category: literaturenote citekey: wangsafetymodelingurbanarterials2015 title: "Safety modeling of urban arterials in Shanghai, China" authors: "Wang, Xuesong; Fan, Tianxiang; Chen, Ming; Deng, Bing; Wu, Bing; Tremont, Paul" year: 2015 date: 2015-00-00 2015 doi: 10.1016/j.aap.2015.07.004 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/j.aap.2015.07.004" zotero_key: R348MVVW zotero_storage: K65D7EGR collections: transpordi_planeerimine folder: 001_artiklid firstAuthor: "Wang, Xuesong"

status: converted

Accident Analysis and Prevention

journal homepage:

Safety modeling of urban arterials in Shanghai, China

Xuesong Wanga,b, *, Tianxiang Fana , Ming Chen^a , Bing Dengc , Bing Wu^a , Paul Tremont^a

^a School of Transportation Engineering, Tongji University, Shanghai 201804, China ^b The Key Laboratory of Road and Traffi^c Engineering, Ministry of Education, China ^c
General Motors Safety Electronics & Innovation, Warren, MI 48090, USA

A R T I C L E I N F O

Article history: Received 26 April 2014 Received in revised form 14 April 2015 Accepted 3 July 2015 Available online 24 July 2015

Keywords: Urban arterial Safety analysis Floating Car Data Poisson-lognormal models Bayesian inference Hierarchical structure

A B S T R A C T

Traffic safety on urban arterials is influenced by several key variables including geometric design features, land use, traffic volume, and travel speeds. This paper is an exploratory study of the relationship of these variables to safety. It uses a comparatively new method of measuring speeds by extracting GPS data from taxis operating on Shanghai's urban network. This GPS derived speed data, hereafter called Floating Car Data (FCD) was used to calculate average speeds during peak and off-peak hours, and was acquired from samples of 15,000+ taxis traveling on 176 segments over 18 major arterials in central Shanghai. Geometric design features of these arterials and surrounding land use characteristics were obtained by field investigation, and crash data was obtained from police reports. Bayesian inference using four different models, Poisson-lognormal (PLN), PLN with Maximum Likelihood priors (PLN-ML), hierarchical PLN (HPLN), and HPLN with Maximum Likelihood priors (HPLN-ML), was used to estimate crash frequencies. Results showed the HPLN-ML models had the best goodness-of-fit and efficiency, and models with ML priors yielded estimates with the lowest standard errors. Crash frequencies increased with increases in traffic volume. Higher average speeds were associated with higher crash frequencies during peak periods, but not during off-peak periods. Several geometric design features including average segment length of arterial, number of lanes, presence of non-motorized lanes, number of access points, and commercial land use, were positively related to crash frequencies.

1. Introduction

Arterials carry most traffic on urban road networks, yet these are the least safe roads. In China's cities, the problem is especially severe with many urban arterials having unusual characteristics including short signal spacing, diverse cross-section configurations, mixed traffic flows, and high volumes (Xie et al., 2013). Previous studies showed roadway geometric and cross-section properties (e.g., segment length) and traffic flow characteristics (e.g., average annual daily traffic) to be important predictors of urban arterial safety (Greibe, 2003; EI-Basyouny and Sayed, 2009; Gomes, 2013). However, these studies did not have an effective method to capture travel speeds throughout their study areas. The present study acquires average travel speeds on selected roadway segments throughout the network in addition to roadway geometric design features, land use, and traffic volumes. This broad spectrum of variables is expected to allow for a more complete analysis of the urban arterial safety problem.

E-mail address: wangxs@tongji.edu.cn (X. Wang).

In Shanghai, travel speeds on the arterial network were acquired using Global Positional System (GPS) data extracted from Shanghai's 50,000+ GPS equipped taxis. These taxis account for about 20% of the traffic on its urban arterials, and this data acquisition approach is hereafter referred to as the Floating Car Data (FCD) method. Compared to fixed-based methods such as radars or loop detectors typically used in speed-safety studies (Garber and Gadiraju, 1989; Baruya, 1998; Taylor et al., 2000), the FCD method is capable of capturing continuous speed data throughout the entire network over any time period of interest. The sample size of more than 15,000 GPS equipped taxis used in this study enabled the calculation of average speeds at an acceptable level of accuracy (Chen and Chien, 2000; Cheu et al., 2002). A total of 176 road segments from 18 arterials in Shanghai were selected for study. Bayesian (rather than classical) models were developed to investigate the relationship between geometric design features, land use, traffic flow, travel speeds, and crash frequency during both peak and off-peak periods.

The classical statistical approach relies on large random samples for accurate estimates, however, in much of transportation research, especially that which considers geometric or land use variables, limited data are available. It is therefore rarely

^* Corresponding author at: School of Transportation Engineering, Tongji University, Shanghai 201804, China.

possible to conduct repeated studies under the same conditions, rendering the classical approach less than ideal. In contrast, another approach that can manage the small sample size problem is available. This approach starts by considering the prevailing conditions prior to the collection of sample data, and defines parameters that reflect these conditions to develop a model (that is, a set of predictive equations). After observing the sample, following Bayes' theorem, (Bayes and Price, 1763), provides a way to calculate probability using prior information or conditions. This Bayesian approach, obtains a posterior distribution for each the unknown parameters by considering both the prior distributions and the current conditions as reflected in the sample. When using the Bayesian approach, the prior distribution is fundamental and represents probabilities for each possible value of the unknown. Two types of prior distributions are used in Bayesian analysis: noninformative prior distributions that do not favor a particular value of the parameter, and are characterized by large variances (Lord and Miranda-Moreno, 2008), and informative prior distributions that assign higher probabilities to values of the parameter that are believed to be more likely to occur (Ntzoufras, 2011). These beliefs are often derived from previous experiments about the issues of interest. An important advantage of the Bayesian approach is its use of iterations to calculate posterior distributions. This has the effect of allowing the Bayesian approach to yield robust predictions in the absence of large samples.

2. Literature review

2.1. Previous urban arterial safety models

Previous safety research has improved our understanding of variables linked to crash rates on urban arterials. In much of this research the analytical models relied mainly on traffic volume, although variables such as segment length, number of intersections, number of access points, pedestrian traffic volumes, road width, lane width, and speed limits have sometimes been considered.

Mountain et al. (1996) developed crash prediction models for roads that included the number of minor junctions (between A-/Broads and C-/unclassified roads), road type, carriageway type (single or dual) and speed limit. They found crash frequencies to be a positively accelerating function of exposure (e.g., annual traffic flow on segment length), and also to be positively associated with the number of minor junctions per kilometer. Bonneson and McCoy (1997) found Average Daily Traffic (ADT), driveway density, unsignalized public- street-approach density, and business land use were all positively correlated with crash frequencies, while raised-curb median treatments were correlated with reduced crash frequencies.

Greibe (2003) developed Generalized Linear Models (GLM) to predict crashes based on data from 142 km of roads located in urban areas in Denmark. The author divided these roads into 314 homogeneous segments averaging 450 m in length. Average Annual Daily Traffic (AADT) was the most powerful predictor of crashes, followed by speed limit, land use, the number of minor side roads per km and parking. