methods. Models relate the number of accidents to selected factors that can be explained by either continuous or class variables. In addition, in the models, the accident number is assumed to follow a certain statistical distribution, e.g. the Poisson or negative binomial distribution.
+
+However, the safety effects from various factors found in this study were not always absolutely comparable to the safety effects found in other studies, e.g. traditional before– after studies. The reason for this could be the internal correlation problems within the data sets as mentioned earlier. It is therefore recommended to interpret the safety effect of a single variable with caution. Nevertheless, the accuracy of safety effects found by modelling must be considered better than that of 'with-or-without' studies, but worse than that of 'before–after' studies.
+
+Currently, the practical use of the developed accident prediction models (black spot identification, safety effects from changes in traffic flow, etc.) described in this paper are being tested and demonstrated in a number of Danish municipalities. In relation to this, a handbook on the use of accident prediction models has been published (Greibe and Hemdorff, 2001).
+
+**Appendix A** Number of junctions and road links according to the number of accidents
+
+| Number of accidents | Road links | Junctions  |                |            |                |  |  |  |
+|---------------------|------------|------------|----------------|------------|----------------|--|--|--|
+|                     |            | 3-Arm      |                | 4-Arm      |                |  |  |  |
+|                     |            | Signalised | Non-signalised | Signalised | Non-signalised |  |  |  |
+| 0                   | 70         | 19         | 278            | 25         | 40             |  |  |  |
+| 1                   | 62         | 13         | 132            | 22         | 34             |  |  |  |
+| 2                   | 41         | 8          | 61             | 28         | 25             |  |  |  |
+| 3                   | 28         | 13         | 29             | 30         | 17             |  |  |  |
+| 4                   | 21         | 11         | 19             | 21         | 11             |  |  |  |
+| 5                   | 18         | 6          | 12             | 27         | 17             |  |  |  |
+| 6                   | 18         | 4          | 9              | 18         | 3              |  |  |  |
+| 7                   | 15         | 4          | 4              | 15         | 4              |  |  |  |
+| 8                   | 11         | 0          | 2              | 13         | 2              |  |  |  |
+| 9                   | 10         | 2          | 1              | 14         | 1              |  |  |  |
+| 10                  | 3          | 1          | 0              | 7          | 0              |  |  |  |
+| 11                  | 3          | 2          | 0              | 7          | 0              |  |  |  |
+| 12                  | 4          | 1          | 0              | 3          | 0              |  |  |  |
+| 13                  | 3          | 0          | 0              | 3          | 0              |  |  |  |
+| 14                  | 1          | 1          | 0              | 2          | 0              |  |  |  |
+| 15                  | 3          | 0          | 0              | 4          | 0              |  |  |  |
+| 16                  | 1          | 0          | 0              | 3          | 0              |  |  |  |
+| 17                  | 0          | 0          | 0              | 2          | 0              |  |  |  |
+| 18                  | 1          | 0          | 0              | 1          | 0              |  |  |  |
+| 19                  | 0          | 0          | 0              | 1          | 0              |  |  |  |
+| 20                  | 0          | 0          | 0              | 2          | 0              |  |  |  |
+| 21                  | 0          | 0          | 0              | 0          | 0              |  |  |  |
+| 22                  | 1          | 0          | 0              | 1          | 0              |  |  |  |
+| 23                  | 0          | 0          | 0              | 0          | 0              |  |  |  |
+| 24                  | 0          | 0          | 0              | 1          | 0              |  |  |  |
+
+Class variable list for road link models
+
+| Explanatory variable    | Value              | Road data              |                                      | Accident data      |                                |                                  |  |
+|-------------------------|--------------------|------------------------|--------------------------------------|--------------------|--------------------------------|----------------------------------|--|
+|                         |                    | Road<br>length<br>(km) | Travelled<br>vehicle<br>(million km) | Total<br>(5 years) | Frequency<br>(per km per year) | Rate (per million<br>vehicle km) |  |
+| Speed limit             | 30–40 km/t         | 4.5                    | 4.0                                  | 15                 | 0.67                           | 0.74                             |  |
+|                         | 50 km/t            | 97.5                   | 185.5                                | 767                | 1.57                           | 0.83                             |  |
+|                         | 60 km/t            | 20.8                   | 53.1                                 | 204                | 1.96                           | 0.77                             |  |
+|                         | 70 km/t            | 13.2                   | 47.8                                 | 54                 | 0.82                           | 0.23                             |  |
+| One-way street          | 80 km/t            | 6.3                    | 37.5                                 | 18                 | 0.57                           | 0.10                             |  |
+|                         | Yes                | 3.3                    | 5.8                                  | 15                 | 0.91                           | 0.52                             |  |
+|                         | No                 | 139.0                  | 322.2                                | 1043               | 1.50                           | 0.65                             |  |
+| Number of lanes         | 1                  | 35.3                   | 42.5                                 | 188                | 1.06                           | 0.89                             |  |
+|                         | 2                  | 97.2                   | 233.9                                | 805                | 1.66                           | 0.69                             |  |
+|                         | 4                  | 9.8                    | 51.6                                 | 65                 | 1.33                           | 0.25                             |  |
+| Road width              | 5.0–6.0 m          | 33.6                   | 49.8                                 | 203                | 1.21                           | 0.82                             |  |
+|                         | 6.5–7.5 m          | 37.2                   | 68.7                                 | 275                | 1.48                           | 0.80                             |  |
+|                         | 8. 0–8. 5m         | 38.1                   | 82.0                                 | 249                | 1.31                           | 0.61                             |  |
+|                         | 9.0–15.0 m         | 33.3                   | 127.5                                | 331                | 1.99                           | 0.52                             |  |
+| Speed reducing measures | Yes                | 16.3                   | 16.8                                 | 81                 | 1.00                           | 0.96                             |  |
+|                         | No                 | 126.0                  | 311.1                                | 977                | 1.55                           | 0.63                             |  |
+| Accesses per km         | 0                  | 27.4                   | 83.3                                 | 130                | 0.95                           | 0.31                             |  |
+|                         | 0–10               | 29.2                   | 84.0                                 | 245                | 1.68                           | 0.58                             |  |
+|                         | 10–20              | 35.0                   | 82.0                                 | 320                | 1.83                           | 0.78                             |  |
+|                         | 20–30              | 18.0                   | 29.5                                 | 174                | 1.93                           | 1.18                             |  |
+|                         | 30–40              | 12.7                   | 24.6                                 | 102                | 1.60                           | 0.83                             |  |
+|                         | >40                | 20.0                   | 24.6                                 | 87                 | 0.87                           | 0.71                             |  |
+| Side roads per km       | 0                  | 26.2                   | 96.6                                 | 140                | 1.07                           | 0.29                             |  |
+|                         | 0–5                | 47.2                   | 102.0                                | 285                | 1.21                           | 0.56                             |  |
+|                         | 5–10               | 48.1                   | 93.6                                 | 425                | 1.77                           | 0.91                             |  |
+|                         | >10                | 20.8                   | 35.7                                 | 208                | 2.00                           | 1.16                             |  |
+| Cyclist facilities      | None               | 58.5                   | 81.2                                 | 314                | 1.07                           | 0.77                             |  |
+|                         | Lane               | 17.2                   | 31.0                                 | 106                | 1.23                           | 0.68                             |  |
+|                         | Track              | 66.6                   | 215.8                                | 638                | 1.92                           | 0.59                             |  |
+| Footway                 | Yes                | 124.6                  | 282.6                                | 1010               | 1.62                           | 0.71                             |  |
+|                         | No                 | 17.6                   | 45.4                                 | 48                 | 0.54                           | 0.21                             |  |
+| Median divider          | Yes                | 12.4                   | 63.8                                 | 149                | 2.41                           | 0.47                             |  |
+|                         | No                 | 129.9                  | 264.1                                | 909                | 1.40                           | 0.69                             |  |
+| Parking                 | Bays at kerb       | 14.8                   | 38.2                                 | 240                | 3.25                           | 1.26                             |  |
+|                         | Prohibited         | 54.0                   | 144.9                                | 384                | 1.42                           | 0.53                             |  |
+|                         | Rarely             | 73.5                   | 144.8                                | 434                | 1.18                           | 0.60                             |  |
+| Bus stop                | Yes                | 98.2                   | 234.4                                | 833                | 1.70                           | 0.71                             |  |
+|                         | No                 | 44.0                   | 93.5                                 | 225                | 1.02                           | 0.48                             |  |
+| Land use                | Shopping           | 4.7                    | 10.2                                 | 85                 | 3.65                           | 1.66                             |  |
+|                         | Block of flats     | 9.3                    | 26.6                                 | 139                | 2.99                           | 1.04                             |  |
+|                         | Residential        | 72.5                   | 132.2                                | 548                | 1.51                           | 0.83                             |  |
+|                         | Scattered housings | 47.7                   | 139.0                                | 218                | 0.91                           | 0.31                             |  |
+|                         | Industry           | 8.0                    | 19.9                                 | 68                 | 1.69                           | 0.68                             |  |
+| Total                   |                    | 142.3                  | 328.0                                | 1058               | 1.49                           | 0.65                             |  |
+
+| Explanatory variable          | Value | 3-Arm          |                  |            |                  | 4-Arm          |                  |            |                  |
+|-------------------------------|-------|----------------|------------------|------------|------------------|----------------|------------------|------------|------------------|
+|                               |       | Non-signalised |                  | Signalised |                  | Non-signalised |                  | Signalised |                  |
+|                               |       | Number         | Accident<br>rate | Number     | Accident<br>rate | Number         | Accident<br>rate | Number     | Accident<br>rate |
+| Lanes in primary direction    | 1     | 68             | 0.08             | 0          | –                | 35             | 0.27             | 0          | –                |
+|                               | 2     | 376            | 0.08             | 14         | 0.09             | 91             | 0.18             | 40         | 0.25             |
+|                               | 3     | 75             | 0.08             | 35         | 0.12             | 19             | 0.15             | 107        | 0.19             |
+|                               | 4     | 17             | 0.08             | 8          | 0.13             | 5              | 0.08             | 33         | 0.18             |
+|                               | 5     | 9              | 0.09             | 3225       | 0.12             | 4              | 0.14             | 39         | 0.21             |
+|                               | 6     | 1              | 0.22             | 5          | 0.11             | 0              | –                | 27         | 0.18             |
+|                               | 7     | 1              | 0.09             | 1          | 0.25             | 0              | –                | 4          | 0.24             |
+| Lanes in secondary direction  | 1     | 100            | 0.06             | 2          | 0.06             | 15             | 0.20             | 3          | 0.22             |
+|                               | 2     | 436            | 0.09             | 38         | 0.10             | 134            | 0.18             | 112        | 0.18             |
+|                               | 3     | 10             | 0.13             | 38         | 0.14             | 4              | 0.24             | 93         | 0.18             |
+|                               | 4     | 1              | 0.00             | 5          | 0.11             | 0              | –                | 24         | 0.24             |
+|                               | 5     | 0              | –                | 2          | 0.13             | 1              | 0.29             | 13         | 0.25             |
+|                               | 6     | 0              | –                | 0          | –                | 0              | –                | 4          | 0.22             |
+|                               | 7     | 0              | –                | 0          | –                | 0              | –                | 1          | 0.34             |
+| Turning lanes in primary      | Yes   | 97             | 0.09             | 71         | 0.12             | 26             | 0.15             | 214        | 0.20             |
+| direction                     | No    | 450            | 0.08             | 14         | 0.10             | 128            | 0.20             | 36         | 0.19             |
+| Turning lanes in              | Yes   | 14             | 0.10             | 48         | 0.13             | 4              | 0.25             | 139        | 0.20             |
+| secondary direction           | No    | 533            | 0.08             | 37         | 0.09             | 150            | 0.18             | 111        | 0.18             |
+| Island at primary direction   | Yes   | 113            | 0.10             | 72         | 0.12             | 43             | 0.16             | 191        | 0.20             |
+|                               | No    | 434            | 0.08             | 13         | 0.09             | 111            | 0.20             | 59         | 0.18             |
+| Island at secondary direction | Yes   | 71             | 0.10             | 45         | 0.12             | 44             | 0.21             | 139        | 0.21             |
+|                               | No    | 476            | 0.08             | 40         | 0.12             | 110            | 0.17             | 111        | 0.18             |
+| Total number                  |       | 547            | 0.08             | 85         | 0.12             | 154            | 0.18             | 250        | 0.20             |
+
+### **References**
+
+- Bélanger, C., 1994. An estimation of the safety of four legged unsignalized intersections. In: Proceedings of the 73rd Annual Meeting of Transportation Research Board, Washington, DC.
+- Brüde, U., Larson, J., 1993. Models for predicting accidents at junctions where pedestrians and cyclists were involved. Anal. Prevention 25 (5), 499–509.
+- Elvik, R., Mysen, A.B., Vaa, T., 1997. Trafikksikkerhetshånbok-3. udgave. TØI.
+- Golias, J.C., 1992. Establishing relationships between accidents. Anal. Prevention 24 (6), 689–694.
+- Greibe, P., Hemdorff, S., 1995. Uheldsmodel for bygader-Del1: Modeller for 3-og 4-benede kryds. Notat 22, The Danish Road Directorate.
+- Greibe, P., Hemdorff, S., 1998. Uheldsmodel for bygader- Del2: Modeller for strækninger. Notat 59, The Danish Road Directorate.
+- Greibe, P., Hemdorff, S., 2001. Håndbog i trafiksikkerhedsberegninger-Brug af uheldsmodeller og andre vurderingsmetoder. Rapport 220, The Danish Road Directorate.
+- Hall, R.D., 1986. Accidents at 4-arm single carriageway urban traffic signals. TRRL, Contractor Report 65.
+- Hauer, E., Jerry, C.N., Lovell, J., 1988. Estimation of Safety at Signalized Intersections, Transportation Research Record 1185.
+- Hemdorff, S., 1996. Introduktion til VISplet. Notat 29. The Danish Road Directorate.
+
+- Kronbak, J., Greibe, P., 1994. Uheldsmodeller for signalregulerede vejkryds. Technical University of Denmark.
+- Kulmala, R., 1995. Safety at rural 3- and 4-arm junctions. Development and application of accident prediction models. VTT Publications 233.
+- Layfield, R.E., Summersgill, I., Hall, R.D., Chatterjee, K., 1996. Accidents at urban priority crossroads and staggered junctions. TRL report 185.
+- Maher, M.J., Summersgill, I., 1996. A comprehensive methodology for the fitting of predictive accidents models. Acci. Anal. Prevention, Vol. 28 (3).
+- Miaou, S.-P., Hu, P.S., Wright, T., Rathi, A.K., Davis, S.C., 1992. Relationship between truck accidents and highway geometric design: a poisson regression approach. Transport Research Record 1376.
+- Mountain, L., Maher, M., Fawaz, B. 1998. The influence of trend on estimates of accident at junctions. Acci. Anal. Prevention 30 (5).
+- Satterthwaite, S.P. 1981. A survey of research into relationships between traffic accidents and traffic volumes. TRRL Supplementary Report 692.
+- Summersgill, I., Kennedy, Janet V., Baynes. D., 1996. Accidents at three-arm priority junctions on urban single-carriageway roads. TRL report 184.
+- Summersgill, I., Layfield, R.E., 1996. Non-junction accidents on urban single-carriageway roads. TRL report 183.
+- Taylor, M.C., Hall, R.D., Chatterjee, K., 1996. Accidents at 3-arm traffic signals on urban single-carriageway roads. TRL report 135.
+- Wass, C., Jørgensen, N.O., Jørgensen, E., 1983. Model for uheld i vejkryds. Vejdatalaboratoriet, Danmarks Tekniske Højskole.

Zotero/001_artiklid/abatbangasanapplicationlowvolumeroad2006.md

@@ -0,0 +1,1404 @@
+---
+category: literaturenote
+citekey: abatbangasanapplicationlowvolumeroad2006
+title: APPLICATION OF LOW-VOLUME ROAD MAINTENANCE MANAGEMENT SYSTEMS IN NEW ZEALAND TO THE PHILIPPINES
+authors: "Abat-Bangasan, Romelda"
+year: 2006
+date: 2006-00-00 2006
+doi: 10.26021/3016
+publication: UC Research Repository  (University of Canterbury)
+zotero_key: QDRDS75H
+zotero_storage: VGVFRPQR
+collections: magistritöö / kohalikud teed
+folder: 001_artiklid
+firstAuthor: "Abat-Bangasan, Romelda"
+status: converted
+---
+# **APPLICATION OF LOW-VOLUME ROAD MAINTENANCE MANAGEMENT SYSTEMS IN NEW ZEALAND TO THE PHILIPPINES**
+
+A thesis submitted in partial fulfillment of the requirements for the Degree of Master of Engineering in Transportation in the University of Canterbury
+
+by
+
+**Romelda Abat-Bangasan** 
+
+Department of Civil Engineering UNIVERSITY OF CANTERBURY Christchurch, New Zealand
+
+# <span id="page-1-0"></span>**Abstract**
+
+Road authorities around the world have been innovating and finding ways to cope with the high cost of road network maintenance, the growing demands of road users and the changing traffic type and volume. A well-maintained road is needed to make the network sustainable for future generations. Improving road maintenance management in the Philippines, based on New Zealand experience, is the goal of this research with the theme of managing the change from method-based specifications to the adoption of performance-based specifications for unsealed low-volume roads.
+
+The New Zealand Local Government Act 2002 prescribes the requirements for the provision, operation, and management of the local road network, consistent with the Land Transport Management Act 2002 and the New Zealand Land Transport Strategy. The maintenance management system used by New Zealand road controlling authorities (RCAs) was determined by survey and a profile of RCAs that have adopted performance-based specifications was established. RCAs that adopted performance-based specifications had employed asset managers, used the Road Asset Maintenance Management (RAMM) system as an asset management tool, engaged consultants for specialised skills, employed more engineers, had highly developed performance specifications, conducted customer surveys, and had more resources in terms of rates and revenues than RCAs that had not adopted performance-based specifications.
+
+The proposed performance-based specifications for sealed and unsealed roads were also presented in this thesis.
+
+The Department of Public Works and Highways of the Philippines has implemented three long-term performance-based maintenance pilot projects, all completed by 2005. The lessons learned from the pilot projects, together with the New Zealand survey results will guide road authorities in the Philippines to improve the implementation of future long-term performance-based maintenance contracts (LTPBMC) on national roads, and possibly apply the same to low-volume roads.
+
+# <span id="page-2-0"></span>**Acknowledgement**
+
+I take honour and pride in accomplishing this thesis which I never thought I am capable of doing. It was difficult and challenging, but in the end, I know it was worth it.
+
+First and foremost, I would like to thank God for giving me wisdom, strength and courage to face the daily challenges of life. Without Him, I can do nothing.
+
+My sincerest gratitude goes to the New Zealand Agency for International Development (NZAID) for the scholarship to undertake postgraduate studies at the University of Canterbury.
+
+I would like to give my sincere thanks to Dr Alan Nicholson, my senior supervisor, for his advice, guidance and logistical support. I am very grateful to a remarkable man, who has been instrumental to achieving my goal, Dr Robert A. Douglas, my technical supervisor. I consider myself very lucky to be one of his supervisees. I learned a lot from him, from writing styles, grammar, organising my report, time management, anecdotes about his professional career, and simple lessons in life. I admire the way he does his job; straightforward, dedicated and well-organised.
+
+Thank you to the Department of Civil Engineering, University of Canterbury staff, Louise Barton, for helping me print the survey questionnaires and envelopes, and Belinda Lansley for printing letters to my interviewees and other clerical services. Thank you to the Transportation Group in Civil Engineering, for the experience and insights shared during our group meetings. I would also like to thank Dr Bryan Pidwerbesky for his time and for sharing his views during the conception of this study. Thank you to the road maintenance staff of Fulton Hogan Ltd. Canterbury for providing samples of performance-based specifications used in the study.
+
+Adjusting to life in New Zealand was complicated, but it was made easy because of the assistance and pastoral care by the staff of the University of Canterbury International Student Support (ISS). Thank you to Gareth Morgan, my former student adviser, who from day one was there to guide me until he left ISS. A special thank you goes to Eunice McKessar, my current student adviser, for being always there to talk to, a friend, a confidant, and a problem solver; and to Maree Thomas who patiently listens to my problems and acts on my requests. I will never forget the warm smiles that greet me every time I go to ISS. Thank you to the rest of the ISS staff, Bex, Jonie, and Sarah.
+
+I am very grateful to the Department of Public Works and Highways for giving me the opportunity to undergo postgraduate studies. I would like to thank DPWH Secretary Hermogenes E. Ebdane, Jr. and DPWH staff who supported this endeavour. Thank you to Dir. B Elizabeth Yap, Diane Wacker, and Engr. Ernante Antonio, for sharing their time and ideas during the interviews. Thank you also to Dir. Luis A. Mamitag, Jr., Engr. Edwin Fortes, Elizabeth P. Pilorin, and Marilou H. Tuñgol, for their efforts in providing relevant information for this work. Thank you to the DPWH-AMMS staff, DPWH-CAR Regional Office staff, and the NEDA scholarship committee for helping me process my papers. I wish to express my sincere appreciation to District Engineer Nerie D. Bueno of the Baguio City District Engineering Office, and the BCDEO staff for their support and encouragement.
+
+To the current and former Filipino NZAID students and Filipinos in New Zealand especially in Christchurch and Lincoln, thank you very much for making me feel at home. I am also thankful to all my friends from Malaysia, Singapore, Bhutan, France, Thailand, New Zealand, Vietnam, China, Germany, Solomon Islands, Tonga, Canada, and USA for helping cope with University life, cheered me up and kept me sane. Thank you also to the Catholic Tertiary Chaplaincy team for the spiritual guidance they have given me.
+
+This thesis is dedicated to my better-half, Severino, whose unceasing love inspired and encouraged me to carry-on with this endeavour. To Papa and Mama, thank you so much for your prayers, you may be far away in Canada but still, I feel you close to my heart. The same goes to my in-laws, my siblings, the rest of my family, and friends in the Philippines and Canada.
+
+#### CHEERS!
+
+<span id="page-4-0"></span>
+
+| ABSTRACT                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   | II                                             |
+|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|------------------------------------------------|
+| ACKNOWLEDGEMENT                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            | III                                            |
+| TABLE OF CONTENTS                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | V                                              |
+| LIST OF TABLES<br>VIII                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     |                                                |
+| LIST OF FIGURES<br>IX                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      |                                                |
+| ABBREVIATIONS AND ACRONYMS                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 | X                                              |
+| 1 GENERAL INTRODUCTION                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     | 1                                              |
+| 1.1<br>INTRODUCTION                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        | 1                                              |
+| 1.2<br>BACKGROUND                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | 3                                              |
+| 1.3<br>CONCEPTUAL FRAMEWORK (JUSTIFICATION)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                | 4                                              |
+| 1.4<br>OBJECTIVES OF THE STUDY                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             | 4                                              |
+| 1.5<br>SCOPE AND LIMITATIONS OF THE STUDY<br>                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | 5                                              |
+| 1.6<br>METHODOLOGY<br>                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     | 5                                              |
+| 1.6.1<br>Review of New Zealand Local Government Act 2002<br>1.6.2<br>Survey of New Zealand Road Controlling Authorities<br>1.6.2.1<br>Road Controlling Authorities<br>1.6.2.2<br>Survey Questionnaire<br>1.6.2.3<br>Grouping of Road Controlling Authorities<br>1.6.2.4<br>Contributing Factors<br><br>1.6.3<br>Review of Maintenance Management Systems in the Philippines<br>1.6.4<br>Comparison of Performance-based specifications<br>1.7<br>REFERENCES:<br><br>2 THE ROAD NETWORKS IN NEW ZEALAND AND THE PHILIPPINES | 5<br>6<br>6<br>6<br>7<br>7<br>7<br>7<br>8<br>9 |
+| 2.1<br>INTRODUCTION                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        | 9                                              |
+| 2.2<br>PHILIPPINE ROAD NETWORK                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             | 9                                              |
+| 2.2.1<br>Reforms<br>2.3<br>NEW ZEALAND ROAD NETWORK<br>                                                                                                                                                                                                                                                                                                                                                                                                                                                                    | 13<br>17                                       |
+| 2.4<br>COMPARISON<br>                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      | 20                                             |
+| 2.4.1<br>Road Authorities<br>2.4.2<br>Road Statistics<br>2.5<br>REFERENCE:                                                                                                                                                                                                                                                                                                                                                                                                                                                 | 20<br>20<br>22                                 |
+| 3 NEW ZEALAND LOCAL GOVERNMENT ACT 2002<br>                                                                                                                                                                                                                                                                                                                                                                                                                                                                                | 23                                             |
+| 3.1<br>INTRODUCTION                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        | 23                                             |
+| 3.2<br>THE LOCAL GOVERNMENT ACT 2002<br>                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   | 23                                             |
+|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |                                                |
+
+|   | 7.2            | ELEMENTS OF A PERFORMANCE-BASED SPECIFICATION<br>         | 66 |
+|---|----------------|-----------------------------------------------------------|----|
+|   | 7.2.1          | Scope of Work<br>                                         | 66 |
+|   | 7.2.2          | Performance Criteria<br>                                  | 66 |
+|   | 7.2.3          | Response Times<br>                                        | 66 |
+|   | 7.2.4          | Traffic Management                                        | 67 |
+|   | 7.2.5          | Environmental Management                                  | 67 |
+|   | 7.2.6          | Basis of Payment                                          | 67 |
+|   | 7.2.7          | Construction Methods or Proposed Methods of Repair        | 67 |
+|   | 7.2.8          | Materials                                                 | 67 |
+|   | 7.2.9          | Equipment<br>                                             | 68 |
+|   | 7.2.10         | Testing Requirements<br>                                  | 68 |
+|   | 7.3            | PERFORMANCE-BASED SPECIFICATIONS IN NEW ZEALAND AND THE   |    |
+|   |                | PHILIPPINES                                               | 68 |
+|   | 7.4            | PERFORMANCE SPECIFICATIONS<br>                            | 72 |
+|   | 7.4.1          | Sealed Roads                                              | 72 |
+|   | 7.4.2          | Unsealed Low-Volume Roads<br>                             | 78 |
+|   | 7.5            | REFERENCES:<br>                                           | 80 |
+| 8 |                | CONCLUSION                                                | 81 |
+|   | 8.1            | ACCELERATORS AND IMPEDING FACTORS USING PERFORMANCE-BASED |    |
+|   | SPECIFICATIONS |                                                           | 81 |
+|   | 8.2            | PROPOSALS FOR PERFORMANCE-BASED SPECIFICATIONS<br>        | 84 |
+|   | APPENDIX 1     |                                                           | 85 |
+|   |                |                                                           |    |
+
+# <span id="page-7-0"></span>**List of Tables**
+
+| 21                                                                             |
+|--------------------------------------------------------------------------------|
+| 35                                                                             |
+| 37                                                                             |
+| 41                                                                             |
+| 45                                                                             |
+| Table 5.5. Values of contributing factors using the median 45                  |
+| Table 5.6. Values of contributing factors using midway between the minimum and |
+| maximum 46                                                                     |
+| Table 5.7. Ranking the contributing factors using three options 46             |
+|                                                                                |
+| Based Specified Maintenance Contracts 70                                       |
+|                                                                                |
+| Zealand's PSMC Contracts 73                                                    |
+|                                                                                |
+| Philippines 74                                                                 |
+|                                                                                |
+| roads 79                                                                       |
+|                                                                                |
+
+# <span id="page-8-0"></span>**List of Figures**
+
+| Figure 2.1.<br>Philippine National Road Network                           | 10 |
+|---------------------------------------------------------------------------|----|
+| Figure 2.2.<br>Paved National Road                                        | 11 |
+| Figure 2.3.<br>Unsealed Low-volume Road                                   | 12 |
+| Figure 2.4.<br>New Zealand's State Highway Network                        | 18 |
+| Figure 2.5.<br>Well maintained New Zealand state highway                  | 19 |
+| Figure 2.6.<br>Well maintained New Zealand Unsealed low-volume road       | 19 |
+| Figure 4.1. Risk Distribution 29                                          |    |
+| Figure 4.2 Value Chain                                                    | 30 |
+| Figure 5.1. Reported duties of personnel in-charge of road maintenance 39 |    |
+| Figure 5.2. Contract Specifications                                       | 42 |
+| Figure 5.3. How specifications were developed                             | 42 |
+| Figure 5.4. Frequency of revisions in specifications                      | 43 |
+| Figure 5.5. Evaluation of contractor's work                               | 44 |
+
+# <span id="page-9-0"></span>**Abbreviations and Acronyms**
+
+- **ADB** Asian Development Bank
+- **BIIPs** Business Improvement Implementation Projects
+- **BOM –** Bureau of Maintenance (Philippines)
+- **CAAC** Complaints and Action Center
+- **CPM –** Contract Performance Measures
+- **CQP –** Contract Quality Plan
+- **DPWH** Department of Public Works and Highways (Philippines)
+- **FWD**  Falling Weight Deflectometer
+- **HDM-4** Highway Development and Management
+- **HSD**  High Speed Data
+- **IRA**  Internal Revenue Allotment
+- **KPI**  Key Performance Measures
+- **LGA 2002** Local Government Act 2002 (New Zealand)
+- **LGNZ**  Local Government New Zealand
+- **LGU**  Local Government Unit
+- **LTCCP** Long-Term Council Community Plan
+- **LTMA**  Land Transport Management Act (New Zealand)
+- **LTNZ**  Land Transport New Zealand
+- **LTPBMC**  Long-Term Performance-Based Maintenance Contract
+- **LVR** Low-Volume Road
+- **M**  Motorways and Expressways
+- **MBC** Maintenance by Contract
+- **MBA** Maintenance by Administration
+- **MPM**  Management Performance Measures
+- **MYPS** Multi-Year Programming and Scheduling
+- **NRIMP** National Roads Improvement and Management Program (Philippines)
+- **NAASRA**  National Association of Australian State Road Authorities
+- **OPM**  Operational Performance Measures
+- **PBSMC** Performance-based Specified Maintenance Contract
+- **PRB**  Philippine Road Board
+
+- **PSMC**  Performance Specified Maintenance Contract
+- **PMS** Pavement Management System
+- **R1** Rural roads with > 10,000 vehicles per day
+- **R2**  Rural roads with 4,000 to 9,999 vehicles per day
+- **R3**  Rural roads with 1,000 to 3,999 vehicles per day
+- **R4** Rural roads with 0 to 999 vehicles per day
+- **RA**  Republic Act (Philippines)
+- **RAMM** Road Asset Maintenance Management
+- **RBIA** Road and Bridge Information Application
+- **RCA** Road Controlling Authority
+- **RIMSS** Road Information and Management Support System
+- **SCRIM**  Sideways Force Coefficient Routine Investigation Machine
+- **TLA** Territorial Local Authority
+- **Transit** Transit New Zealand
+- **WB –** The World Bank
+
+# <span id="page-11-0"></span>**1 GENERAL INTRODUCTION**
+
+#### *1.1 Introduction*
+
+The roads less travelled, traditionally known as low-volume roads (LVR), are perceived to be one of the pillars for socio-economic growth in developed countries like New Zealand and developing countries like the Philippines. These roads, carrying fewer than 500 vehicles per day, are essential as they support a nation's leading income generators like agriculture (i.e. farming, sheep and cattle raising, dairy, and wine making), forestry and tourism.
+
+Improving road maintenance in the Philippines, based on New Zealand experience, is the goal of this research with the theme of making a move from prescriptive specifications to performance-based (end-result) specifications for unsealed low volume roads. The procurement method used for road maintenance has a great impact on the delivery of service and can generate the best value for the roading dollar.
+
+Road authorities manage the maintenance of unsealed low volume roads based on plans and strategies that are adaptable to the locality's geographic, economic, social, cultural, environmental and climatic conditions. Assessment of desired outcomes is key to evaluating the level of service. Assessment may be in terms of method specifications – how the work is to be performed by the contractor, or the performance-based specifications – outcomes and performance required of the network (Transfund New Zealand 2001). Some New Zealand road controlling authorities (RCAs) have implemented the latter.
+
+The 74 Territorial Local Authorities (TLA) in New Zealand are RCAs responsible for maintaining about 82,000 kms of local roads, 41 percent of these, unsealed low volume roads[1](#page-11-1) . Maintenance is outsourced by RCAs, subsidised by Land Transport New Zealand (LTNZ, formerly Transfund New Zealand). In 2003, 58% of the total
+
+<span id="page-11-1"></span>
+
+ http:// [www.transfund.govt.nz.](http://www.transfund.govt.nz/) Transfund New Zealand. *Roading Statistics*. Visited 13 July 2004.
+
+roading maintenance was funded by LTNZ to augment limited resources of RCAs for such activities. A major thrust to this endeavour is embodied in the Local Government Act 2002 (LGA 2002) and the Land Transport Management Act 2002.
+
+The New Zealand Local Government Act 2002 is aimed at assuring the present and future social, economic, environmental and cultural welfare of communities (Wilson and Salter 2003). For local government to achieve this objective, it has to provide sustainable roads, which are vital requisites for socio-economic development. Local Authorities are required to have a Long Term Council Community Plan (LTCCP), covering a period of 10 years. The LTCCP encompasses details concerning local authorities' policies, management plans, activities, community outcomes, decisions, budget, and finances supported by an audit report. Furthermore, local authorities are also required to identify community outcomes at least once every 6 years with the intention to evaluate desired community outcomes, prioritise identified outcomes, quantify accomplishments, and assess community resources. Since the thrust of LGA 2002 is into community involvement, there is a need to adopt a valuation scheme for maintenance management systems that can be visualised and comprehended by nontechnical individuals.
+
+Road controlling authorities are responsible for delivering a level of service acceptable to the communities in terms of management, maintenance and development of roads. Consequently, RCAs and contractors have entered into longterm performance-based contracts, from 3 to 10 years, which give contractors the opportunity to innovate and improve their maintenance management systems. Also, contractors are given the option to carry out maintenance activities where and when they are needed, and how they are undertaken (Douglas et al. 2004). The key performance indicators are that there is minimal deterioration up to an acceptable threshold level on the road network throughout the duration of the contract, high quality work is delivered on time, is within the budget and should be accepted by the community. A survey conducted on local authorities (Transfund New Zealand 2001) disclosed that the best practice for maintenance is to specify outcomes, rather than methods. However, some RCAs still practise the use of method specifications rather than performance-based specifications in the maintenance of unsealed low volume roads. The challenges now are how to manage a change from the prescriptive to end<span id="page-13-0"></span>results methods and determining the level of service and outcomes expected by communities.
+
+In the Philippines, local roads are managed by Local Government Units, with more than 50 percent unsealed low volume roads. The Department of Public Works and Highways (DPWH) through the Bureau of Maintenance operates and maintains national roads, 37 percent of which are unsealed and more than 30 percent low volume. Moreover, the DPWH provides farm-to-market roads for rural communities by assisting other agencies of government like the Department of Agriculture and Department of Land Reform. Farm-to-market roads are vital links from the remote barangays (villages) to urban centres. This is in support of the President's campaign to achieve economic growth and development through fast delivery and low transportation cost by providing rural areas with high quality infrastructure facilities [2](#page-13-1) . Considering the present economic and road network condition of the Philippines, it is imperative to import expertise from developed countries like New Zealand, which is applicable and adaptable to the Philippine setting.
+
+The World Bank supported options for road reforms in the Philippines similar to New Zealand wherein the road fund is separate, funds all road networks, specifies criteria for economic justification of expenditures and operates under performancebased contract agreements (World Bank 2000).
+
+#### *1.2 Background*
+
+The Local Government Act 2002 of New Zealand requires Local Councils acting as Road Controlling Authorities to provide sustainable roads, assuring the present and future social, economic, environmental and cultural welfare of communities. RCAs are expected to carry out maintenance of roads to satisfy outcomes required by the stakeholders.
+
+<span id="page-13-1"></span><sup>2</sup> [http://www.dpwh.gov.ph/News/2005/apr%20may%20jun.asp#239-KM%20OF%20FARM%20TO%](http://www.dpwh.gov.ph/News/2005/apr may jun.asp#239-KM%20OF%20FARM%20TO% 20MARKET%20CONSTRUCTED%20WITHIN%20FIRST%20100%20DAYS%20OF%20EBDANE%20LEADERSHIP)  [20MARKET%20CONSTRUCTED%20WITHIN%20FIRST%20100%20DAYS%20OF%20EBDAN](http://www.dpwh.gov.ph/News/2005/apr may jun.asp#239-KM%20OF%20FARM%20TO% 20MARKET%20CONSTRUCTED%20WITHIN%20FIRST%20100%20DAYS%20OF%20EBDANE%20LEADERSHIP) [E%20LEADERSHIP.](http://www.dpwh.gov.ph/News/2005/apr may jun.asp#239-KM%20OF%20FARM%20TO% 20MARKET%20CONSTRUCTED%20WITHIN%20FIRST%20100%20DAYS%20OF%20EBDANE%20LEADERSHIP) Department of Public Works and Highways. 239 Kilometers of Farm to Market Constructed within First 100 Days of Ebdane Leadership. Visited 5 October 2005.
+
+<span id="page-14-0"></span>New Zealand has been in the forefront in the procurement of services for the maintenance management of the road network. RCAs are treating asset improvement and asset management as a business venture, outsourcing total network maintenance to the private sector. Maintenance management of roads has evolved from setting inputs to requiring outcomes.
+
+#### *1.3 Conceptual Framework (Justification)*
+
+For the past 5 years, the Philippines, through the DPWH, have been introducing reforms in the operation and maintenance management of the road network, as a condition of a loan provided by the World Bank[3](#page-14-1) . It supported options for road reforms in the Philippines similar to New Zealand.
+
+This research will focus on the operation under performance-based contract agreements. With the on going reforms in the Philippines, three long-term performance-based maintenance pilot projects were implemented in 2002 under the World Bank funded National Road Improvement and Management Program (NRIMP). If these projects are successful, this type of outsourcing maintenance will be expanded to other provinces under later NRIMP phases.
+
+New Zealand study of road controlling authorities will be a guide for the researcher to determine how to manage the change from method specifications to performancebased specifications.
+
+#### *1.4 Objectives of the Study*
+
+The objectives of this study were:
+
+1. To study the effect of changes stipulated in the New Zealand Local Government Act 2002 on the maintenance of low volume roads;
+
+<span id="page-14-1"></span> [http://web.worldbank.org/external/projects/main?pagePK=104231&piPK=73230&theSitePK=40941](http://web.worldbank.org/external/projects/main?pagePK=104231&piPK=73230&theSitePK=40941&menuPK=228424&Projectid=P039019) [&menuPK=228424&Projectid=P039019.](http://web.worldbank.org/external/projects/main?pagePK=104231&piPK=73230&theSitePK=40941&menuPK=228424&Projectid=P039019) The World Bank Group. First National Roads Improvement Project. Visited 17 October 2005.
+
+- <span id="page-15-0"></span>2. To survey New Zealand road controlling authorities to see how far have they come in adopting and implementing performance-based specifications;
+- 3. To determine the factors affecting adoption of the new system, what made it easy using performance-based specifications and what are the impedances;
+- 4. To make recommendations on how to manage the change from prescriptive methods to end-result methods in the Philippines;
+- 5. To compare the assessment of road maintenance in New Zealand and the Philippines in terms of techniques, equipment and personnel involved;
+- 6. To make preliminary recommendations on what the performance-based specifications should be, the acceptable limits and how they should be quantified.
+
+# *1.5 Scope and Limitations of the Study*
+
+The scope of this study is limited to evaluating the management of performancebased specifications for the maintenance of unsealed low volume roads by RCAs in compliance with guidelines stipulated in the New Zealand LGA 2002. This research will not delve into the technology used for road maintenance but will be limited to the assessment of outcomes as a basis of acceptance of work accomplished.
+
+#### *1.6 Methodology*
+
+#### **1.6.1Review of New Zealand Local Government Act 2002**
+
+A thorough review of the New Zealand Local Government Act 2002 (LGA 2002) was conducted in relation to its effects on maintenance management systems for unsealed low-volume roads. The LGA 2002 required local authorities to act as road controlling authorities in their respective areas. RCAs are the owners of the local road network, therefore, they are responsible for its operation and maintenance. Section 93 of LGA 2002 stipulates the provisions for Long Term Community Council Plans (LTCCP) for all local authorities, covering all council activities and <span id="page-16-0"></span>management of assets including the road network. As such, the LTCCPs of local authorities were studied relative to the operation and maintenance of the local road network.
+
+#### **1.6.2Survey of New Zealand Road Controlling Authorities**
+
+#### **1.6.2.1 Road Controlling Authorities**
+
+The road network in New Zealand is made up of the state highways, motorways and local roads. The latter is operated and managed by local councils acting as road controlling authorities, while the rest of the network is controlled by Transit New Zealand.
+
+A survey questionnaire was sent to 52 of a total of 74 Road Controlling Authorities (RCAs) in New Zealand with roading asset managers or personnel in charge of the maintenance of unsealed low-volume roads as the target respondents. The RCAs were chosen on the basis of the significant length (at least 100 km) of unsealed lowvolume roads being maintained.
+
+#### **1.6.2.2 Survey Questionnaire**
+
+A survey was conducted to identify RCAs that have adopted performance-based specifications and the extent of implementation. It was a tool to verify the systems in place and the schemes used in the maintenance management of the local road network. The questionnaire was intended to find out the accelerating and impeding factors in adopting performance-based specifications.
+
+This research is qualitative in nature. Questions in the survey are open-ended and designed for the respondents to impart their views and insights on the systems utilised in the maintenance management of unsealed low volume roads. There are no definite answers, thus, responses vary from different RCAs.
+
+#### <span id="page-17-0"></span>**1.6.2.3 Grouping of Road Controlling Authorities**
+
+Responses from the survey were used to assess the RCAs and divide them into RCAs that used performance-based specifications and RCAs that use method specifications. Some ambiguities in the responses were verified by reading through available resources particularly the Long Term Council Community Plans (LTCCP) [4](#page-17-1) of Territorial Local Authorities.
+
+#### **1.6.2.4 Contributing Factors**
+
+The internal and external contributing factors were established based on the survey results and attributes relative to RCAs in New Zealand. Analysis on the contributing factors was conducted to identify any patterns there might be for RCAs that have adopted performance-based specifications.
+
+#### **1.6.3Review of Maintenance Management Systems in the Philippines**
+
+The present maintenance management system in the Philippines was examined by reviewing existing laws and Department Orders of the Department of Public Works and Highways (DPWH). Interviews were conducted with key personnel at the Bureau of Maintenance, the consultant for the Roadway Information and Management Support System (RIMSS), and the Deputy Project Director for RIMMS.
+
+#### **1.6.4Comparison of Performance-based specifications**
+
+A comparison of performance-based specifications in New Zealand and the Philippines was conducted. The elements of a performance specification were discussed and typical performance specifications for both countries were presented in Chapter 7.
+
+<span id="page-17-1"></span> 4 http:/[/www.localcouncils.govt.nz](http://www.localcouncils.govt.nz/). The Department of Internal Affairs. Local Councils. Visited 16 July 2005.
+
+<span id="page-18-0"></span>
+
+This chapter presented the general introduction to the study on the road management systems in New Zealand that can be applied in the Philippine road network. The outline of the thesis and manner by which the study was conducted were shown in detail.
+
+The following chapter will describe the road networks of New Zealand and the Philippines. A comparison between the two countries in terms of road network statistics and road management is given to visualise the setting for which this research was initiated.
+
+# *1.7 References:*
+
+- D. Michael Cleary and Partners, (2003). "Annual NRIMP-1BIIPs Subcomponent Benefits/Cost Monitoring Report with Initial Baseline Measures and Values." D. Michael Cleary and Partners, Inc., Manila.
+- Douglas, R. A., Mitchell, S. A., and Pidwerbesky, B. D. (2004). "Adaptation of a Grading Management System for Unsealed Road Networks in New Zealand." Proceedings Pavements Unbound, 6th International Symposium (Unbar 6, 6-8 July 2004, Knottingham, England). AA Balkema Publishers. London.
+- Philippine Road Board. (2001). "Philippine Road Board Operating Procedures Manual." Philippine Road Board. Manila.
+- Transfund New Zealand. (2001). "Survey of Local Authority Maintenance Management Process." *PM00/875A*, Transfund New Zealand. Wellington.
+- Wilson, V., and Salter, J. (2003). *A Guide to the Local Government Act 2002*, Brookers Ltd., Wellington.
+
+World Bank. (2000). "Project Appraisal Document on a Proposed Loan for the Republic of the Philippines for the First National Roads Improvement and Management Program." *19754-PH*, The World Bank. The document can be retrieved from http://www-wds.worldbank.org/external/default/WDSContentServer/IW3P/ IB/2000/02/18/000094946\_00020205301940/Rendered/PDF/multi\_page.pdf.
+
+# <span id="page-19-0"></span>**2 THE ROAD NETWORKS IN NEW ZEALAND AND THE PHILIPPINES**
+
+#### *2.1 Introduction*
+
+The Philippine and New Zealand road networks have vital roles in supporting the economic, social, cultural and environmental development of both countries. The road networks in these countries have characteristics that are on the extremes. The individual road networks are described in detail and then a comparison is made in terms of the road statistics and road management.
+
+# *2.2 Philippine Road Network*
+
+The road network is the key element in the transport and communication infrastructure in the Philippines. Its role is vital in the socio-economic growth of the country by integrating rail, air, and sea transport. The road network is a basic part of transport that provides access from remote communities to urban areas supporting economic, agricultural, social, cultural, environmental needs of the community. The management of the road network represents a sizeable portion of the governments' investments and expenditures, presenting a great impact on the nation's progress.
+
+The Philippines has an extensive road network consisting of 28,500 km (2005)[5](#page-19-1) of national roads[6](#page-19-2) and 171,900 km (2002)[7](#page-19-3) of local roads[8](#page-19-4) (Figure 2.1). In 2000, the Philippines ranked 16th in the world for the total length of the road network[9](#page-19-5) . Only
+
+ <sup>5</sup> <http://www.dpwh.gov.ph/>. Department of Public Works and Highways. Existing National Roads (kilometers) by Surface Type (as of August 2005). Visited 12 September 2005.
+
+National roads are state highways; these are main arterial roads that link provinces. 7
+
+<span id="page-19-3"></span><span id="page-19-2"></span><span id="page-19-1"></span>Philippines. Department of Public Works and Highways. Existing Roads and Bridges By System Classification and Pavement Type by Region, Province, and Legislative District (Updated as of December 2001).
+
+<span id="page-19-4"></span>Local roads consist of provincial roads (secondary roads within provinces that interconnect municipalities), municipal and city roads (roads in urban areas and cities), and barangay or village roads (roads that link the villages to urban areas and classified as farm-to-market roads). 9 [http://www.nationmaster.com/graph-T/tra\\_hig\\_tot&int=24](http://www.nationmaster.com/graph-T/tra_hig_tot). Nation Master. Visited 22 September
+
+<span id="page-19-5"></span><sup>2005.</sup> 
+
+**Figure 2.1. Philippine National Road Network**
+
+![](_page_20_Figure_1.jpeg)
+
+Source: Department of Public Works and Highways. Planning Service. Infrastructure Planning Research and Statistics Division. Copy received 10 January 2006.
+
+21% of the total road network is paved, either concrete (Figure 2.2) or asphalt, and the rest is gravel (Figure 2.3) or earth surfaced. The proportion of paved surfaces for national and local roads is 70% and 14%, respectively. Average road density in the Philippines is 0.67 km/km2 [10](#page-21-0), which is comparable to most Asian countries.
+
+![](_page_21_Picture_2.jpeg)
+
+**Figure 2.2. Paved national road.** 
+
+The Department of Public Works and Highways (DPWH) is responsible for the management of national roads, the main arterial roads that link provinces. Moreover, the DPWH is responsible for the improvement of local roads under "congressional initiatives". The national roads in the Philippines correspond to state highways managed by Transit New Zealand and the local roads in the Philippines are administered by Local Government Units (LGUs) corresponding to Road Controlling Authorities (RCAs) in New Zealand.
+
+ 10 Total length of road divided by the total land area of the Philippines.
+
+<span id="page-21-0"></span>
+
+![](_page_22_Picture_1.jpeg)
+
+**Figure 2.3. Unsealed low-volume road.** 
+
+According to a study conducted by the Asian Development Bank (ADB)[11](#page-22-0), the road network in the Philippines is generally adequate in extent, but many roads are in poor condition due to inadequate management that includes planning, design, construction and maintenance. The increasing traffic, heavy vehicles and bad weather conditions contribute greatly to the deterioration of these roads. An Asian Development Bank (ADB) study[12](#page-22-1) pointed out the deficiency in the planning process of the DPWH where project selection is influenced by politics and is not based on systematic analysis of the general network needs. Furthermore, priorities are not frequently determined in terms of economics and technical appraisals, therefore, influencing funding allocation and project selection. The ADB also recognised the fact that the problem of maintaining the non-national roads (local roads), which make up more than 80% of the road network cannot be ignored. Encouraging good governance is imperative to dealing with this problem.
+
+<span id="page-22-0"></span> 11 Rural Road Development Policy Framework, a research paper conducted by the Asian Development Bank. 2001.
+
+<span id="page-22-1"></span><sup>12</sup>[http://www.asiandevbank.org/Documents/PERs/IE50.pdf#search='Philippine%20Transport%20Strat](http://www.asiandevbank.org/Documents/PERs/IE-50.pdf#search=) [egy%20Study](http://www.asiandevbank.org/Documents/PERs/IE-50.pdf#search=)'. Asian Development Bank. Impact Evaluation Study of Bank Operations in the Road Sector in the Philippines Dec. 1997. Visited 17 October 2005.
+
+<span id="page-23-0"></span>In order to meet the demands and expectations of the community, the primary beneficiaries of an effective and efficient road network, a cost-effective management of the asset is crucial. Studies conducted by the Asian Development Bank and the World Bank brought about significant reforms in the management of this vital asset in the Philippines. The policy framework of the DPWH is founded on its Mission and Vision[13](#page-23-1), which brought about reforms, with the needs of the customers and other stakeholders as its main concern.
+
+#### **DPWH Mission:**
+
+To provide and manage quality infrastructure facilities and services responsive to the needs of the Filipino people in the pursuit of national development objectives.
+
+#### **DPWH Vision:**
+
+DPWH is a model agency in government, improving the life of every Filipino through quality infrastructure.
+
+#### **2.2.1 Reforms**
+
+In 1997, the Road Information and Management Support System (RIMSS) Project was established under the World Bank financed Highway Management Project. The objective of the RIMSS is to introduce reforms in the DPWH relating to network planning and programming, design review and contract management, maintenance, procurement, financial management, human resource and information management. The RIMSS project, together with Better Roads Philippines (BRP) Study were the basis for the World Bank First National Roads Improvement and Management Project (NRIMP) in 2000 [14](#page-23-2) . The NRIMP was developed to guarantee the preservation of the national road system (NRS) through enhancement in design, initiation and operation. The specific aims of NRIMP are: "a) to involve road users in managing the roads as well as administering the funds they contribute, and b) manage the roads in a commercial fashion, rather than a social service". To achieve
+
+<span id="page-23-1"></span> 13[http://www.dpwh.gov.ph/.](http://www.dpwh.gov.ph/) Department of Public Works and Highways. Mission and Vision. Visited 12 September 2005.
+
+<span id="page-23-2"></span><sup>14</sup>[http://www.wds.worldbank.org/servlet/WDSContentServer/WDSP/IB/2000/02/18/000094946\\_0002](http://www.wds.worldbank.org/servlet/WDSContentServer/WDSP/IB/2000/02/18/000094946_00020205301940/Rendered/PDF/multi_page.pdf) [0205301940/Rendered/PDF/multi\\_page.pdf](http://www.wds.worldbank.org/servlet/WDSContentServer/WDSP/IB/2000/02/18/000094946_00020205301940/Rendered/PDF/multi_page.pdf). The World Bank Group. National Road Improvement and Management Project-Project Appraisal Document. Visited 17 October 2005.
+
+these objectives, NRIMP is concentrating on two main components: 1. civil works, which include: a) road upgrading, b) preventive maintenance, and c) long term performance based maintenance aiming at multi-year contract performance that included routine and periodic maintenance activities, and 2. institutional strengthening, which incorporates creation of road maintenance fund, institutional reforms, designing an independent organisation for policy making, financial and human resource management, and business improvement.
+
+This research is focused on the NRIMP Project's Civil Works component, Performance-Based Maintenance sub-component, which is discussed in detail in the NRIMP Project Appraisal Document[15](#page-24-0):
+
+#### **Project Component 3** - **US\$** 9.96 **million**
+
+**A.3 Long-Term, Performance-Based Maintenance (LTPBM).** This component aims to test the performance of multi-year routine, periodic and preventive maintenance contracts. Payments under the LTPBM component will be based on outcomes; that is, whatever task the contractor is expected to perform must meet the established standard (minimum service level), and not simply have completed a certain quantity of physical work.
+
+Under NRIMP- 1, two pilot contracts for 231 km of national roads in Laguna and Quezon provinces will be issued for an estimated P375 million, including contingencies and consultant services, that will help contractors prepare bids and BOM supervise the contracts.
+
+The component will be implemented in two contracts, each over three years beginning right after project effectiveness. The first contract involves the 97.1 km Famy Infanta Road and Pagsanjan -Luisiana-Lucban-Tayabas Road and will cost an estimated P137 million. The second involves Daan-Maharlika Highway, Tiaong-Lucena Junction and the Pagbilao to Camarines Norte Boundary sections of approximately 134.3 km, and will cost an estimated P166 million. Each contract includes three major maintenance components for preventive work, catch-up routine work and performance (routine and periodic work). Preventive maintenance is designed to improve the roads' structural condition. Catch-up routine maintenance is designed to reduce the present maintenance backlog, particularly with respect to shoulders and drainage. Some minor improvements may be included such as additional drainage structures, slope protection, guard rails, road signs, markings and reconstruction of short sections. After preventive and catch-up routine maintenance are completed, performance maintenance will begin. The
+
+<span id="page-24-0"></span><sup>15</sup>[http://www.wds.worldbank.org/servlet/WDSContentServer/WDSP/IB/2000/02/18/000094946\\_0002](http://www-wds.worldbank.org/servlet/WDSContentServer/WDSP/IB/2000/02/18/000094946_00020205301940/Rendered/PDF/multi_page.pdf) [0205301940/Rendered/PDF/multi\\_page.pdf](http://www-wds.worldbank.org/servlet/WDSContentServer/WDSP/IB/2000/02/18/000094946_00020205301940/Rendered/PDF/multi_page.pdf). The World Bank Group. National Road Improvement and Management Project-Project Appraisal Document. Visited 17 October 2005.
+
+preventive and catch-up routine maintenance contracts will be executed and paid for in the usual manner (based on the quantity of work completed). The performance maintenance, however, will be executed according to minimum standards set in the contract. If contractors fail to maintain them, the monthly lump sum payment will be reduced, according to the penalties for noncompliance delineated in the contract.
+
+**NRIMP-2 and-3.** If successful, this initiative will be expanded to other provinces under future NRIMP phases. Because NRIMP-I is a limited pilot in one sub-region of the country, further pilots will probably be needed to incorporate a broader range of physical, social and economic conditions: NRIMP-II will be designed to address them. Under NRIMP-III, the LTPBM sub-component may be expanded throughout the country on a small scale to serve as a training ground for this type of maintenance program. Growth from then on will reflect the readiness of DPWH and market conditions.
+
+**Implementation arrangements.** The BOM, which will be responsible for managing the project, will supervise the LTPBM contract. The regional office will coordinate with the districts and provide specialists (for controlling quality and surveying quantities). The BOM-assigned engineer, along with the district offices, will be responsible for supervising the contracts daily, which will cover work in progress and monitoring compliance with performance criteria. DPWH will be assisted with an international consultant who will work with the LTPBM team. The PIP provides further details on implementation arrangements.
+
+Performance-based maintenance contracts were adopted on a trial basis by way of two pilot projects in DPWH Region IV-A[16](#page-25-0). At the project preparation stage, the consultant deemed it necessary to split one pilot project into two projects due to its large scope. Bidding for these projects was conducted in August 2001 and were awarded winning contractors a year after. Prior to the bidding process, BCEOM Société Francaise D' Ingenierie was awarded a contract for consultancy services for long-term performance-based maintenance.
+
+It is worth mentioning that "the World Bank supported the evolution to a model similar to New Zealand in which the Road Fund is: (i) separate, (ii) funds all road networks, (iii) specifies criteria for economic justification of expenditures, and (iv) operates under performance-based contract agreements with the beneficiary
+
+<span id="page-25-0"></span><sup>16</sup>[http://web.worldbank.org/external/projects/main?menuPK=228443&theSitePK=40941&pagePK=23](http://web.worldbank.org/external/projects/main?menuPK=228443&theSitePK=40941&pagePK=233764&piPK=233766&Projectid=P039019) [3764&piPK=233766&Projectid=P039019](http://web.worldbank.org/external/projects/main?menuPK=228443&theSitePK=40941&pagePK=233764&piPK=233766&Projectid=P039019). The World Bank Group. Visited 17 October 2005.
+
+implementing agencies on one hand, and with Government on the other hand for the authorization of the total revenues to be raised and budget to be spent".[17](#page-26-0)
+
+To address the preceding recommendations from financial sponsors, the Government of the Philippines approved Republic Act (RA) 8794, a law on Motor Vehicle User's Charge and It's Implementing Rules and Regulations, whereby the Philippine Road Board and the DPWH Road Program Office were created in November 2000. OPUS International Consultants provided technical assistance under the NRIMP Project's Policy and Institutional Reform Component, Support to Commercialisation subcomponent. The Road Board has the following functions (Philippine Road Board 2001):
+
+- 1. Operation of special funds
+- 2. Management of special funds
+- 3. Approval of work programs
+- 4. Approval of special budgets
+- 5. Review of work programs
+- 6. Complementary work programs under other funding
+- 7. Procedures for monitoring performance and managing programs
+- 8. Approval of contracting methods
+- 9. Utilisation of special funds
+- 10. Public awareness and reports
+- 11. Supervisory authority
+
+Section 7 of Republic Act 8794 classified Special Funds under the following:
+
+- 1. Special Road Support Fund 80% to be used for the maintenance and improvement of drainage of national roads;
+- 2. Special Road Safety Fund 7.5% to be used for the installation of traffic lights and safety devices;
+- 3. Special Local Road Fund 5% to be used for the maintenance of local roads, traffic management and road safety devices;
+- 4. Special Vehicle Pollution Control Fund 7.5% of the revenue.
+
+<span id="page-26-0"></span> 17[http://www.wds.worldbank.org/servlet/WDSContentServer/WDSP/IB/2000/02/18/000094946\\_0002](http://www.wds.worldbank.org/servlet/WDSContentServer/WDSP/IB/2000/02/18/000094946_00020205301940/Rendered/PDF/multi_page.pdf) [0205301940/Rendered/PDF/multi\\_page.pdf](http://www.wds.worldbank.org/servlet/WDSContentServer/WDSP/IB/2000/02/18/000094946_00020205301940/Rendered/PDF/multi_page.pdf). The World Bank Group. National Road Improvement and Management Project-Project Appraisal Document. Annex 12.Visited 17 October 2005.
+
+<span id="page-27-0"></span>The Philippine road network had been described in detail with the important aspects in place. The following section will illustrate the features of the New Zealand road network.
+
+#### *2.3 New Zealand Road Network*
+
+The road network is the backbone for the transport system in New Zealand, linking water, rail and air transport. Its role is vital in the economic, social, and cultural development of the country. The management of the road network is embodied in the Local Government Act 2002, the Land Transport Management Act 2002 and the New Zealand Land Transport Strategy, aiming to achieve an integrated, safe, responsive, and sustainable transport system. The governments' objectives for transport are: 1) assisting economic development, 2) assisting safety and personal security, 3) improving access and mobility, 4) protecting and promoting public health, and 5) ensuring environmental sustainability[18](#page-27-1).
+
+The New Zealand road network is ranked number 30 in the world with a total length of more than 92,000 km[19](#page-27-2) . Almost 60 percent of the extensive road network is sealed[20](#page-27-3) with either chip seal surface, asphalt concrete, porous asphalt or slurry seal. State highways (Figure 2.4), which are planned, developed and maintained by Transit New Zealand, have a length of 10,700 km and carry 46 percent of all New Zealand traffic[21](#page-27-4). About 0.4% of the total road network is motorway, carrying 9% of the traffic[22](#page-27-5). The local road network, with a length of 81,700 km, carries 55 percent of the traffic. The 74 Territorial Local Authorities acting as the road controlling authorities in their jurisdictions oversee the local roading asset.
+
+<sup>18</sup> [http://www.transport.govt.nz](http://www.transport.govt.nz/). Ministry of Transport. New Zealand Transport Strategy. December 2002. Chapter 1. Visited 14 July 2004.
+
+<span id="page-27-2"></span><span id="page-27-1"></span><sup>19</sup> [http://www.nationmaster.com/graph-T/tra\\_hig\\_tot&int=24](http://www.nationmaster.com/graph-T/tra_hig_tot). Nation Master. Visited 22 September 2005.
+
+<span id="page-27-3"></span><sup>20</sup> [http://www.transfund.govt.nz](http://www.transfund.govt.nz/). Transfund New Zealand. Roading Statistics. Visited 9 July 2004. 21 [http://www.transport.govt.nz](http://www.transport.govt.nz/). Ministry of Transport. New Zealand Transport Strategy December 2002. Visited 14 July 2004.
+
+<span id="page-27-5"></span><span id="page-27-4"></span><sup>22</sup> [http://www.transport.govt.nz](http://www.transport.govt.nz/). New Zealand Transport Strategy December 2002. Visited 14 July 2004.
+
+![](_page_28_Figure_1.jpeg)
+
+**Figure 2.4. New Zealand's State Highway Network**[23](#page-28-0)
+
+<span id="page-28-0"></span><sup>23</sup> http:www.stats.govt.nz. Statistics New Zealand, Census of Population and Dwellings 2001. Visited 5 October 2005.
+
+New Zealand is one of the countries in the world with the best-managed road network (Figures 2.5 and 2.6). This is a reflection of the support given by the national government through its programs and cooperation of the RCAs through the LTCCP and Annual District Plans. Professional organisations in New Zealand are
+
+![](_page_29_Picture_2.jpeg)
+
+**Figure 2.5. Well maintained New Zealand state highway.** 
+
+![](_page_29_Picture_4.jpeg)
+
+**Figure 2.6. Well maintained New Zealand unsealed low-volume road.** 
+
+<span id="page-30-0"></span>serious about improving the transport sector. Road asset management is one of the primary concerns that involve a systematic approach to maintaining, upgrading and operating the road assets cost effectively by combining engineering principles with sound business practices and economics[24](#page-30-1).
+
+#### *2.4 Comparison*
+
+#### **2.4.1 Road Authorities**
+
+The Department of Public Works and Highways manages national roads and bridges in the Philippines. The fund for its operation and maintenance is allocated from the General Appropriations Act (GAA) from the government and from foreign grants and loans. On the other hand, New Zealand's state highways are managed by Transit New Zealand and resources are allocated by Land Transport New Zealand (formerly Transfund New Zealand).
+
+Local roads are managed by the local government in both countries based on their territorial jurisdiction. In the Philippines, the provincial, municipal and city governments operate their local roads while Territorial Local Authorities (TLA) in New Zealand act as the road controlling authorities as mandated in the Local Government Act 2002. Funding for these roads are sourced by the local governments and subsidised by the national government and LTNZ, for the Philippines and New Zealand respectively.
+
+#### **2.4.2 Road Statistics**
+
+The Philippines and New Zealand are opposites in many aspects of the road network including condition, usage, traffic type, traffic volume, and density, as shown in Table 2.1 The Philippines is about 30,000 km2 larger than New Zealand in terms of
+
+<span id="page-30-1"></span><sup>24</sup> <http://www.zietlow.com/docs/r296-059.pdf>. Dr Gunter Zietlow. Norwell, G. 1997. Managing the Road Asset in Australia and New Zealand. Visited 24 February 2006.
+
+land area but the road length in the Philippines is twice that of New Zealand. More than 58,000 km of roads in New Zealand is paved, accounting for 63 percent of the total road network, while a little more than 40,000 km is paved in the Philippines representing only 21% of the total road network. In 2003, the total maintenance expenditures were NZ\$356M and NZ\$125M for New Zealand and the Philippines,
+
+**Table 2.1. Road statistics.** 
+
+|                                               | New Zealand | Philippines | Philippines<br>New Zealand |
+|-----------------------------------------------|-------------|-------------|----------------------------|
+| State Highways                                |             |             |                            |
+| - Length (km)                                 | 10,700      | 28,500      | 2.70                       |
+| - % Sealed                                    | 100%        | 70%         | 0.70                       |
+| Local Roads                                   |             |             |                            |
+| - Length (km)                                 | 81,700      | 171,900     | 2.10                       |
+| - % Sealed                                    | 59%         | 14%         | 0.24                       |
+| Total Roads                                   |             |             |                            |
+| - Length (km)                                 | 92,400      | 200,400     | 2.20                       |
+| - Unsealed Length (km)                        | 34,300      | 159,600     | 4.70                       |
+| - % Sealed                                    | 63%         | 21%         | 0.33                       |
+| Vehicle Abundance (vehicles/per km2<br>)      | 25          | 8           | 0.32                       |
+| Motor Vehicles (vehicles/1,000 people)        | 560         | 31          | 0.055                      |
+| Highways-total per capita (km/1,000 people)   | 23          | 2.5         | 0.11                       |
+| Population Density (people/ km2<br>)          | 14          | 266         | 19                         |
+| Land Area (km2<br>)                           | 268,000     | 298,000     | 1.10                       |
+| Road Density (km/ km2<br>)                    | 0.35        | 0.70        | 2.00                       |
+| Maintenance Expenditure (2003)                | NZ\$356M    | NZ\$125M    | 0.35                       |
+| Maintenance Expenditure per kilometre (\$/km) | NZ\$3,900   | NZ\$620     | 0.16                       |
+
+respectively. Philippine roads are twice as dense as New Zealand (0.67 vs. 0.34 km/ km2 ) yet vehicle ownership in New Zealand is 18 times more than the Philippines (560 vs. 31 motor vehicles/1,000 people)[25](#page-31-0). Vehicle abundance in the Philippines is about a third that of New Zealand (7.42 vs. 25.26 vehicles/km<sup>2</sup> ). Although the
+
+<span id="page-31-0"></span><sup>2</sup>[5http://www.nationmaster.com/graph-T/tra\\_mot\\_veh&int=90](http://www.nationmaster.com/graph-T/tra_mot_veh&int=90). Nation Master. Visited 22 September 2005.
+
+<span id="page-32-0"></span>Philippines has more roads, there are fewer vehicles using the roads, compared to New Zealand, as shown by the figures. The low population density in New Zealand (13.6 people/ km2 ) contributes much to the high highways total per capita of 22.81 km/1,000 people. New Zealand ranked 11th in the world for the highway per capita, while the Philippines is ranked 125th (2.29 km/1,000 people) [26](#page-32-1) due to the high population.
+
+The road networks in New Zealand and the Philippines were described in detail. A comparison of the road networks and road authorities for both countries was established to set the focal point of this research.
+
+Chapter 3 is about the New Zealand Local Government Act 2002 which prescribes the requirements for the provision, operation, and management of the local road network.
+
+### *2.5 Reference:*
+
+Philippine Road Board. (2001). "Philippine Road Board Operating Procedures Manual." Philippine Road Board. Manila.
+
+<span id="page-32-1"></span><sup>26</sup> [http://www.nationmaster.com/graph-T/tra\\_tot\\_cap&int=164.](http://www.nationmaster.com/graph-T/tra_tot_cap&int=164) Nationa Master. Visited 22 September 2005.
+
+# <span id="page-33-0"></span>**3 NEW ZEALAND LOCAL GOVERNMENT ACT 2002**
+
+#### *3.1 Introduction*
+
+The Local Government Act 2002 is aimed at assuring the present and future social, economic, environmental and cultural welfare of communities (Wilson and Salter 2003). For local government to achieve this objective, it has to provide sustainable roads, which are vital requisites for socio-economic development. Local Authorities are required to have a Long Term Council Community Plan (LTCCP), covering a period of 10 years. The LTCCP encompasses details concerning Local Authorities' policies, management plans, activities, community outcomes, decisions, budget, and finances supported by an audit report. Furthermore, Local Authorities are also required to identify community outcomes at least once every 6 years with the intention to evaluate desired community outcomes, prioritise identified outcomes, quantify accomplishments, and assess community resources.
+
+# *3.2 The Local Government Act 2002*
+
+The 1974 Local Government Act was prescriptive with details on the requirements for roads, land drainage, and waste management (The Department of Internal Affairs 1974). It set out what local authorities must do, what they could do, and how they were to do things. The Act empowered local councils to control, maintain and operate all roads excluding state highways. The provisions relating to roads have been retained in the Local Government Act 2002 (LGA 2002). At the turn of the century, trends have been on annual planning with a formal consultation process for input to proposed activities, service levels, and funding. At this stage community participation is being integrated into the system, thus there is a need for change in the structure.
+
+The Local Government Act 2002, which received Royal acceptance on December 2001, is a major reform. The Act confers generalized power on all local authorities to have full capacity to do anything for the purpose of their role, on behalf of communities. In this context, the purpose of local government is to "enable democratic local decision-making and action by, and on behalf of, communities, and promote the social, economic, environmental, and cultural well-being of communities, in the present and for the future" (Local Government New Zealand 2003).
+
+The fundamental nature of this change is manifested in the detailed decision-making and accountability provisions in Part 6 (Wilson and Salter 2003), emphasizing sustainable outcomes. The 1974 and 2002 Acts empower local councils to build, upgrade and maintain local roads, as they see fit depending on Government requirements and consistent with the community's desire for high quality infrastructure services. It explicitly defines the obligations of local authorities on consultations, defining the nature and use of consultative procedures and identifying and reporting community outcomes, all integrated into a 10-year planning document, the Long Term Council Community Plan (LTCCP). Local authorities are tasked with identifying the outcomes that their communities value through consultation. The local authority duty comes with promoting and delivering services, how it will do so, at what costs, and where funding will be sourced.
+
+Community outcomes in general terms are the expectations in the long-term, encompassing the promotion of social, economic, environmental, and cultural wellbeing of the general public. These are priorities identified by the community, through consultation ensuring a well-designed future appropriate to the local setting. Major considerations for identifying community outcomes are attainability and applicability. The community outcomes are essential for the district council to determine the initiatives and services that should be provided to the community to meet their needs. Services delivered, in all aspects, have specific community outcomes at defined levels of service. The Act empowers councils to be more accountable to their communities by ensuring community outcomes are prioritised in a way that reflects the overall preferences of the community.
+
+The LGA 2002 was prescriptive in the specifying outcomes expected by the community in terms of the service and performance of the road network. Performance targets that address the actual levels of service were observed including the implementation process towards the achievement of the outcomes. Most district councils have included specific outcomes or levels of service in their LTCCPs as far as maintenance management of the roading asset is concerned. These form part of the activities and outputs required to achieve high-level community outcomes.
+
+Activity management plans form part of the LTCCP with community consultation as the basis for inclusion. Local government must constantly balance the multitude of roles that they play. These roles include community advocate, infrastructure service provider, regulator, and promoter of economic development. Local governments are required to remain conscious of the need to clearly separate these various roles and prevent conflicts of interest from arising. The local government's need for a comprehensive asset management program, with community outcomes as its primary concern, emanates from its function as an infrastructure service provider. In order to address the requirements of the Act, local authorities must be armed with asset management tools for it to be efficient and effective. These tools include a database capable of storing and reporting the asset extent and performance measures, coupled with an analysis tool for optimisation and decision-making. Forward works programming (10 years) is required as an input for the LTCCP and Annual Plans (Mitchell and Salter 2003). Local governments are constantly improving their asset management techniques and systems with greater focus on customer service, local government reforms, technical and financial policies, and national legislation.
+
+Section 14, Subpart 2 of Part 2 of the Local Government Act 2002 (Wilson and Salter 2003) describes the principles relating to local authorities in performing their role. It authorises a local authority to "conduct business in an open, transparent and democratically accountable manner and give effect to its identified priorities and desired outcomes in an efficient and effective manner". In doing so, local authorities should carry out transactions according to reliable business practices. It should take into account the opinions and interest of its current and future communities, including opportunities for Maori.
+
+<span id="page-36-0"></span>
+
+The Local Government Act, enacted in 2002, was aimed at assuring the present and future welfare of communities. The LGA 1974 prescribed the requirements for the operation and management of the road network, and these were retained in the LGA 2002. In the new Act, local councils are required to have a 10-year LTCCP wherein the desired community outcomes and expected levels of service of the road network are identified.
+
+The LGA 2002 has changed the regulatory regime for road management providing new requirements to ensure levels of service and desired community outcomes. Because of these changes, performance-based specified maintenance contracts work better as opposed to method-based specifications.
+
+The next chapter will deal with the maintenance management systems used in New Zealand and the Philippines. The evolution of performance-based maintenance contracts will be discussed in detail and will be compared with the traditional method-based specified maintenance contracts.
+
+#### *3.3 References:*
+
+- Local Government New Zealand. (2003). *The Local Government Act 2002: An Overview*, Wellington.
+- Mitchell, P., and Salter, J. (2003). *Seminar on Local Government Act 2002*, New Zealand Law Society. Wellington.
+- The Department of Internal Affairs. (1974). *The Local Government Act 1974, A Guide to Its Operation*, Wellington.
+- Wilson, V., and Salter, J. (2003). *A Guide to the Local Government Act 2002*, Brookers Ltd., Wellington.
+
+# <span id="page-37-0"></span>**4 MAINTENANCE MANAGEMENT SYSTEMS**
+
+#### *4.1 Introduction*
+
+In the 1990's, road controlling agencies throughout the world were innovating to cope with pressures of increasing traffic on the road network and limited funding, for the sustainability of the network. In response to this challenge, New Zealand has been in the forefront in evolving from prescribing method-based specifications to performance-based specifications in the road network maintenance management.
+
+This chapter will differentiate method-based maintenance contracts from performance-based maintenance contracts, giving the advantages and disadvantages of each. A discussion of the evolution of performance-based maintenance contracts and New Zealand and the Philippines is presented.
+
+# *4.2Method-Based Specified vs. Performance-Based Specified Maintenance Contracts*
+
+#### **4.2.1 Method-Based Specified Maintenance Contracts**
+
+A method-based maintenance contract is a traditional procurement model wherein the road controlling authority, referred to as the client, is responsible for managing the network and the maintenance of physical works are outsourced. This requires the client to have sound asset management skills. In this model, the client demands the contractor what work is to be done, when to do it, and the extent of the work. The contractor is paid on the basis of a defined output or quantity accomplished, and the schedule of rates. Risk transfer is very low in this model as the client retains most of the risk involved in the contract. This type of procurement model does not encourage the contractor to innovate, as the client's engineer is required full-time supervision and is responsible for work identification and programming.
+
+#### <span id="page-38-0"></span>**4.2.2 Performance-Based Specified Maintenance Contracts**
+
+Performance specified maintenance contracts (PSMC) are called performance-based specified maintenance contracts (PBSMC) in some road authorities. In this research, it is referred to as PBSMC. Performance-based contracts define what goods and services are required, not how to produce them (Robertson 2003). The expected outcomes are explicitly defined in the contract and paid on a fixed lump sum price.
+
+In this procurement model, the contractor is responsible for all aspects of road asset management, professional services and physical works. As the contractor is in full control of the network, he must know and understand the current condition and future needs of the asset, thus, the contractor will be able to introduce innovations and be proactive in his maintenance management programme. The goal is to prescribe performance specifications that allow contractors to demonstrate their individual expertise, creativity, and resources without controlling them with predetermined methods or processes. Since there is a substantial risk transfer from the client to the contractor, the latter must have strong asset management skills to be able to mitigate the risks involved. The model involves a low level of supervision, requiring only verification of outcomes on the part of the client. The contractor is expected to have more initiative in preparing forward works and programmes, requiring high- level skills and expertise.
+
+#### **4.2.3 Advantages of Performance Specified Maintenance Contracts**
+
+Road authorities are continuously improving in obtaining levels of service that would benefit the stakeholders and road users. Hardy (Hardy 2001) described benefits as "a) the same level of service at a reduced cost or, b) a better level of service at the same cost or, c) a better level of service at a reduced cost". Road agencies in New Zealand and in other countries that are outsourcing maintenance through performance-based specifications, have attested to cost savings from 15 to 38 percent (Porter 2005, Zietlow 2004, Hardy 2001). The cost savings incurred by the client give better value for money. Performance-based specifications increase the probability of achieving best results in terms of products and services at less cost. The model allows the contractor to utilise best practices that give opportunity to determine work processes and improve levels of service. Cost savings, for the road authority, are derived from the need for less supervision and control since the contractor is responsible for the quality control (Zietlow 2004).
+
+Performance specifications are focused not only on the pavement requirements but also on the customers' needs. Since the outcomes are aligned with road user requirements, road users are more proactive in supporting maintenance programmes. With this development, the road agency can have an alliance with customers to evaluate the efficiency and effectiveness of the contractor, and the quality of service delivered.
+
+The level of risk transferred to the contractor increases as the procurement model moves from method specified to performance specified maintenance contracts, thus, reducing the risks of the road agency. Figure 4.1 shows the distribution of risk to road agencies and contractors with the different types of procurement models (Zietlow 2004). At the tendering stage, the contractor is well informed of the possible
+
+![](_page_39_Figure_4.jpeg)
+
+**Figure 4.1. Risk distribution (after Zietlow, 2004)** 
+
+risks involved in project implementation. The contractor is expected to have strong risk assessment and risk management skills and to come up with a comprehensive risk management programme to soften the impact of these risks.
+
+Performance-specified maintenance contracts involve the contractor's innovation and high technical expertise to come up with maintenance programmes that require intervention at the optimum time, with the right activity at the right timing. This will result in the primary benefit of better value for money, cost-savings in terms of <span id="page-40-0"></span>manpower, materials, and equipment, as there is price certainty for a defined level of service.
+
+Improving road condition with the confirmation of savings is one of the important benefits of PBSMC contracts, maintaining a certain level of service over a period of time. The extended term of the contract permits the contractor to experience a sense of ownership of the asset. This increases his initiative to improve the asset by employing and training staff armed with appropriate technical skills.
+
+The move to adopting performance-based specified maintenance contracts permits the reduction of the road agency's staff, as it will be concentrating more on policy formulation and validation of works. The road agency need not maintain road equipment used for in-house maintenance. This will result in further reductions in agency costs.
+
+#### *4.3Performance-Based Maintenance Contracts in New Zealand*
+
+#### **4.3.1 Evolution of Performance-Based Maintenance Contracts**
+
+Outsourced road management and maintenance has been evolving from specifying required inputs to desired outcomes. Porter (2005) described the evolution of highway maintenance contracts, through a value chain in Figure 4.2, which also illustrates the development of maintenance specifications. New Zealand is in the forefront of this new development, followed by most developed countries. Over time, road authorities have expanded contracts from maintenance activities to all attributes of road network management (Porter 2005).
+
+![](_page_40_Figure_7.jpeg)
+
+**Figure 4.2. Value Chain (after Porter, 2005)** 
+
+<span id="page-41-0"></span>About one-third of state highway maintenance in New Zealand is outsourced through PBSMC (Transit New Zealand December 2000) wherein both network management and physical works are contracted for a lump sum price. These long-term contracts, usually 10 years in duration, define outcomes in terms of the levels of service and performance measures. The first performance-based contract in New Zealand was let in 1998 for the maintenance of 406 km of state highways (Zietlow 2004).
+
+Maintenance management of roads has evolved from setting inputs to requiring outcomes, as most road controlling authorities in New Zealand have adopted performance-based specifications. A survey of RCAs was conducted and the results will be discussed further in the next chapter.
+
+#### *4.4 Performance-Based Maintenance Contracts in the Philippines*
+
+#### **4.4.1 Evolution of Performance-Based Maintenance Contracts**
+
+The maintenance management of roads in the Philippines is method-based specifying what work is to be done and how it is done. In the value chain, maintenance management is evolving and moving from left to right. The maintenance by contract projects in the Philippines provided schedules which also specify when maintenance work is to be done. The World Bank funded National Road Improvement and Management Program (NRIMP) has introduced a new procurement model, long-term performance-based maintenance contracts, by way of pilot projects.
+
+Three pilot projects were bid in August 2001, under the civil works component of the World Bank NRIMP:
+
+- 1. LTPBMC 1 Performance-based maintenance, preventive maintenance and maintenance backlog reduction component of Famy-Infanta, Pagsanjan-Luisiana-Tayabas-Junction Lucena Road (109 km);
+- 2. LTPBMC 2a Performance-based maintenance, preventive maintenance and maintenance backlog reduction component of Tiaong-Junction Lucena Road (33 km); and
+
+3. LTPBMC 2b – Performance-based maintenance, preventive maintenance and maintenance backlog reduction component of Pagbilao-Camarines Norte Boundary Road (112 km)
+
+The pilot projects commenced in 2002, with a contract time of 3 years. Under the same loan package from the World Bank, a separate contract for the Consultancy Services for Long Term Performance Based Maintenance was tendered in September 2000.
+
+The road and bridge performance-based maintenance, which included regular routine and periodic maintenance activities, was one of the three components of the pilot projects. The table defining the performance requirements, the response times and penalties for non-compliance, will be examined in Chapter 7.
+
+The construction supervision teams for the pilot projects had undergone training prior to the commencement of the contracts and during the construction period (BCEOM Societe Francaise D'Ingenierie 2005). The administrative, financial, and reporting procedures were established and standardised for all contracts. Much emphasis was given on the performance-based maintenance component of the contract as it was new to the supervising engineers. The assessment of the contractors' non-compliance to performance requirements was important to determine the monthly payment to the contractors.
+
+In its completion report, BCEOM Societe Francaise D'Ingenierie (2005) recommended that more pilot projects in performance-based maintenance, with longer network lengths and extended terms, be considered for future funding.
+
+Two types of maintenance management systems, method-based specified and performance-based specified contracts were described in this chapter. Transit New <span id="page-43-0"></span>Zealand has been moving from requiring inputs to outcomes for the maintenance of the state highway network. Many road authorities in New Zealand have adopted performance-based specifications. The Philippines had implemented three performance-based pilot projects and the consultant has recommended the adoption of PBSMC for future road maintenance.
+
+The results of the survey conducted on local road authorities will be discussed in the following chapter. The next chapter will also investigate the facilitating factors in the adoption of performance-based specified contracts.
+
+#### *4.5 References:*
+
+- BCEOM Societe Francaise D'Ingenierie. (2005). "Completion Report for Consulting Services for the implementation of of the Long-term Performance-Based Maintenance Project." BCEOM Societe Francaise D'Ingenierie. Manila.
+- Hardy, P. "Austroads Review of Performance Contracts: The Potential Benefits of Performance Contracts." *Contracting the Future NZIHT Symposium*, 28.
+- Porter, T. "Procurement Models for Road Maintenance." *Annual Conference of the Transportation Association of Canada*, Calgary, Alberta, Canada, 14.
+- Robertson, D. G. (2003). "How to Develop Performance-Based Specifications." *Government Fleet*(September/October 2003), 12 - 13.
+- Transit New Zealand. (December 2000). "Long Term Procurement Strategy." Transit New Zealand. Wellington.
+- Zietlow, G. (2004). "Implementing Performance-Based Road Management and Maintenance Contracts in Developing Countries-An Instrument of German Technical Cooperation." The document can be retrieved from http://www.zietlow.com.
+
+# <span id="page-44-0"></span>5 **SURVEY OF NEW ZEALAND ROAD CONTROLLING AUTHORITIES**
+
+#### *5.1 Introduction*
+
+A survey of New Zealand road controlling authorities (RCAs) was conducted from September 2004 to May 2005, to verify the systems in place and the procedures used in the management of the maintenance of local road networks. The survey was designed to obtain pertinent data and information regarding the extent of implementation of performance-based specifications among RCAs in New Zealand and was used as a tool to establish the profile of RCAs adopting performance-based specifications.
+
+A structured questionnaire (Appendix 1) was sent to 52 of the total of 74 RCAs in New Zealand. The first part of the survey comprised questions related to the RCAs' organisations, which included functions and duties of personnel directly involved in the management of the maintenance of local road networks. The second part consisted of questions pertaining to specifications used, as well as the development and frequency of the revision of maintenance specifications. The third and fourth parts of the survey included questions relative to the typical maintenance activities performed on the road network and the evaluation of contractors' work, respectively.
+
+Roading asset managers or personnel in charge of the maintenance of unsealed lowvolume roads were the target respondents of this survey. The RCAs were chosen on the basis of having a significant length (at least 100 km) of unsealed low-volume roads to maintain. The survey had a response of 80%. Forty responses were returned out of the 52 surveys sent. The 40 responses were used to sort the RCAs into (1) those that had adopted performance-based specifications, identified as the PBS group, and (2) those that still employed method specifications in the maintenance of unsealed low-volume roads (Table 5.1), identified as the MBS group. One RCA returned the questionnaire unanswered, noting that the questions were too broad while another RCA sent a letter expressing regret that they did not have available time or resources to complete the survey due to staffing shortages.
+
+The research was qualitative in nature. Questions in the survey were open-ended and designed for the respondents to indicate their views and insights on maintenance management systems for unsealed low-volume roads. Some ambiguities in the responses were resolved by reading through available electronic resources [27](#page-45-0) , particularly the Long Term Council Community Plans (LTCCP) of the Territorial Local Authorities (TLAs).
+
+RCAs were classified based on the responses in the survey questionnaire, stressing responses in Question 11 (Appendix 1) wherein typical maintenance activities performed on unsealed roads were listed. RCAs identified what triggered or initiated these maintenance activities and the frequency at which these activities were performed. On one hand, maintenance activities executed on a cyclic basis and with definite schedules are most likely to be carried out by RCAs employing methodbased specifications. On the other hand, maintenance activities that are dependent on road conditions and service expected of the network are performed by RCAs using performance-based specifications. Some RCAs indicated in the questionnaire the type of maintenance delivery used, thus facilitating their classification. At least 8 RCAs returned the completed questionnaire with sample performance-based specifications used in their maintenance contracts.
+
+Table 5.1 shows a significant number of RCAs in both the North Island and South Island were using performance-based specifications for the maintenance of the local
+
+**Table 5.1. RCA grouping.** 
+
+|                 | Number<br>of<br>RCAs | Percentage<br>of<br>respondent<br>RCAs | Maintenance<br>Delivery        | Number<br>of<br>RCAs | Percentage of<br>RCAs per<br>Island |
+|-----------------|----------------------|----------------------------------------|--------------------------------|----------------------|-------------------------------------|
+| North<br>Island | 25                   | 63                                     | Method<br>Specified (MBS)      | 4                    | 16                                  |
+|                 |                      |                                        | Performance<br>Specified (PBS) | 21                   | 84                                  |
+| South<br>Island | 15                   | 37                                     | Method<br>Specified (MBS)      | 3                    | 20                                  |
+|                 |                      |                                        | Performance<br>Specified (PBS) | 12                   | 80                                  |
+
+<span id="page-45-0"></span><sup>27</sup> [http://www.localcouncils.govt.nz](http://www.localcouncils.govt.nz/). The Department of Internal Affairs. Local Councils. LTCCP. Visited 15 June 2005.
+
+<span id="page-46-0"></span>road network. As mentioned in Chapter 4, about one-third of the state highways in New Zealand employed performance-based specifications. This is an indication that road authorities in New Zealand were moving from method-specified contracts toward performance-based contracts.
+
+# *5.2 Contributing Factors in the Adoption of Performance-Based Specifications*
+
+The items presented in Table 5.2 could be potential contributing factors for the adoption of performance-based specifications or could possibly reveal impedances to adopting performance-based specifications. Contributing factors were derived from an analysis of the responses to the survey questionnaire and data from Statistics New Zealand, including road length, population, land area, roading expenditure and revenue.
+
+In context, these contributing factors also may be classified as internal and external, based on how they are controlled. Internal factors are those that are directly controlled by the organisation while external factors are those that cannot be controlled by the organisation (Robinson *et al*. 1998). Factors 1 to 6 are the internal contributing factors. Those remaining in the list are classified as external contributing factors.
+
+It was desirable to divide RCAs into PBS accepting and PBS rejecting groups on some objective numerical basis for each external factor (7-16). The division was made using the measures of central tendency in statistics, which are the mean, the true median, and the value midway between the minimum and maximum observed values. The three options were considered because there had to be a consistent, statistically driven and impartial solution to distinguish one group from the other. By using the three simple statistical characteristics, a consistent and valid basis for comparison for each of the different categories was established.
+
+The difference of percentage between the PBS RCAs and MBS RCAs were determined in each analysis. The researcher cannot give arbitrary boundaries for each factor because the differences will depend on the values selected as boundaries. An arbitrary boundary cannot be justified because of the different criterion for each of the factors and dissimilar units of measurement. An objective basis was sought to discriminate the factors.
+
+**Table 5.2. Contributing Factors** 
+
+| Factor<br>No. | Contributing Factors                      | Description                         |
+|---------------|-------------------------------------------|-------------------------------------|
+| 1             | Asset Managers                            | employ asset managers               |
+| 2             | Consultant                                | outsource consultancy services      |
+| 3             | RAMM                                      | utilise RAMM as a management tool   |
+| 4             | Customer Survey                           | conduct customer surveys            |
+|               |                                           | TNZ 'C' Specifications              |
+| 5             | Specifications Used                       | Modified TNZ'C' Specifications      |
+|               |                                           | RCAs own maintenance specifications |
+| 6             |                                           | compliance to specifications        |
+|               |                                           | audits/inspections                  |
+|               | Evaluation of Work<br>Accomplished        | marking/scoring system              |
+|               |                                           | ratepayer's feedback                |
+|               |                                           | 6 monthly performance reviews       |
+| 7             | Annual Maintenance<br>Expenditure/road km | < \$xx,xxx                          |
+| 8             | Rates/road km                             | < \$x,xxx                           |
+| 9             | Revenue/road km                           | < \$xx,xxx                          |
+| 10            | % Rural Road                              | > xx%                               |
+| 11            | % Unsealed Rural Road                     | > xx%                               |
+| 12            | Total % Unsealed Road                     | > xx%                               |
+| 13            | Road Length per Engineer<br>(km/engineer) | > xxx km/engineer                   |
+| 14            | Road Density<br>(km/km2<br>)              | < xx (km/km2<br>)                   |
+| 15            | Population Density<br>(persons/ km2<br>)  | < xx (persons/ km2<br>)             |
+| 16            | Persons/road km                           | < xx (persons/ road km)             |
+
+<span id="page-48-0"></span>In the end, a compelling argument could not be assembled, but all possibilities were explored and the researcher believed that comparing the results of the three options was the best approach to deal with the problem. The argument is weak as it is sensitive to what exactly is the boundary. It may possibly be the mean, the median, or the value midway between the minimum and maximum, but these options showed fairly consistent results.
+
+One RCA was excluded in the analysis of external contributing factors because the results were biased. The situation and conditions of this RCA are different from the rest of the group that makes the results unjustifiable. The values for the contributing factors of this RCA are opposites with the values of the other RCAs in the group.
+
+#### **5.2.1 Internal Contributing Factors**
+
+Internal contributing factors in the survey results are those over which the roading authority is perceived to have control. These contributing factors include the services of an asset manager, outsourcing of consultants, using the RAMM as an asset management tool, conducting customer surveys, and developing specifications. They have a great impact on the management of the maintenance of the road network.
+
+#### **5.2.1.1 Asset Managers**
+
+The two groups show a significant difference in employment of asset managers in the organisation. A substantial number of RCAs in the PBS Group have asset managers to oversee operations and control roading assets. Roading engineers, roading supervisors, contract managers, contract supervisors, works managers, rural roading engineers, area engineers and consultants are under the supervision of an asset manager in 64% of the RCAs in the PBS group as shown in Table 5.3, whereas, only 29% of the RCAs in the MBS group are supervised by an asset manager. Figure 5.1 shows the duties of the positions related to maintenance of roads as stated in the questionnaire responses. The MBS RCAs conducted more inspections and audits than the PBS RCAs. The PBS RCAs concentrated more on administering contracts, supervision and management. The specific functions of the asset managers include:
+
+- <span id="page-49-0"></span>1. Authorising works
+- 2. Financial control of physical works, setting and managing budgets
+- 3. Monitoring expenditures
+- 4. Approving and certifying payments
+- 5. Management/overall fiscal control
+
+The survey results show a very low percentage of PBS RCAs performing QA audits which suggest that this duty is passed on to the consultant and contractor in a performance-base specified contract. All of the MBS RCAs give more importance to inspections and audits rather than supervision and management.
+
+![](_page_49_Figure_7.jpeg)
+
+**Figure 5.1. Reported duties of personnel in-charge of road maintenance.**
+
+#### **5.2.1.2 Consultants**
+
+Survey results revealed that more than half of the PBS group used consultants outsourced by councils, whereas this figure was 29% for the MBS RCAs (Table 5.3). Services of consultants were engaged where specialist skills were required. Consultants were employed to prioritise and identify projects, manage maintenance <span id="page-50-0"></span>contracts, manage budgets, conduct random audits and regular inspections, develop specifications, and monitor levels of service.
+
+#### **5.2.1.3 Road Asset Maintenance Management**
+
+The use of the Road Asset Maintenance Management (RAMM) system as a technical management tool by most RCAs in the PBS Group (64%) conformed to the recognition of asset managers as a primary contributing factor based on the survey results (Table 5.3). RAMM software is mainly inventory database storage for road structures, drainage and surfacing plus condition data including skid resistance, rutting, and cracking. It contains the treatment selection algorithm (TSA), plus national optimisation of maintenance allocation by decade (NOMAD), which stores the 10 year forward works program (Transit New Zealand 1996a). The TSA was made to indicate which works should be performed in the coming year. RAMM databases are essential for the long term council community plan (LTCCP) as embodied in the Local Government Act 2002 (Wilson and Salter 2003), and are used to support applications for maintenance funding through Transfund's National Land Transport Program. Transfund's Performance Monitoring Group is tasked to review the databases as to their integrity, validity, comparison to actual road conditions, and to evaluate staff competency (Merrifield 2004). This will ensure that RCAs have good quality data that can be relied upon.
+
+#### **5.2.1.4 Customer Surveys**
+
+Table 5.3 shows that a great proportion of RCAs in the PBS Group (85%) relied on customer surveys. In contrast, 57% of RCAs in the MBS Group did the same. These PBS RCAs recognised the importance of ratepayers' opinions on the maintenance of the roading network. Customer surveys, conducted and analysed monthly, quarterly, yearly or at random are measures of the performance of key players in the maintenance of roads and performance of the network.
+
+<span id="page-51-0"></span>**Table 5.3. Values of internal contributing factors based on survey.** 
+
+| Factor<br>No. | Contributing<br>Factors | Description                                    |        | RCAs using<br>Method<br>Specifications | RCAs using<br>Performance<br>based<br>Specifications |                     |
+|---------------|-------------------------|------------------------------------------------|--------|----------------------------------------|------------------------------------------------------|---------------------|
+|               |                         |                                                | 7 RCAs |                                        | 33 RCAs                                              |                     |
+|               |                         |                                                | Number | % of<br>MBS<br>RCAs                    | Number                                               | % of<br>PBS<br>RCAs |
+| 1             | Asset Managers          | - employ asset<br>managers                     | 2      | 29                                     | 21                                                   | 64                  |
+| 2             | Consultant              | - outsource<br>consultancy services            | 2      | 29                                     | 18                                                   | 55                  |
+| 3             | RAMM                    | - utilise RAMM as a<br>management tool         | 2      | 29                                     | 21                                                   | 64                  |
+| 4             |                         | Customer Surveys - conduct customer<br>surveys | 4      | 57                                     | 28                                                   | 85                  |
+
+#### **5.2.1.5 Specifications**
+
+This contributing factor was divided into three sub-groups as shown in Figure 5.2: (1) reliance on Transit New Zealand (TNZ) "C" Standard Specifications; (2) reliance on TNZ "C" Specifications – modified to suit local network conditions and conform to council requirements; and (3) RCAs with their own maintenance contract specifications – developed from local knowledge and experience of engineers, consultants and contractors; a collaboration of experts and resources. Review of specifications is vital before the next tendering period to incorporate changes in technology, new trends, changes in environment, best practices of other RCAs, and in conjunction with an assessment of community expectations.
+
+The figures in this factor show a distinction between the two regimes for specifications. A significant percentage of RCAs, 85% in the MBS group, had either TNZ "C" specifications or modified TNZ "C" specifications. Only 14% had their own maintenance contract specifications. With the PBS adopters, almost half had their own maintenance contract specifications and none of them used the TNZ "C" specifications any longer. They had some sort of maturity of the specifications, using either modified specifications or new ones.
+
+![](_page_52_Figure_1.jpeg)
+
+**Figure 5.2. Contract Specifications.**
+
+An analysis of the survey responses on the development and improvement of maintenance specifications by New Zealand road controlling authorities is presented in Figure 5.3. The specifications were continuously modified to suit local conditions and desired outcomes, incorporating expertise and experience of technical people involved, best practices and new trends. Figure 5.4 shows the frequency of revisions
+
+![](_page_52_Figure_4.jpeg)
+
+**Figure 5.3. How specifications were developed.** 
+
+<span id="page-53-0"></span>in specifications by RCAs from the survey results. Almost 40% of RCAs in the PBS group revised their maintenance specifications as required. The other RCAs had definite schedules for review and revision, between 3 to 5 years. About 10% revised the specifications after the contract period or when there is a new contract.
+
+![](_page_53_Figure_2.jpeg)
+
+**Figure 5. 4. Frequency of revisions in specifications.** 
+
+#### **5.2.1.6 Evaluation of performance of contractor**
+
+Figure 5.5 shows the mode of assessing the contractor's performance. Method specified contracts rely on monthly audits and regular site inspections more than performance-specified contracts. Evaluation of the contractor is based only on the contractor's compliance to contract specifications. Both procurement models give importance to ratepayer's feedback and 6-monthly performance reviews. In performance-specified contracts, the contractor is responsible for conducting inspections, and the engineer validates the contractor's report, giving scores for the work accomplished. This matrix can be the basis for incentives, penalties, and computation of monthly billing. A good performance by the contractor is an indication that the procurement model used is effective.
+
+<span id="page-54-0"></span>![](_page_54_Figure_1.jpeg)
+
+**Figure 5.5. Evaluation of contractor's work.** 
+
+#### **5.2.2 External Contributing Factors**
+
+The external contributing factors were identified based on road statistics, population, and land area of TLAs[28](#page-54-1). These contributing factors were classified as such because RCAs cannot influence or manipulate the values of these contributing factors. The computation of boundaries for each of the external contributing factors was discussed in Section 5.2. Tables 5.4, 5.5, and 5.6 show the summary of contributing factors based on the survey and on data from Statistics New Zealand2 and local councils[29](#page-54-2) using the mean, the median and the value midway between the minimum and the maximum observed values, respectively. The values in these tables were used to identify any patterns there might be for RCAs that have adopted performance-based specifications. In this case, a comparison was made on the percentage differences of MBS RCAs and PBS RCAs using the three options, for each of the external contributing factors. A summary of the percentage differences, which were ranked accordingly, is presented in Table 5.7.
+
+<span id="page-54-1"></span><sup>28</sup> [http://www.stats.govt.nz](http://www.stats.govt.nz/). Statistics New Zealand. Statistics by Territorial Local Authority. Visited 18 July 2005.
+
+<span id="page-54-2"></span><sup>29</sup> [http://www.localcouncils.govt.nz](http://www.localcouncils.govt.nz/). Local Councils. LTCCP. Visited 15 June 2005.
+
+**Table 5.4. Values of contributing factors using themean.** 
+
+| Factor<br>No. | Contributing Factors                       | Mean     |        | RCAs using Method<br>Specifications<br>(6 RCAs) |        | RCAs using<br>Performance-based<br>Specifications<br>(33 RCAs) | Diffe<br>rence |
+|---------------|--------------------------------------------|----------|--------|-------------------------------------------------|--------|----------------------------------------------------------------|----------------|
+|               |                                            |          | Number | % of MBS<br>RCAs                                | Number | % of PBS<br>RCAs                                               | %              |
+| (1)           | (2)                                        | (3)      | (4)    | (5)                                             | (6)    | (7)                                                            | 5-7            |
+| 7             | Annual Maintenance<br>Expenditure /road km | < \$7690 | 5      | 83                                              | 18     | 55                                                             | 28             |
+| 8             | Rates/road km                              | < \$3710 | 4      | 67                                              | 19     | 58                                                             | 9              |
+| 9             | Revenue/road km                            | < \$8350 | 4      | 67                                              | 18     | 55                                                             | 12             |
+| 10            | % Rural Road                               | > 86.83% | 3      | 50                                              | 21     | 64                                                             | 14             |
+| 11            | % Unsealed Rural<br>Roads                  | > 50.35% | 3      | 50                                              | 17     | 52                                                             | 2              |
+| 12            | Total % Unsealed Road                      | > 44.61% | 3      | 50                                              | 17     | 52                                                             | 2              |
+| 13            | Road Length per<br>Engineer (km/engineer)  | > 628.33 | 4      | 67                                              | 13     | 40                                                             | 27             |
+| 14            | Road Density (km/km2<br>)                  | < 0.38   | 3      | 50                                              | 17     | 52                                                             | 2              |
+| 15            | Population Density<br>(persons/ km2<br>)   | < 10.29  | 4      | 67                                              | 20     | 61                                                             | 6              |
+| 16            | Persons/road km                            | < 24.24  | 4      | 67                                              | 18     | 55                                                             | 12             |
+
+**Table 5.5. Values of contributing factors using the median.** 
+
+| Factor<br>No. | Contributing Factors                       | Median   |        | RCAs using Method<br>Specifications<br>(6 RCAs) |        | RCAs using<br>Performance-based<br>Specifications<br>(33 RCAs) | Diffe<br>rence |
+|---------------|--------------------------------------------|----------|--------|-------------------------------------------------|--------|----------------------------------------------------------------|----------------|
+|               |                                            |          | Number | % of MBS<br>RCAs                                | Number | % of PBS<br>RCAs                                               | %              |
+| (1)           | (2)                                        | (3)      | (4)    | (5)                                             | (6)    | (7)                                                            | 5-7            |
+| 7             | Annual Maintenance<br>Expenditure /road km | < \$7010 | 4      | 67                                              | 16     | 48                                                             | 19             |
+| 8             | Rates/road km                              | < \$3380 | 4      | 67                                              | 16     | 48                                                             | 19             |
+| 9             | Revenue/road km                            | < \$7030 | 4      | 67                                              | 16     | 48                                                             | 19             |
+| 10            | % Rural Road                               | > 89.26% | 5      | 83                                              | 18     | 55                                                             | 28             |
+| 11            | % Unsealed Rural<br>Roads                  | > 51.70% | 3      | 50                                              | 17     | 52                                                             | 2              |
+| 12            | Total % Unsealed Road                      | > 45.07% | 3      | 50                                              | 17     | 52                                                             | 2              |
+| 13            | Road Length per<br>Engineer (km/engineer)  | > 550    | 4      | 67                                              | 15     | 45                                                             | 22             |
+| 14            | Road Density (km/km2<br>)                  | < 0.37   | 3      | 50                                              | 16     | 48                                                             | 2              |
+| 15            | Population Density<br>(persons/ km2<br>)   | < 6.76   | 4      | 67                                              | 15     | 45                                                             | 22             |
+| 16            | Persons/road km                            | < 21.49  | 4      | 67                                              | 16     | 48                                                             | 19             |
+
+**Table 5.6. Values of contributing factors using midway between the minimum and maximum.** 
+
+| Factor<br>No. | Contributing Factors                       | RCAs using<br>Midway<br>RCAs using Method<br>Performance-based<br>(Min &<br>Specifications<br>Specifications<br>Max)<br>(6 RCAs)<br>(33 RCAs) |        |                  | Diffe<br>rence |                  |     |
+|---------------|--------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------|--------|------------------|----------------|------------------|-----|
+|               |                                            |                                                                                                                                               | Number | % of MBS<br>RCAs | Number         | % of PBS<br>RCAs | %   |
+| (1)           | (2)                                        | (3)                                                                                                                                           | (4)    | (5)              | (6)            | (7)              | 5-7 |
+| 7             | Annual Maintenance<br>Expenditure /road km | < \$9910                                                                                                                                      | 5      | 83               | 25             | 76               | 7   |
+| 8             | Rates/road km                              | < \$5790                                                                                                                                      | 6      | 100              | 27             | 82               | 18  |
+| 9             | Revenue/road km                            | < \$1093                                                                                                                                      | 5      | 83               | 24             | 73               | 10  |
+| 10            | % Rural Road                               | > 78.79%                                                                                                                                      | 6      | 100              | 27             | 82               | 18  |
+| 11            | % Unsealed Rural<br>Roads                  | > 47.80%                                                                                                                                      | 5      | 83               | 19             | 58               | 25  |
+| 12            | Total % Unsealed Road                      | > 44.44%                                                                                                                                      | 4      | 67               | 17             | 52               | 15  |
+| 13            | Road Length per<br>Engineer (km/engineer)  | > 891.43                                                                                                                                      | 3      | 50               | 5              | 15               | 35  |
+| 14            | Road Density (km/km2<br>)                  | < 0.40                                                                                                                                        | 3      | 50               | 19             | 58               | 8   |
+| 15            | Population Density<br>(persons/ km2<br>)   | < 17.36                                                                                                                                       | 4      | 67               | 27             | 82               | 15  |
+| 16            | Persons/road km                            | < 35.38                                                                                                                                       | 4      | 67               | 25             | 76               | 9   |
+
+Ranking the contributing factors using the three options, Table 5.7, shows fairly consistent findings. The ranking had been investigated further to find out which of the contributing factors are constantly within the top 3, top 4, and top 5 of the list.
+
+**Table 5.7. Ranking the contributing factors using three options.** 
+
+|      |            | Mean       | Median     |            |            | Midway (Min & Max) |
+|------|------------|------------|------------|------------|------------|--------------------|
+| Rank | Factor No. | Difference | Factor No. | Difference | Factor No. | Difference         |
+| 1    | 7          | 28         | 10         | 28         | 13         | 35                 |
+| 2    | 13         | 27         | 13         | 22         | 11         | 25                 |
+| 3    | 10         | 14         | 15         | 22         | 8          | 18                 |
+| 4    | 9          | 12         | 7          | 19         | 10         | 18                 |
+| 5    | 16         | 12         | 8          | 19         | 12         | 15                 |
+| 6    | 8          | 9          | 9          | 19         | 15         | 15                 |
+| 7    | 15         | 6          | 16         | 19         | 9          | 10                 |
+| 8    | 11         | 2          | 11         | 2          | 16         | 9                  |
+| 9    | 12         | 2          | 12         | 2          | 14         | 8                  |
+| 10   | 14         | 2          | 14         | 2          | 7          | 7                  |
+
+In investigating the data, it was found there are big differences in the percentage of MBS RCAs and PBS RCAs in three out of three cases for contributing factor 13 (road length per engineer) and two out of three cases for contributing factor 10 (% rural road), when the top three factors were considered. Contributing factors 10 and 13 came out in all three cases when the top four were analysed, whereas, contributing factor 7 (annual maintenance expenditure/road km) appeared in two out of three cases. It was also observed on the next level ranking that contributing factors 9 (revenue/road km) and 8 (rates/road km) turned up in two out of three cases.
+
+It appeared in the analysis that a greater percentage of the RCAs adopting performance-based specifications had more percentage rural roads than the rejectors (MBS RCAs). The adopters of performance-based specifications, PBS RCAs, seem to be associated with having less road length per engineer. The adopters had more engineers to oversee road network maintenance since they have more remote roads as seen in the rural road percentage. This implies that RCAs in the PBS group have more resources, illustrated by the number of engineers involved in the maintenance of local roads. Engineers of RCAs in the MBS group had a greater length of road to look after and may not have had the time or inclination to make the change to performance-based specifications.
+
+The PBS RCAs seemed to have higher rates and revenue per road kilometre. Consequently, the annual maintenance expenditure per road kilometre was higher than that of the MBS RCAs.
+
+Chapter 5 presented the survey of road controlling authorities. The survey responses were used to identify those RCAs that had adopted performance-based specifications and those that still use method specifications. The contributing factors, both internal and external were discussed.
+
+In observing the PBS RCAs, it was found that they had more resources in terms of rates and revenues. They placed more importance on the whole road network as they <span id="page-58-0"></span>spent more money, had asset managers, engaged consultants for specialised skills, employed more engineers, had highly developed specifications and conducted customer surveys.
+
+In general, it is implied that the RCAs that are more likely to adopt performancebased specifications will have the following characteristics:
+
+- 1. Employ asset managers to be in charge of the overall maintenance of the roading network;
+- 2. Outsource consultants providing specialist skills;
+- 3. Use maintenance management tools like RAMM;
+- 4. Conduct customer surveys to know ratepayers' opinions, thus, validating the effectiveness and efficiency of the maintenance of the network;
+- 5. Have written and modified their own maintenance specifications;
+- 6. Have more resources in terms of rates and revenue per road kilometre;
+- 7. Have more annual maintenance expenditure per road kilometre;
+- 8. Have a higher percentage of rural roads;
+- 9. Have less road length per engineer;
+- 10. Evaluate contractor's accomplishments on the basis of performance required of the road network by using a marking and scoring system.
+
+The contributing factors and the possible impeding factors have been discussed. These factors will be used in the following chapter to set the atmosphere for the transition stage in the Philippines, managing change from the prescriptive method specifications to performance-based specifications.
+
+# *5.3 References:*
+
+Merrifield, R. (2004). "RAMM databases to be reviewed." Transfund News, Issue 61. Wellington.
+
+Robinson, R., Danielson, U., and Snaith, M. (1998). *Road Maintenance Management*, Palgrave, New York.
+
+- Transit New Zealand. (1996). *State Highway Asset Management Manual*, Transit New Zealand, Wellington.
+- Wilson, V., and Salter, J. (2003). *A Guide to the Local Government Act 2002*, DSL Publishing, Wellington.
+
+# <span id="page-60-0"></span>**6 TRANSITION – MANAGING CHANGE**
+
+#### *6.1 Introduction*
+
+The internal and external contributing factors for the adoption of performance-based maintenance contracts in New Zealand were investigated and analysed in the previous chapter. Subsequent sections will discuss the transition stage, managing the change from method specifications to performance-based specifications in the Philippines.
+
+The Department of Pubic Works and Highways (DPWH) in the Philippines initiated reforms in the operation and management of the road network with the inception of the Road Information and Management Support System (RIMSS) in 1997. Through the World Bank funded National Roads Improvement Project (NRIMP), three longterm performance-based maintenance pilot projects were implemented in 2002. Performance-based maintenance, which included routine and periodic maintenance activities, was one of the three components for these pilot projects. The other two components included annual preventive maintenance and maintenance back-log reduction.
+
+The researcher gathered first-hand information on the on-going reforms in the DPWH through a meeting with Director B. Elizabeth E. Yap, RIMSS-PO Deputy Project Director and Diane Wacker of D.Michael Cleary and Partners, Inc., RIMSS Integration and Coordination Consultant. The meeting was held at the office of Director Yap, DPWH-Central Office, Manila, on 14 December 2005. An interview was also conducted with the project engineer of pilot project LTPBMC 2a, Engineer Ernante Antonio of the DPWH-Bureau of Maintenance, where the researcher obtained feedback on the implementation of the performance-based maintenance pilot projects. The interview was conducted on 14 December 2005 at the DPWH-Bureau of Maintenance, Manila.
+
+### <span id="page-61-0"></span>*6.2 Internal Factors*
+
+#### **6.2.1. Asset Managers**
+
+The role of an asset manager in road authorities in the Philippines to oversee the management of roading assets is important. The asset manager has total operational and fiscal control of roads. The role of the asset manager includes defining activities, planning, allocating resources, organising and motivating personnel, controlling work, monitoring and evaluating performance and feeding back results to seek improvement (Robinson et al. 1998). In the Philippine setting, these functions are present in the Central, Regional and District offices of the DPWH and local road authorities, however, these tasks are performed separately by specialised staff under the supervision of the Head of Office. Consolidation of these functions, to be handled by an individual, is necessary for effective and efficient management of the roading asset.
+
+Roads have to be maintained in an acceptable condition to obtain value for money and to reduce vehicle operating costs. This is where the role of a roading asset manager comes in, to identify and prioritise projects within a given budget without compromising the needs and safety of stakeholders.
+
+#### **6.2.2 Consultants**
+
+There are a number of consulting firms, both domestic and foreign, that offer professional services for the management of roads in the Philippines. Under Republic Act Number 9184, the client is assured high quality service as these consultants are accredited and monitored by an umbrella of consulting organizations, the Confederation of Filipino Consulting Organizations (COFILCO) [30](#page-61-1) . Member
+
+ 30 http://www.cofilco.org/about.asp. Confederation of Filipino Consulting Organizations. Visited 23 September 2005.
+
+<span id="page-61-1"></span>
+
+<span id="page-62-0"></span>consulting firms that offer professional services for the management of roads include the following:
+
+- Council of Engineering Consultants, Inc. (CECOPHIL) composed of corporations which include domestic and foreign consultants
+- Association of Consultant Civil Engineers of the Philippines, Inc. composed of consulting firms principally engaged in branches of civil engineering including roads, bridges, portworks, etc.
+- Construction Project Managers Association of the Philippines, Inc. specializes in construction management and supervision of infrastructure projects.
+
+There are many local consultants in the Philippines but most lack skills in asset management. The local consultants have to compete with foreign consultants. Most consultancy services in the DPWH are awarded to foreign consultants because of the expertise and advanced technology these consultants introduce to the road agency. The employment of foreign consultants is usually one of the conditions for foreignfunded projects or foreign loans. In some cases, foreign consultants are awarded contracts because they are pre-qualified for bidding, and local contractors cannot compete with them because of a lack of resources and experience. With this situation in the Philippines, strengthening the local consulting industry is imperative to make them competitive in the industry. Employing local consultants will help local employment and at the same time save costs on foreign exchange.
+
+#### **6.2.3 Road Asset Maintenance Management**
+
+Roading asset managers in New Zealand currently use the Road Asset Maintenance Management (RAMM) system as a technical management tool having high quality inventory data covering road network conditions and history of maintenance activities. Likewise, the Road Information Management and Support System (RIMSS)[31](#page-62-1) project was developed in the Philippines to improve support for decisionmaking through the provision of modern analytical tools and efficient modern
+
+<span id="page-62-1"></span><sup>31</sup> [www.dpwh.gov.ph/reforms/rimss/index.htm](http://www.dpwh.gov.ph/reforms/rimss/index.htm). Department of Public Works and Highways. RIMSS Overview. Visited 7 September 2005.
+
+information technology. The DPWH is now in the process of training engineers in pavement management systems (PMS), which provide needs analyses, multi-year programming and budgeting. They are used for evaluating various scenarios and generating data required for long-term plans for road development and preservation. The extent of implementation of PMS will depend greatly on the availability of traffic and road condition data, which is available through the Road and Bridge Information Application [32](#page-63-0) (RBIA) of the DPWH. Domingo (2002) developed a simple and practical PMS for the local road network in the Philippines. The proposed PMS included techniques on prioritising road maintenance projects using the pavement condition index, taking into consideration the severity and type of distress.
+
+RBIA has information related to inventory consisting of the visual condition assessment, roughness, video imaging, pavement strength, pavement thickness, centreline survey, and skid resistance (Department of Public Works and Highways March 2004). The challenge faced by the DPWH was the expense of outsourcing the collection of special surveys, which was expensive. The special surveys that need specialised equipment are those like roughness, centreline surveys, highway imaging, local referencing of road and bridges, pavement strength, pavement thickness, and skid resistance (Department of Public Works and Highways April 2004). The consultant looked into in-house data collection for some of the special surveys but did not have great success due to logistical problems: there was sufficient training of DPWH engineers to collect data but the available equipment were not well maintained, and/ or there were problems obtaining equipment with the basic requirements (e.g. vehicle with odometer). In some field offices, data collection had not been finished for a cycle (usually 1 year), and they were already behind in the next cycle. The DPWH thus opted to outsource special surveys to consultants or contractors.
+
+The availability of relevant, up-to-date, and accurate inventory data of the road network is imperative, not only for the road authority but also for the contractor. The road agency uses the data to benchmark the condition of the network at the beginning of the contract. The data can be used to assess the risks transferred to the contractor
+
+<span id="page-63-0"></span><sup>32</sup> [http://www.dpwh.gov.ph/imprvmnt\\_areas/road-bridge\\_info.htm](http://www.dpwh.gov.ph/imprvmnt_areas/road-bridge_info.htm)**.** Department of Public Works and Highways. Road and Bridge Information Application. Visited 31 January 2006.
+
+<span id="page-64-0"></span>with the implementation of a performance-based contract, and find ways to mitigate them. At the tendering stage, the contractor must know the present condition of the network and understand the risks involved.
+
+#### **6.2.4 Customer Surveys**
+
+The DPWH has a Complaints and Action Center (CAAC) to receive complaints, queries, requests for assistance, opinions, suggestions and recommendations. The CAAC is a means of reaching out to the public and encouraging interaction with stakeholders. Obtaining data through CAAC is one way of improving service delivery to the public. To give meaning to these data, the DPWH should encourage CAAC to conduct and analyse customer surveys to determine significant changes in the system. Results from the analyses are useful tools for roading asset managers to evaluate the effectiveness and efficiency of the management systems.
+
+The Secretary of the DPWH recognised the importance of customer's views on the management of the roading asset. He said that "In pursuing the national infrastructure plans and programs, the DPWH will continue to rely on the voice of the people and turn concerns into opportunities for better management strategies."[33](#page-64-1)
+
+It is acknowledged that involving ratepayers in the maintenance management of the road network is important to obtain feedback. At the same time, the road users and other stakeholders (i.e. politicians) ought to be well informed and educated on the implementation of performance-based maintenance contracts. The road users have to know what to expect from the road agency and the contractor.
+
+#### **6.2.5 Specifications**
+
+The DPWH has three types specifications used for the maintenance of national roads and still uses the activity standards on the Philippine Highway Maintenance Management System for routine maintenance.
+
+<span id="page-64-1"></span> 33[http://www.dpwh.gov.ph/News/2005/apr%20may%20jun.asp#road%20confab.](http://www.dpwh.gov.ph/News/2005/apr may jun.asp#road%20confab) Department of Public Works and Highways. DPWH Chief stresses Quality Roads during Road Engineers Confab. Visited 15 October 2005.
+
+The DPWH has its standard specifications (Department of Public Works and Highways 1995) for the construction and maintenance of national roads, widely adopted by local road authorities. The specifications are prescriptive, giving details on the methods of construction, materials, equipment and basis of payment for specific items of work. The standard specifications, generally known as "the Blue Book", come in three volumes. Volume 2, specifically for highways, bridges, and airports, comprises nine parts.
+
+- 1. Part A Facilities for the Engineer, which includes offices, laboratories, vehicles and assistance to the engineer;
+- 2. Part B Other General Requirements such as offices, shops, stores and workmen's accommodation for the contractor, and medical room and first aid facilities;
+- 3. Part C Earthwork;
+- 4. Part D Subbase and Base Course;
+- 5. Part E Surface Courses;
+- 6. Part F Bridge Construction;
+- 7. Part G Drainage and Slope Protection Structures;
+- 8. Part H Miscellaneous Structures;
+- 9. Part I- Materials Details.
+
+The specifications in the Blue Book were used for maintenance activities or items of work not covered in the activity standards[34](#page-65-0) for the Philippine Highway Maintenance Management System. The specifications and activity standards are used for in-house routine maintenance, periodic maintenance, and small maintenance contracts involving combined routine and periodic work. The activity standards provide details on the description, purpose, and scheduling of maintenance activities. They are prescriptive as they give particulars to the typical crew, typical equipment, typical materials and typical work methods for maintenance activities.
+
+<span id="page-65-0"></span><sup>34</sup> Ministry of Public Works and Highways. Revised 1985. List of Activity Standard on the New Highway Maintenance Management System.
+
+<span id="page-66-0"></span>The Bureau of Maintenance of the DPWH had been using specifications which formed part of the Maintenance by Contract Manual (Kampsax International A/S 1991). Section K of the manual has 42 method specifications for the maintenance of unpaved road and shoulder surfaces, bituminous surfaces, concrete surfaces, base materials, and replacement of pavement. The specifications were used for the implementation of routine and periodic maintenance by contract projects.
+
+The consultant for the study on the long-term performance-based maintenance contracts (LTPBMC), Kampsax International, developed performance-based specifications for the pilot projects in the Philippines [35](#page-66-1) . The performance-based specifications were included in the study conducted by Kampsax International A/S (1999). The LTPBMC pilot projects were awarded in 2001 but only commenced in 2002. The specifications had to be reviewed to consider changes in the road network from the time of the study to the implementation of the projects. The specifications were reviewed by BCEOM Société Francaise d'Ingénierie, the in-house consultant of the Bureau of Maintenance for the implementation of the pilot projects. The performance specifications, which were part of the tender documents, had general specifications that covered the required activities, construction method, traffic management, environmental management, materials and testing. Aside from general specifications, performance requirements for individual maintenance activities were also discussed in detail.
+
+#### *6.3 External Factors*
+
+As just shown, the Philippines is generally well prepared to adopt performance-based specified maintenance contracts as far as comparing the internal contributing factors with those of New Zealand is concerned but there is a great contrast between the Philippines and New Zealand relative to the external factors.
+
+The Philippines has about 10% more land area than New Zealand, and the population is twenty times as much. The total length of roads in the Philippines is more than
+
+<span id="page-66-1"></span><sup>35</sup> A copy of the performance specifications and requirements was obtained from Bureau of Maintenance OIC Director Luis A. Mamitag, Jr., through Ms. Elizabeth P. Pilorin, OIC-Public Information Division, DPWH. Copy received 18 October 2005.
+
+twice as much as in New Zealand but only a third as much is paved. All state highways and almost 60% of the local road network are paved in New Zealand. In the Philippines only 70% and 15% are paved for the national roads and local roads, respectively.
+
+Road density in the Philippines is twice as much as that of New Zealand. Vehicle abundance per km2 and motor vehicle ownership in New Zealand is about three times and eighteen times more than the Philippines, respectively (refer to Table 2.1). This is an indication that there are more low-volume roads in the Philippines, more roads yet a lesser number of vehicles. New Zealand has fewer roads yet they carry more traffic. New Zealand roads are exposed to a wider temperature range. Ms. Wacker acknowledged the differences of the road network and road users in the Philippines and New Zealand. Roads in New Zealand are of better quality than most Philippine roads.
+
+There is no ideal organisational structure. The structure for road management is not a one-size fits all entity, but in this case, the Philippines can apply the best practices in New Zealand in terms of the adopting performance-based specified contracts. Basically, the maintenance is equally important to both countries despite the fact that there are huge differences as far as external factors are concerned.
+
+In the previous chapter, the contributing external factors were investigated and identified. There were at least five key external factors that made the adoption of performance-based specified contracts easy for RCAs: 1) road length per engineer, 2) % rural road, 3) annual maintenance expenditure per kilometre, 4) revenue per road kilometre, and 5) rates per road kilometre.
+
+In New Zealand, the engineers of most PBS RCAs manage lesser road lengths (<600 km/engineer) than the MBS RCAs. The DPWH maintenance engineers are managing an average of 160km of road per engineer[36](#page-67-0). This figure is far below the length of roads managed by engineers in the New Zealand PBS RCAs. As shown earlier in section 4.4.1, the Philippine pilot projects, which were managed by the project
+
+<span id="page-67-0"></span> 36 Figures were computed from the length of national roads and assuming one maintenance engineer each for the 167 DPWH District Offices.
+
+engineers, had lengths ranging from 33 to 112 kilometres. The Philippines has a great advantage on the adoption of performance-based specified contracts, as far as this contributing external factor is concerned.
+
+In Section 5.5.2 it appeared in the analysis that the RCAs adopting performancebased specifications had a higher percentage rural roads than the rejectors (MBS RCAs). The PBS RCAs had more engineers to oversee road network maintenance since they had more remote roads as seen in the rural road percentage. The pilot projects in the Philippines completed in 2005, showed positive outcomes on the adoption of performance-based specifications on highly trafficked main arterial roads. In the case of New Zealand, it appeared that there was also great success for this type of maintenance management system when applied to rural and unsealed roads. It was a matter of defining the desired levels of service for the different types and hierarchy of roads. As mentioned earlier, there is no ideal organizational structure, at the same time, there is no ideal performance specification that is applicable to all types of road.
+
+The analysis in Chapter 5 showed that the rates and revenues per road kilometre are important to the adoption of performance-based specifications. The road rates and revenues have a great effect on the annual maintenance expenditure. To attain success in adopting the change, the availability of sufficient funding must be established. This is one of the bases for setting the required minimum level of service, the size of the contract, and the duration of the contract.
+
+It is recognized that there is a need to upgrade the road network to cope with higher levels of service required by customers due to traffic growth and the changing type of traffic. In the future, road users will expect more from the road network to support social and economic activities. Thus, road authorities in the Philippines must update the needed performance specifications to be responsive to the expectations of the ratepayers. The performance specifications should be attainable, realistic, and measurable. With the reforms introduced through the RIMSS project, proper planning and prioritization of projects will be achieved and correspondingly, funds will be optimised and managed properly.
+
+### <span id="page-69-0"></span>*6.4 Policies and Reforms*
+
+The Local Government Act (2002) of New Zealand requires road controlling authorities to maintain the roading network based on desired community outcomes. The government supports this endeavour through the Land Transport Management Act. Transit New Zealand has developed the State Highway Asset Management Manual (Transit New Zealand 1996) and RCAs are required to prepare asset management plans. On the other hand, the Philippine government is guided by the Philippine Transport Strategy[37](#page-69-1) and supports reforms in the DPWH.
+
+The DPWH developed a Highway Management Plan that initiated the creation of a comprehensive Road Information Management Support System (RIMSS). Its primary purpose is to change business practices within the DPWH to be in line with the trend in progressive road authorities around the world. These business practices will include separating the road-related functions of the DPWH from its non-road activities and focusing more on road users' needs, re-allocating DPWH service functions to contractors by outsourcing its management and maintenance activities to the private sector, and separating road maintenance and construction activities. The DPWH Road Program Office[38](#page-69-2) was created in 2000 and was tasked to 1) prepare a business plan for the Office; 2) prepare standards and procedures for local government road maintenance; and 3) prepare standard contracts for national road maintenance (long-term performance based maintenance contracts and preventive maintenance contracts).
+
+The institutional reforms in the DPWH were implemented by the RIMSS through Business Improvement Implementation Projects (BIIPs) subcomponent of the NRIMP to improve the quality and delivery of services focusing on customer needs, improved efficiency and effectiveness, and use of information technology (D. Michael Cleary and Partners Inc. 2003). The processes and procedures for long-term network planning and multi-year programming and scheduling are incorporated in
+
+<span id="page-69-1"></span>37 http:/[/www.adb.org/documents/cosss/phi.pdf](http://www.adb.org/documents/cosss/phi.pdf). Asian Development Bank. Philippine Transport Strategy (1997) Technical Assitance to the Republic of the Philippines for Rural Road Development Policy Framework. Visited 29 September 2005.
+
+<span id="page-69-2"></span><sup>38</sup>Department of Public Works and Highways Department Order No. 249 Series 2000 dated 27 December 2000, Annex "C".
+
+<span id="page-70-0"></span>the Highway Planning Manual (Department of Public Works and Highways 2003), which was created through the NRIMP.
+
+The DPWH is currently conducting training with technical courses, business and management courses and employee development courses. It was acknowledged by the DPWH Secretary that engineers lack skills in road asset management. Provision of appropriate training for DPWH personnel as well as local contractors and consultants is critical to the improvement of road administration and privatisation efforts. The DPWH Secretary urged local contractors and consultants to be generally responsible for the training of personnel in their respective projects.[39](#page-70-1)
+
+During the implementation of the LTPBMC pilot projects, three engineers who were trained for the pilot projects left the DPWH for reasons beyond the control of the agency. BCEOM Société Francaise D'Ingenierie (2005) recommended in the completion report that the Bureau of Maintenance should ensure that project staff with expertise in performance-based maintenance contracts are retained in the agency. The DPWH should tap the skills of the trained engineers to transfer technology to other regions and district offices.
+
+### *6.5 Funding*
+
+The availability of sufficient funds is essential for the success of the management of the maintenance of road networks. In New Zealand, the preservation of local road assets is funded from rates and revenues collected by local councils and is subsidised by Land Transport New Zealand (LTNZ) formerly Transfund. The state highways are funded by LTNZ. In the Philippines, the maintenance of local roads is funded from rates, known as the internal revenue allotment (IRA), and is subsidised by the national government. The funds for the maintenance of national roads come from the national government through the Philippine Road Board and foreign loans (foreignassisted projects).
+
+<span id="page-70-1"></span><sup>39</sup> [http://www.dpwh.gov.ph/News\\_index.asp#Ebdane](http://www.dpwh.gov.ph/News_index.asp#Ebdane). Department of Public Works and Highways. Reports on Training Needs for DPWH Engineers. Visited 15 October 2005.
+
+The Philippine Road Board was created under Republic Act 8794 (Philippine Road Board 2001). The functions of the board include: a) operations of special funds, b) management of special funds, c) approval of work programs, d) approval of special budgets, e) review of work programs, f) complementary work programs under other funding, g) procedures for monitoring performance and managing programs, h) approval of contracting methods, i) utilisation of the special funds, j) public awareness and reports, and k) supervisory authority.
+
+The main purpose of the Philippine Road Board is to operate and manage special funds from the Motor Vehicles Users' Charge (MVUC) and overloading penalties. The special funds are primarily used for the maintenance of national roads, improvement of drainage along national roads, maintenance of local roads, road safety and pollution control. Eighty percent of the revenue is intended for national roads while only five percent is allocated for local roads (Philippine Road Board 2001). It appears that the government has given more emphasis to the maintenance of national roads compared to the local roads, although figures showed that local roads account for 85 % of the total road network. The government should consider the importance of local roads as pillars of economic development. The ratepayers do not only need new roads but they also need sustainable and well-maintained roads for accessibility and mobility for daily activities. It is recommended to review the funds allocated for the national roads and local roads. There should be proper management and distribution of funds to be able to sustain the road network for future generations.
+
+Improving low-volume road maintenance in the Philippines based on a New Zealand experience prompted the researcher to study the management of change to the adoption of performance-based specifications. A research proposal was submitted in August 2004. The researcher then learned about the LTPBMC pilot projects in January 2005, during the "home located research" in the Philippines. Consequently, some changes in the outline of the thesis had been made to link the pilot projects to the study. The lessons learned from the survey conducted on RCAs in New Zealand and reports on the completed pilot projects have been analysed and investigated. The analysis was used to determine the contributing factors for the adoption of performance-based specification for unsealed low-volume roads in the Philippines.
+
+The Philippines is moving forward and is improving road maintenance to be in line with the trend in progressive road authorities around the world. The DPWH through the RIMSS has developed systems to improve quality and delivery of services by initiating a more customer-driven culture and establishing a coherent and diverse organisation. The LTPBMC pilot projects demonstrated a positive outlook on the adoption of performance-based specifications. Likewise, the reforms relative to road maintenance that were in operation, were effective tools that facilitated the management of change. The success of the projects convinced the consultant to recommend longer terms and longer lengths of road to be considered for future performance-based maintenance contracts.
+
+Domingo (2002) proposed a simple PMS for local roads in the Philippines. If this system is accepted, it will a basis for local road authorities to consider adopting performance-based specifications since the PMS will have the road inventory needed, the types of treatment and prioritisation of road maintenance projects. It is recommended that performance-based specification be applied to low-volume roads on a small scale so that it will be easier for local engineers to manage and cope with the limited resources of local road authorities. The smaller contracts would also help the small contractors in the industry, and generate employment in the local government units.
+
+Managing the change is a challenge. To attain full implementation of performancebased specifications, the government must support the program and be open-minded to the transformation to the new system. The Philippine road network will be sustainable through the provision of sufficient funding, employment of skilled asset managers, provision of appropriate training to DPWH and local road authority engineers, provision of adequate information technology resources, involvement of <span id="page-73-0"></span>road-users and stakeholders, and having confidence in local consultants and local contractors.
+
+It would take time and a lot of funding to prepare local roads in the Philippines to change to performance-based specifications. Assuming that all the resources are in place, the road authorities would be confronted with the problem of the present condition of the roads, whether they are maintainable or not. The local roads must be in good condition to be able to see the effectiveness of the system in place. In the case of the pilot projects implemented, preventive and catch-up routine maintenance were included to reduce the maintenance backlog. After the roads were brought up to good condition, the performance-based maintenance component started.
+
+With New Zealand in the forefront of performance-based specified contracts and the Philippines in the initial stage of adoption, a comparison of performance-based specifications will be discussed in the succeeding chapter.
+
+# *6.6 References:*
+
+- BCEOM Société Francaise D'Ingenierie. (2005). "Completion Report for Consulting Services for the implementation of of the Long-term Performance-Based Maintenance Project." BCEOM Societe Francaise D'Ingenierie. Manila.
+- D. Michael Cleary and Partners. (2003). "Annual NRIMP-1BIIPs Subcomponent Benefits/Cost Monitoring Report with Initial Baseline Measures and Values." D. Michael Cleary and Partners, Inc. Manila.
+- Department of Public Works and Highways. (1995). *DPWH Standard Specifications*, Department of Public Works and Highways. Manila.
+- Department of Public Works and Highways. (2003). "Highway Planning Manual." Department of Public Works and Highways. Manila.
+- Department of Public Works and Highways. (April 2004). "Manual for Road Data Collection Special Surveys." Department of Public Works and Highways. Manila.
+- Department of Public Works and Highways. (March 2004). "Road Data Collection, Quality Assurance and Management Manual." Department of Public Works and Highways. Manila.
+
+- Domingo, R. C. (2002). "Adopting A Pavement Management System (PMS) for Local Governments." *A Compendium of Graduate Theses in Transportation (1993-2003) National Center for Transportation Studies, University of the Philippines Diliman*, 81-86.
+- Kampsax International A/S. (1991). "Maintenance by Contract Manual, Third Edition." Kampsax International A/S. Manila.
+- Kampsax International A/S. (1999). "Advisory Consulting Services for the Study on the Long-term Performance-Based Maintenance Contracts." Kampsax International A/S. Manila.
+- Philippine Road Board. (2001). "Philippine Road Board Operating Procedures Manual." Philippine Road Board. Manila.
+- Robinson, R., Danielson, U., and Snaith, M. (1998). *Road Maintenance Management*, Palgrave, New York.
+- Transit New Zealand. (1996). "State Highway Asset Management Manual." Transit New Zealand. Wellington.
+
+# <span id="page-75-0"></span>**7 COMPARISON OF PERFORMANCE-BASED SPECIFICATIONS IN NEW ZEALAND AND THE PHILIPPINES**
+
+#### *7.1 Introduction*
+
+Developing performance-based specifications consists of several key steps that include: a) identifying functional road requirements, b) identifying the required level of service, c) determining performance acceptability and compliance, d) setting remedies, incentives and penalties, e) developing a quality assurance plan to determine how performance will be measured[40](#page-75-1) . Performance specifications will need to guarantee the quality and durability of the end product. The criteria for performance specifications which define the outcomes include roughness, surface texture, skid resistance, rutting, and pavement strength for sealed and unsealed roads. Corrugations and minimum level of dust are also included for unsealed roads.
+
+Performance specifications are the basis of determining whether the contractor is conforming to the terms and conditions of the contract. The contractor is paid on the basis of the performance requirements regardless of the quantity of the actual items of work accomplished (Kampsax International A/S 1999). The performance specifications incorporate requisites like scope of work activities, performance criteria, response times, traffic management, environmental management, and basis of payment. The performance-based specifications for the LTPBMC pilot project in the Philippines also included construction methods or proposed methods of repair, materials, equipment and testing requirements. Since performance-based maintenance was new to the industry, contractors needed a guide or benchmark to comply with performance requirements. There are 2 key elements identified for a performance-based specification: "a definition of the performance required and a requirement that a defined performance shall prevail over a suitable period of time" (Hardy 2001). It is essential for performance specifications to be customised to the
+
+<span id="page-75-1"></span><sup>40</sup> [http://www.mercury-assoc.com/resources/performance-based-specifications.pdf.](http://www.mercury-assoc.com/resources/performance-based-specifications.pdf) Mercury Associates Inc. Dave Robertson. 2003. How to Develop Performance-Based Specifications. Visited 6 May 2005.
+
+<span id="page-76-0"></span>specific needs of a particular area while maintaining consistency of service across the road network[41](#page-76-1). Performance targets must be realistic and easily measured.
+
+#### *7.2 Elements of a Performance-Based Specification*
+
+#### **7.2.1 Scope of Work**
+
+The scope of work is an introduction to the performance specification and describes the title of the specification. It enumerates required activities that give details on particular tasks to be accomplished by the contractor.
+
+#### **7.2.2 Performance Criteria**
+
+This section specifies the criteria used to measure the performance of the contractors citing the level of service required of the road network. The performance criteria give details on the condition of the pavement, e.g. roughness, surface texture, skid resistance, rutting, size of potholes, height of vegetation, extent and severity of pavement distress, cross-fall, corrugations, maximum level of dust for unsealed roads, and visibility of pavement markings and road signs.
+
+#### **7.2.3 Response Times**
+
+The maximum tolerable time to correct defects and deficiencies of the pavement and roadside structures are set out as a basis for penalties and incentives to contractors. The response time depends on the type of road, road classification, traffic volume, severity and magnitude of defect, and the dangers than can possibly affect the safety of the road user. Response times can be specified in hours, days, weeks, months, or at all times.
+
+<span id="page-76-1"></span> <sup>41</sup> <http://www.highways.gov.uk/roads/projects/dps/index.htm>. Highways AgencyDeveloping Performance Specifications Consultation Paper. April 2003. Highways Agency Contracts and Specifications. Visited 19 June 2005.
+
+#### <span id="page-77-0"></span>**7.2.4 Traffic Management**
+
+This section describes the traffic management scheme required for the project to reduce risks for both motorists and road workers, avoid delays and prevent traffic congestion.
+
+# **7.2.5 Environmental Management**
+
+The preservation of the environment is an important aspect in the maintenance of the road network. The contractor is required to develop an environmental plan on how to maintain a sustainable environment by specifying measures for its preservation and the proper disposal of construction wastes and debris.
+
+#### **7.2.6 Basis of Payment**
+
+This section gives information on how the contractor's monthly accomplishment is evaluated. Payment to the contractor is based on the compliance to performance required, work considered complete based on specifications, the complaints received by the engineer, and other conditions identified by the road authority as stipulated in the contract.
+
+#### **7.2.7 Construction Methods or Proposed Methods of Repair**
+
+The detailed activities to be performed in order to accomplish certain tasks are stated in sequence in this section. It gives references to the DPWH Standard Specifications for Highways, Bridges and Airport[42](#page-77-1).
+
+#### **7.2.8 Materials**
+
+Suitable materials to be used for the activity are given in this section. The physical properties and composition of the materials are specified. This gives the contractor
+
+<span id="page-77-1"></span><sup>42</sup> Department of Public Works and Highways. 1995. DPWH Standard Specification for Highways, Bridges and Airport, Volume II. Manila.
+
+<span id="page-78-0"></span>the option to use high quality materials from different sources but of comparable properties.
+
+#### **7.2.9 Equipment**
+
+Appropriate equipment used to carry out the maintenance activities are defined to achieve best results in the maintenance of the road network.
+
+#### **7.2.10 Testing Requirements**
+
+Test requirements for materials, such as AASHTO[43](#page-78-1) standard tests and test frequency are the main components of this section. The sampling of materials, type and number of tests performed depend much on the kind of material and the quantity incorporated into the work.
+
+# *7.3 Performance-Based Specifications in New Zealand and the Philippines*
+
+New Zealand road authorities have been accumulating experience with performancebased specifications since the late 1990s, making them experts in the field, while the Philippines is still in the primary stage. Over the years, transportation engineers in New Zealand have been continuously developing and modifying performance specifications to comply with stakeholder needs, local road conditions, climate and geographic conditions, and changing levels of service required. The difference in the performance-based specifications in both countries is a result of varied expertise of engineers, local conditions, desired levels of service, years of experience, and availability of resources.
+
+The contractor must be motivated to perform well and sustain a long-term contract. In order to achieve this, New Zealand performance specifications have incentives for contractors for good performance and productivity improvement and at the same
+
+ 43 Department of Public Works and Highways. IBRD-NRIMP Long Term Performance Based Maintenance Contracts. LTPBMC 2b Bidding Documents. Section 5 – Specifications.
+
+<span id="page-78-1"></span>
+
+time impose tough penalties for non-compliance. The performance specifications encourage contractors to be proactive in implementing maintenance works by giving incentives and encouraging appropriate use of resources. The performance specifications for the LTPBMC pilot projects prepared by the consultant in the Philippines incorporated penalties to be imposed on contractors for non-conformity. The penalties were stipulated in the matrix used by the Project Engineer when conducting monthly inspections and deducted from the monthly lump sum payment to the contractor.
+
+The performance specifications in New Zealand have evolved to cover all aspects relative to road asset management. This is due to the advance of technology and the abundance of engineers with technical expertise and experience in the field. Performance appraisals, which are noted on a network score card, are made on four major components: management performance measures, key performance measures, operational performance measures, and contract performance measures. Management performance measures set out processes that apply to the planning management and implementation of the contract. They cover the contract quality plan, contractor's program, contractor's report, contractor's customer care, and traffic management plan. Key performance measures illustrate the overall condition and function of the road network. They describe the drivers for periodic maintenance and rehabilitation programmes of the contractor, which include network reliability, surface texture, skid resistance, and roughness. Table 7.1 illustrates the key performance measures currently adopted for Transit New Zealand's performance-based specified maintenance contracts. Operational performance measures associate with the daily activities on the road network that define routine maintenance and emergency response programs. They provide details on contract standards and response times (see Table 7.2) for pavement maintenance, shoulder maintenance, detritus, drainage system maintenance, bridge maintenance, roadside structure maintenance, vegetation, lighting, road sign and pavement marking maintenance. Contract performance measures are records of all information and data pertaining to the contract, which are the bases the consultant uses to update the network scorecard.
+
+**Table 7.1. Key Performance Measures for Transit New Zealand's Performance-Based Specified Maintenance Contracts[44](#page-80-0)**
+
+| Parameter                        | Key Performance Measures                                                                                               | Details Of Measurement                                                                                                                       |
+|----------------------------------|------------------------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------|
+| Roughness                        | Percent with roughness<br>>NAASRA1<br>threshold                                                                        | Annual with HSD2                                                                                                                             |
+| Texture                          | Percent with mean texture<br>depth <lower td="" threshold<=""><td>Annual, mean profile depth with HSD2</td></lower>    | Annual, mean profile depth with HSD2                                                                                                         |
+| Texture                          | Percent with mean texture<br>depth>upper threshold                                                                     | Annual, mean profile depth with HSD2                                                                                                         |
+| Skid Resistance                  | Percent with Sideways Force<br>Coefficient <threshold< td=""><td>Annual, using SCRIM3<br/>compatible</td></threshold<> | Annual, using SCRIM3<br>compatible                                                                                                           |
+| Rutting                          | Percent with depth>20mm                                                                                                | Annual with HSD2                                                                                                                             |
+| Surface Life                     | Minimum surface life index                                                                                             | Years 8-10 only, an empirical index<br>based on expected life for different<br>surface types                                                 |
+| Structural Condition             | Structural condition index                                                                                             | Years 3, 6, 8 and 10. Volume of<br>overlay required across network to<br>achieve a 25 year pavement design<br>based on FWD4<br>back analysis |
+| Minimum resurfacing<br>length    | Resurfacing length by lane-km                                                                                          | Annual, proposed by tenderer, chip seal<br>and AC surfacings                                                                                 |
+| Minimum<br>rehabilitation length | Rehabilitation length by lane<br>km                                                                                    | Annual, proposed by tenderer                                                                                                                 |
+
+NAASRA (National Association of Australian State Road Authorities) has an accepted unit of measure of road roughness
+
+In the Philippines, the performance specifications used for the LTPBMC pilot contracts were developed by the consultants to meet the requirements based on the present condition of the network, minimum level of service, road use and traffic condition.
+
+The performance specifications for New Zealand consider customer complaints when a contractor's accomplishment for monthly payment is evaluated. RCAs involve ratepayers to be proactive, and actively participating in the management of roads. In the Southland District Council, one criterion measuring the performance of a contractor is the number of complaints received by the engineer during the contract
+
+HSD (High Speed Data) using laser profilometers
+
+<sup>3</sup> SCRIM (Sideways Force Coefficient Routine Investigation Machine) 4
+
+FWD (Falling Weight Deflectometer)
+
+<span id="page-80-0"></span><sup>44</sup> [http://www.rims.org.nz/NR/rdonlyres/2C6A9E57-7CEF-4946-8E45-08BE28DF858D/0/Parkman](http://www.rims.org.nz/NR/rdonlyres/2C6A9E57-7CEF-4946-8E45-08BE28DF858D/0/ParkmanARRBPSMCRisks.pdf)  [ARRBPSMCRisks.pdf](http://www.rims.org.nz/NR/rdonlyres/2C6A9E57-7CEF-4946-8E45-08BE28DF858D/0/ParkmanARRBPSMCRisks.pdf). Road Information Management Steering Group. Parkman, C., *et.al*. Pavement Deterioration Modelling in Long-Term Performance Based Contract: How Far does it Mitigate the Risk for Client and Contractor? Visited 31 January 2006.
+
+period[45](#page-81-0). Customer complaints in the Philippines are acted upon but these are not taken into account in the monthly payment to the contractors.
+
+Monthly reporting on work accomplished is the responsibility of the contractor in New Zealand. The reports are submitted to the road controlling authority for random audit and verification, and then processed for the contractor's monthly payment. In the Philippines, a daily accomplishment report is recorded by the DPWH project inspector. This report is for the internal use of the DPWH to be used to compare the accomplishment with the other procurement methods used. The daily accomplishment report is also used to verify if the performance requirements are fulfilled by the contractor. The performance requirements are further validated by a joint inspection by representatives of the DPWH, the Commission on Audit, and the contractor (Kampsax International A/S 1999). The consultant's completion report showed that the pilot projects had one project engineer, one materials engineer and one project inspector each. As mentioned earlier, the length of the pilot projects ranged from 33 to 111 km. Judging from the circumstances cited, the researcher thinks that the conduct of daily inspections would not be possible for one project inspector. The responsibility may be passed on to the contractor and the daily reports may be regularly or randomly checked by the project inspector. One option would be to assign more project inspectors for a single project to allow for a reasonable length of road inspected daily. Another option would be not to conduct daily inspection but on a regular basis, say, twice a week, so that the project inspector will have time to cover the whole stretch of the project.
+
+As New Zealand is in the advanced stages of implementing performance-based specifications, it can be seen that road controlling authorities have given the contractors full control of the maintenance of the road network. On the other hand, the Philippines had to guide the contractors with the adoption of the new system of performance-based specifications. With the pilot projects, the DPWH had to devise a system to compare method-based specified maintenance contracts and performancebased contracts. The quantities, resources used, and costs were compared using the daily accomplishment report recorded by the DPWH project inspector. The
+
+<span id="page-81-0"></span><sup>45</sup> Southland District Council. Contract Number 05/02. Part 5. Network Maintenance and Management Contract. North Western Area.
+
+<span id="page-82-0"></span>consultant monitored and compared performance-based maintenance activities with the DPWH's quantity estimate, and in all cases, the former far exceeded the latter. The cost-effectiveness of performance-based maintenance as compared to maintenance by contract (MBC) and maintenance by administration (MBA) was also examined. Results in the final assessment report (BCEOM Société Francaise D'Ingenierie 2005) showed that in all cases, the actual accomplishment of the performance-based maintenance contractors surpassed those of the MBC and MBA, which were method-based.
+
+#### *7.4 Performance Specifications*
+
+#### **7.4.1 Sealed Roads**
+
+Table 7.2 and Table 7.3 show some examples of the operational performance measures for New Zealand and performance standards used in the PSMC pilot projects in the Philippines, respectively. The operational performance measures show the road features, the performance required and the response time to correct defects. The performance measures for the pilot projects in the Philippines also include the penalties for non-compliance to performance requirements.
+
+Transit New Zealand has adopted comprehensive operational performance measures that cover the total maintenance of the state highways. There are at least 22 operational performance measures for the maintenance of pavements, bridges, shoulders, drainage systems, barriers, lighting, pavement markings, road signs, sight rails, edge marker post, litter removal, and vegetation control. The OPMs also include crash and damage reporting, frost and snow clearance, incident response and work practices. The maintenance specifications[46](#page-82-1) describe clearly the performance requirements and define technical terms used. The performance measures are very specific to the type of road feature and the level of service required. New Zealand roads require a higher level of service to be able to satisfy the demands of the ratepayers. This is one of the reasons why the roads are in better condition and
+
+ 46Transit New Zealand. Maintenance Specification. General Maintenance Project. SM032Transit Contract.
+
+<span id="page-82-1"></span>
+
+**Table 7.2. Some Selected Operational Performance Measures for Transit New Zealand's PSMC Contracts[47](#page-83-0)**
+
+| Feature<br>Contract Standard                     |                                                                                                                                                           |                 |  |
+|--------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------|-----------------|--|
+| Potholes on all highways                         | No potholes greater than 150 mm diameter                                                                                                                  | 48 hours        |  |
+| Repair surfacing on all<br>highways              | Surplus and/or loose chip does not create potential<br>traffic hazard or create public complaints                                                         | 2 hours         |  |
+| Cracking on moisture<br>sensitive pavements      | The total area within any continuous kilometre is less<br>than 10m2                                                                                       | 1 month         |  |
+| Heaves and shoves on M,<br>R1 and R2             | There are no heaves and/or shoves greater than 20mm                                                                                                       | 2 weeks         |  |
+| Depressions and rutting<br>on all highways       | There is no ponding greater than 30 mm in depth at any<br>location. This includes existing pavement subsidence<br>sites                                   | 6 months        |  |
+| Edge break on all<br>highways                    | There is not more than 2m of edge break within any<br>continuous kilometre less than 0.5m wide                                                            | 1 month         |  |
+| Service covers on all<br>highways                | All service covers are within + 10 mm of the<br>surrounding pavement surface                                                                              | 2 months        |  |
+| Work practices on all<br>highways                | All completed work must comply with maintenance<br>specification, clauses 5.16                                                                            | At all<br>times |  |
+| Shoulder maintenance on<br>all highways          | The maximum length of low shoulder, including edge<br>rutting, is less than 100m in any continuous kilometre<br>section                                   | 2 months        |  |
+| Sealed surface detritus on<br>all highways       | There is a maximum of 50 grams of detritus per two<br>square metres of sealed surface                                                                     | 1 week          |  |
+| Small slips on all<br>highways                   | Small slips are removed                                                                                                                                   | 2 weeks         |  |
+| Lined channels on all<br>highways                | There are no lined channels with more than 10% of the<br>cross- section area obstructed, and lined channels are<br>maintained vegetation free             | 1 week          |  |
+| Sumps, manholes and<br>catchpits on all highways | There is not more than 30% of the volume of any<br>structure filled with debris                                                                           | 3 months        |  |
+| Culverts on all highways                         | There is no culvert with more than 10% of the cross<br>sectional depth of the culvert inlet, outlet or barrel filled<br>with debris                       | 2 weeks         |  |
+| Cleanliness on all bridges                       | All components are free of moss, vegetation, detritus,<br>etc                                                                                             | 6 months        |  |
+| Structural integrity of all<br>bridges           | All structural damage is reported to the consultant                                                                                                       | 48 hours        |  |
+| Structural integrity of all<br>bridges           | All structural deterioration is reported to the consultant                                                                                                | 6 months        |  |
+| Barrier maintenance on all<br>highways           | All damaged barriers are permanently repaired                                                                                                             | 1 month         |  |
+| Functionality of raised<br>pavement markers      | There are not more than 2 dysfunctional raised<br>reflective pavement markers (RRPMs) within any 10<br>continuous RRPMs                                   | 2 weeks         |  |
+| Uniformity of pavement<br>markings               | There is not more than 1 location within any continuous<br>5km where the pavement markings do not comply with<br>the manual of traffic signs and markings | 1 month         |  |
+
+<span id="page-83-0"></span><sup>47</sup> Transit New Zealand. Maintenance Specification. General Maintenance Project. SM032Transit Contract.
+
+**Table 7.3. Performance Specifications for LTPBMC Pilot Project in the Philippines** 
+
+| Feature                                              | Performance<br>Requirements/Description                                                                                        | Response Time or<br>Maximum<br>Tolerable Degree of<br>Defect                            | Penalty for non<br>compliance                                                                                                                       |
+|------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------|
+| General appearance                                   | Road, bridges, structures<br>shall be clean, free of garbage<br>and obstructions and<br>maintained to the required<br>standard | Any given time                                                                          | P2,000 per km per<br>week of non<br>compliance                                                                                                      |
+| Asphalt pavement                                     |                                                                                                                                |                                                                                         |                                                                                                                                                     |
+| Potholes                                             | Hole or depression larger<br>than 15 cm x 15 cm and<br>deeper than 5 cm                                                        | Within 24 hours                                                                         | P1,000 per pothole<br>not repaired per day                                                                                                          |
+| Pavement damage                                      | A total of 100 m2<br>of alligator<br>cracking or 400m of cracks or<br>a combination thereof, width<br>of a crack is 25 mm      | To be sealed within<br>10 to 30 working<br>days depending on<br>AADT                    | P1,000 per pavement<br>damage not sealed<br>within response time<br>and P2,000 for every<br>succeeding month of<br>non repair                       |
+| Pavement markings                                    | Considered in good condition<br>when it is clearly visible<br>during day and night                                             | 60% to 90% of the<br>markings in good<br>condition depending<br>on AADT                 | P1,000 per km if not<br>remedied within one<br>month and P2,000<br>per km for every<br>succeeding month of<br>non-compliance                        |
+| Concrete pavement                                    |                                                                                                                                |                                                                                         |                                                                                                                                                     |
+| Local damage,<br>depression failed<br>slabs (blocks) | Hole or depression larger<br>than 15 cm x 15 cm, but less<br>than the size of one slab<br>(block) and deeper than 5 cm         | Within 24 hours                                                                         | P1,000 per local<br>damage, depression<br>not repaired per day                                                                                      |
+| Failed slabs (blocks)                                | Any concrete slab with more<br>than 8 metres of cracks or not<br>in level with adjacent slabs                                  | To be repaired within<br>10 to 20 working<br>days depending on<br>AADT                  | P4,000 for every<br>concrete slab not<br>repaired within the<br>response time and<br>P8,000 for every<br>succeeding month of<br>non-repair          |
+| Joints/cracks                                        | Joints/cracks are considered<br>sufficiently sealed when<br>filled with sealant to the level<br>of the pavement surface        | 60% to 90% of the<br>joints/cracks shall be<br>sufficiently sealed<br>depending on AADT | P1,000 for every km<br>with joints/cracks not<br>sealed within one<br>month and P2,000<br>per km for every<br>succeeding month of<br>non-conformity |
+| Pavement markings                                    | Considered in good condition<br>when it is clearly visible<br>during day and night                                             | 60% to 90% of the<br>markings in good<br>condition depending<br>on AADT                 | P1,000 per km if not<br>remedied within one<br>month and P2,000<br>per km for every<br>succeeding month of<br>non-compliance                        |
+
+| Feature                                                | Performance<br>Requirements/Description                                                                                                                                                                      | Response Time or<br>Maximum<br>Tolerable Degree<br>of Defect                                                                        | Penalty for non<br>compliance                                                                                                                |
+|--------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-------------------------------------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------|
+| Shoulders/roadside                                     |                                                                                                                                                                                                              |                                                                                                                                     |                                                                                                                                              |
+| Shoulder damage                                        | A total area of 100m2<br>of<br>potholes and/or depressions<br>deeper than 10cm                                                                                                                               | To be repaired<br>within 10 to 30<br>working days<br>depending on<br>AADT                                                           | P1,000 for every<br>shoulder damage<br>not repaired within<br>the response time<br>and P2,000 for<br>every succeeding<br>month of non-repair |
+| Sufficient level and<br>cross-slope                    | The level of the shoulder<br>along the pavement edge is<br>equal to the level of the<br>pavement or is no more than<br>5 cm lower. The shoulder<br>cross-slope is between 2% to<br>4% away from the pavement | To be repaired<br>within 10 to 30<br>working days<br>depending on<br>AADT                                                           | P1,000 for every 1<br>km not remedied<br>within response<br>time and P2,000 per<br>km for every<br>succeeding month<br>of non-remedy         |
+| Vegetation                                             | Roadside area within 5<br>metres from the edge of the<br>pavement                                                                                                                                            | Height of grass and<br>vegetaion shall not<br>exceed 15 cm at any<br>time                                                           | P5,000/ km if not<br>remedied within<br>one month and<br>P5,000/km for<br>every month of<br>non-compliance                                   |
+| Drainage                                               |                                                                                                                                                                                                              |                                                                                                                                     |                                                                                                                                              |
+| Side drains, culverts<br>and drainage system           | The drainage facility's<br>capacity is reduced by more<br>than 25%                                                                                                                                           | Any disruption of<br>the free flow of<br>surface water shall<br>be remedied within<br>10 to 30 working<br>days depending on<br>AADT | P500 per location<br>not remedied within<br>the response time<br>and P1,000 per<br>location for every<br>month of non<br>remedy              |
+| Side drains, culverts<br>and drainage system           | Minimal accumulation of silt<br>and debris                                                                                                                                                                   | Siltation and debris<br>shall not exceed 15<br>cm at any time                                                                       | P1,000/km if not<br>remedied within<br>one month and<br>P2,000/km for<br>every month of<br>non-compliance                                    |
+| Bridges                                                |                                                                                                                                                                                                              |                                                                                                                                     |                                                                                                                                              |
+| Bridge deck,<br>drainage system,<br>outlets & waterway | Minimal disruption of free<br>flow of water                                                                                                                                                                  | Any disruption of<br>the free flow of<br>water shall be<br>remedied within 10<br>to 30 working days<br>depending on<br>AADT         | P500 per bridge not<br>remedied within the<br>response time and<br>P1,000 per bridge<br>for every month of<br>non-remedy                     |
+| Bridge painting and<br>signage                         | The bridge painting,<br>markings, warning and<br>regulatory signs shall be<br>clear of obstructions, clean<br>and readable                                                                                   | Any given time                                                                                                                      | P1,000 per brigde if<br>not remedied within<br>one month and<br>P2,000 per bridge<br>for every month of<br>non-compliance                    |
+
+| Feature                   | Performance<br>Requirements/Description                                                                                          | Response Time or<br>Maximum<br>Tolerable Degree<br>of Defect | Penalty for non<br>compliance                                                                                                                                                                                                                                                     |
+|---------------------------|----------------------------------------------------------------------------------------------------------------------------------|--------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
+| Signage and<br>guardrails |                                                                                                                                  |                                                              |                                                                                                                                                                                                                                                                                   |
+| Signage and<br>guardrails | Road signs and other<br>regulatory or warning<br>devices and guardrails shall<br>be clear of obstructions,<br>clean and readable | Any given time                                               | P100 per sign or<br>device not remedied<br>within one month<br>and P200 per sign<br>for every month of<br>non-compliance.<br>P1,000 for every<br>100 m of guardrails<br>not remedied within<br>one month and<br>P2,000 for every<br>100 m for every<br>month of non<br>compliance |
+
+Kampsax International A/S. 1999. Advisory Consulting Services for the Study on the Long Term Performance Based Maintenance Contracts. Annex B. Unpublished Report. Department of Public Works and Highways
+
+with better quality than the Philippines.
+
+The performance specifications for the pilot projects in the Philippines required the total maintenance for the main road features but do not have the details on particular defects. An example is the required specific level of service for rutting and edge break of asphalt pavements. The repair of potholes on asphalt pavements should have some exceptions due to the heavy penalties which are counted per pothole per day. The researcher believes that the repair of potholes would not be practical for the contractor especially during the rainy season. Continuous rains would not permit the correction of defects according to the prescribed standards. The corrections might yield unsatisfactory results which would end up with further deterioration and wasted resources. This is also true for other defects which worsen the road condition, but cannot be remedied immediately within the prescribed time because of circumstances beyond the control of the contractor. Suspensions for the imposed penalties on the contractor must be considered.
+
+The New Zealand performance measures for surface detritus on roads specify a measurable quantity (i.e. maximum of 50 grams/2m2 of sealed surface) and cleanliness of bridges define the requisites (i.e. free of moss, vegetation, and detritus) for the feature. On the other hand, the general appearance of roads and bridges in the Philippines require the structures to be clean and maintained to the required standard. The use of the term 'required standard' is ambiguous and misleading, unless it was defined in the contract documents. The contracting parties might interpret it differently hence, there is a need to clearly describe performance specifications to avoid conflicting ideas during project implementation.
+
+The maintenance of the drainage system is as important as pavement maintenance. The trigger factors for maintenance compliance are 10% and 25% reduced capacity of drainage facility, for New Zealand and the Philippines, respectively. The researcher has observed that the drainage systems along the state highways in New Zealand are smaller in size but more efficient compared to the Philippines. This is due to the high level of service required of the drainage structures. They are expected to function to optimum capacity as most of New Zealand roads are asphalt that needs to be well drained to prevent rapid deterioration.
+
+The OPM for bridges in New Zealand covers the over-all maintenance of bridge components including reporting the structural integrity of bridges to the network consultant. In the Philippines, only the physical bridge condition and waterway was given emphasis. Performance-based specified contracts are usually long-term, thus, there is a need to include the inspection of structural damage and deterioration of bridges so that remedial measures are done immediately.
+
+Road signs are important to inform and guide motorists for safe travel. New Zealand's OPMs for sign maintenance are broad covering all types of road signs (permanent and seasonal), the presence of visible and correctly aligned road signs, inventory of signs, and particular about missing road signs. In the Philippines, only the existing signs are required to be maintained, and there are no provisions for missing signs. Since there had been cases of burglaries of road signs, the performance specifications must assure the presence of the road signs to warn road users.
+
+<span id="page-88-0"></span>The performance requirements for the pilot projects in the Philippines are simple compared to the thorough performance measures of New Zealand which have evolved through the years. The researcher believes that lessons learned from the pilot projects, including new trends from New Zealand and other countries will help develop more systematic and detailed performance requirements for the maintenance of Philippine roads.
+
+#### **7.4.2 Unsealed Low-Volume Roads**
+
+Unsealed roads include gravel and earth roads that require performance measures that are simple and inexpensive to measure and control (Zietlow 2004). To make them sustainable, it is important that they are maintained with at least a minimum level of service. The road must be clean, accessible, open to traffic and free of obstruction at all times. The comfort of the road user should be considered based on acceptable limits of rutting, corrugations, potholes and surface defects. Performance specifications must ensure road users are safe and can drive safely at the specified average speed. The drainage structures must be in good condition and vegetation must be less than an acceptable height.
+
+Table 7.4 shows the operational performance measures for unsealed low-volume roads from four road controlling authorities in New Zealand. The performance requirements for the maintenance of unsealed roads differ among the RCAs. The differences may be due to the following: 1) the levels of service expected by the ratepayers and customers, 2) the maintenance funds available for the road, 3) the geographical location of the RCA, 4) the social and economic activities in the RCA, and 5) the cultural background of the community.
+
+The RCAs have to consider a level of service that is sustainable. Since most of the unsealed low-volume roads are rural by nature, their primary purpose is for transporting agricultural and forestry products to processing plants or to urban centres. The Local Government New Zealand (LGNZ) has acknowledged the significant benefits of the additional productivity in the rural sector. The wear and tear of rural roads posed by heavy vehicles prompted LGNZ to ask Government to increase financial assistance for the maintenance of existing roads[48](#page-89-0). The rural road network must be upgraded and maintained to adapt to the changing traffic volume and type of traffic. The maintenance effort has to be balanced with minimised costs, without compromising safety of the road users and comfort for smaller communities.
+
+**Table 7.4. Operational Performance Measures for New Zealand Unsealed Low-volume Roads.** 
+
+| Feature          | Contract Standard                                                                                                                                                                                  | Response<br>Time                                                       |
+|------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------|
+| Potholes         | There are no potholes greater than 200mm<br>diameter and depth less than 35mmab<br>Less than 25mm depthc<br>There are no potholes greater than 400mm<br>diameter and depth less than 35mmd         | Maximum level<br>of service shall<br>not be<br>exceeded at any<br>time |
+| Corrugations     | There shall be no corrugations exceeding 20mm<br>from crest to troughab<br>Less than 10mm height over any 500m section c<br>There shall be no corrugations exceeding 25mm<br>from crest to troughd | Maximum level<br>of service shall<br>not be<br>exceeded at any<br>time |
+| Rutting          | There shall be no rutting exceeding 50mmabd<br>Less than 10mm over any 50m section per 500m<br>for local roads and less than 20mm for local access<br>roadsc                                       | Maximum level<br>of service shall<br>not be<br>exceeded at any<br>time |
+| Surface scouring | No surface scouring for local roads, less than<br>25mm deep for local access roadsc                                                                                                                | Maximum level<br>of service shall<br>not be<br>exceeded at any<br>time |
+| Loose metal      | Less than 15mm deep over any 50m section per<br>500m, no loose aggregate shall be greater than<br>40mm in diameterc                                                                                | Maximum level<br>of service shall<br>not be<br>exceeded at any<br>time |
+
+a – Ruapehu District Council
+
+The researcher could not present examples of performance-based specifications for unsealed low-volume roads in the Philippines as the LTPBMC pilot projects were implemented on paved and highly trafficked national roads.
+
+b – South Taranaki District Council
+
+c – Central Otago District Council
+
+d – Dunedin City Council
+
+<span id="page-89-0"></span> <sup>48</sup> <http://www.localgovtnz.co.nz/news/pr1088138752.html>. Local Government New Zealand. Barker, M. Provincial and Rural Roads Left Behind. Visited 8 July 2004.
+
+<span id="page-90-0"></span>
+
+A comparison of performance-based specifications in New Zealand and the Philippines was presented. The specifications in the Philippines were customised to define the performance required of the road network within a period of time, and the penalties imposed on the contractors. The general performance-based specifications for unsealed low-volume roads in New Zealand were also discussed.
+
+#### *7.5 References:*
+
+- BCEOM Société Francaise D'Ingenierie. (2005). "Completion Report for Consulting Services for the implementation of of the Long-term Performance-Based Maintenance Project." Manila.
+- Hardy, P. "Austroads Review of Performance Contracts: The Potential Benefits of Performance Contracts." *Contracting the Future NZIHT Symposium*, 28.
+- Kampsax International A/S. (1999). "Advisory Consulting Services for the Study on the Long-term Performance-Based Maintenance Contracts." Manila.
+- Zietlow, G. (2004). "Implementing Performance-Based Road Management and Maintenance Contracts in Developing Countries-An Instrument of German Technical Cooperation." The document can be retrieved from http://www.zietlow.com.
+
+# <span id="page-91-0"></span>**8 CONCLUSION**
+
+# *8.1 Accelerators and Impeding Factors using Performance-Based Specifications*
+
+New Zealand road authorities have been accumulating experience and gaining benefits with performance-based specifications since 1998, while the Philippines is still in the initial stages of adoption. Performance-based specifications have been successfully implemented on New Zealand state highways and have gained recognition with local road controlling authorities. From the survey conducted, about 80% of RCAs have moved from method-based specifications to adopting performance-based specifications.
+
+The New Zealand Local Government Act of 1974 and 2002 empowered local councils to build, upgrade and maintain local roads, as they see fit depending on Central Government requirements and consistent with the community's desire for high quality infrastructure services. The LGA 2002 required local councils to have a 10-year Long-Term Council Community Plans (LTCCP) where the desired community outcomes and expected levels of service of the road network are identified. The management of the road network is also embodied in the Land Transport Management Act 2002 and the New Zealand Land Transport Strategy, aiming to achieve an integrated, safe, responsive, and sustainable transport system.
+
+Improving road maintenance management in the Philippines, based on a study of RCAs in New Zealand, was the goal of this research with the theme of managing the change from method-based specifications to performance-based specifications. The profile of RCAs that are more likely to adopt performance-based specifications was established. Generally, the RCAs that have adopted performance-based specifications have the following characteristics:
+
+- 1. Employ asset managers to be in charge of the overall maintenance of the roading network;
+- 2. Outsource consultants providing specialist skills;
+- 3. Use maintenance management tools like RAMM;
+- 4. Conduct customer surveys to know ratepayers' opinions, thus, validating the effectiveness and efficiency of the maintenance of the network;
+- 5. Have written and modified their own maintenance specifications;
+- 6. Have more resources in terms of rates and revenue per road kilometre;
+- 7. Have more annual maintenance expenditure per road kilometre;
+- 8. Have a higher percentage of rural roads;
+- 9. Have less road length per engineer;
+- 10. Evaluate contractor's accomplishments on the basis of performance required of the road network by using a marking and scoring system.
+
+The Philippines is moving forward and is improving road maintenance to be in line with the trend in progressive road authorities around the world. The initial reforms implemented by the DPWH were effective tools that facilitated the management of change. The contributing factors learned from this study will guide road authorities in the Philippines to improve the implementation of future LTPBMC projects on national roads, and possibly to apply the same to low-volume roads. To gain success with managing change, the government must support the program and be openminded to the transformation to the new system.
+
+DPWH engineers have the skills and expertise on road maintenance but need to be guided more on asset management to prepare for the adoption of performance-based specifications on a wider scope. The DPWH has been training engineers nationwide to gain skills and expertise on the reforms introduced through the RIMSS project. For the LTPBMC pilot projects, training was limited to engineers directly involved with the projects (i.e. project engineer, materials engineer and project inspector). During the implementation of the pilot projects, there were issues with the turn-over of employees; trained engineers left the DPWH for better opportunities abroad or other private companies. The government should have measures to mitigate the risk of losing skilled engineers. Engineers in the DPWH should have training courses on topics such as asset management, contract management, and developing performance specifications. Training courses should also be extended to local consultants and local contractors to strengthen the local industry.
+
+Modern analytical tools for asset management have been in operation and continuously developing in the Philippines through the reforms introduced in the RIMSS project. The Road and Bridge Information Application (RBIA), the warehouse for traffic and road condition data, is in place. The data in RBIA are used for the pavement management system (PMS), which provides needs analyses, multiyear programming and budgeting. The DPWH must ensure the integrity and sustainability of the data as it will be the basis of forward planning works.
+
+Involving ratepayers in the maintenance management of the road network is essential to obtain feedback. The DPWH has to strengthen the functions of the Complaints and Action Center (CAAC) to give meaning to the data they are receiving. They should be encouraged to conduct and analyse customer surveys to determine the effectiveness and efficiency of the maintenance management systems. Through the customer surveys, the ratepayers and other stakeholders (i.e. politicians) will be well informed and educated on the implementation of the systems in place, at the same time encouraged them to be involved in proactive and reactive maintenance.
+
+To gain success in managing the change, the government must assure the availability of sufficient funds to make the road network sustainable for future generations. This is possible through the foreign grants or loans and the prudent management of maintenance funds by the Philippine Road Board. As mentioned in Chapter 5, a review of the percentage allocation for national roads and local roads is needed to cope with the increasing demands of the local road network.
+
+Developing suitable, adaptable, and measurable performance-based specifications is an important aspect to adopting the new system. The performance specifications should be clear, precise and leave no ambiguities to prevent conflicts in project implementation. The performance requirements should encompass all the elements of all road and roadside structures and should be modified or reviewed for revision from time to time to cope with the changing traffic patterns and road conditions.
+
+<span id="page-94-0"></span>The contractor must be motivated to perform well and sustain a long-term contract. The Philippines impose tough penalties for non-compliance but can also adopt New Zealand's provision of incentives to contractors for good performance and productivity improvement.
+
+# *8.2 Proposals for Performance-Based Specifications*
+
+Performance specifications need to guarantee the quality and durability of the end product. The comfort and safety of the road users are important factors to consider when developing performance specifications. The criteria for performance specifications which define the outcomes include roughness, surface texture, skid resistance, rutting, and pavement strength for sealed roads. Unsealed roads require lower levels of service in terms of roughness, rutting, corrugations, potholes, surface defects, and a maximum level of dust. The acceptable limits differ based on local road conditions, geography, climate, economic and social activities, and community requirements. To make unsealed roads sustainable, it is important they are maintained to a minimum by keeping them clean, accessible, free from obstructions, and with functioning drainage and well-maintained roadside structures.
+
+The DPWH has adopted performance-based specifications and progress was well on its way. This research hopes to help in the process of maintaining sustainable roads for future generations.
+
+# <span id="page-95-0"></span>**Appendix 1**
+
+#### **Survey Questionnaire**
+
+Dear Respondent,
+
+This material has been prepared as an instrument to guide the researcher in determining the best practices in the maintenance management of unsealed lowvolume roads in New Zealand. Be assured that all information gathered will be kept confidential.
+
+Thank you for spending valuable time to answer the questions and contributing to this project. All respondents will be provided with a survey summary upon completion of the analysis of results.
+
+Yours truly,
+
+Researcher
+
+#### **Romelda A. Bangasan**
+
+| Email: rab131@student.canterbury.ac.nz                                                               |
+|------------------------------------------------------------------------------------------------------|
+| Road Controlling Authority                                                                           |
+| 1. Please furnish a copy of the organisational chart of your Road Controlling<br>Authority.          |
+| 2. Which position oversees the maintenance of unsealed roads in the District/City?<br>               |
+| 3. Describe in 1 or 2 lines, the duties of the positions related to the maintenance of<br>roads.<br> |
+|                                                                                                      |
+
+4. What is the title/name of the specifications document used in the maintenance of unsealed roads? \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
+
+\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
+
+5. How were the specifications developed? \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
+
+| 6. By what processes were the specifications developed?           |        |                 | <br>                                                                                       |
+|-------------------------------------------------------------------|--------|-----------------|--------------------------------------------------------------------------------------------|
+| 7. On what basis are revisions (of specifications) made?          |        |                 | <br>                                                                                       |
+| 8. How frequent are revisions (of specifications) made?           |        |                 | <br><br>                                                                                   |
+| 9. What is the protocol for handling customer complaints?         |        |                 | <br>                                                                                       |
+| analysis?                                                         |        |                 | <br>10. Do you survey and analyse customer complaints? If so, what is the frequency of<br> |
+| the frequency and what triggers (initiates) these activities?     |        |                 | <br>11. What typical maintenance activities are performed on unsealed roads? What is       |
+| Maintenance Activity                                              | Yes/No | How frequently? | What triggers the activity?                                                                |
+| Light Grading                                                     |        |                 |                                                                                            |
+| Heavy Grading                                                     |        |                 |                                                                                            |
+| Gravel Resurfacing                                                |        |                 |                                                                                            |
+| Additional Metal                                                  |        |                 |                                                                                            |
+| Restoring Drainage                                                |        |                 |                                                                                            |
+| System                                                            |        |                 |                                                                                            |
+| Ditch/Culvert                                                     |        |                 |                                                                                            |
+| Cleaning                                                          |        |                 |                                                                                            |
+| Vegetation Control                                                |        |                 |                                                                                            |
+| Dust Control                                                      |        |                 |                                                                                            |
+| Reshaping of Shoulders                                            |        |                 |                                                                                            |
+| Restoration of Signs                                              |        |                 |                                                                                            |
+| Guardrail Maintenance                                             |        |                 |                                                                                            |
+| Restoration of                                                    |        |                 |                                                                                            |
+| Roadside Furniture                                                |        |                 |                                                                                            |
+| Others (Specify)                                                  |        |                 |                                                                                            |
+| 12. How do you evaluate the acceptability of a contractor's work? |        |                 | <br>                                                                                       |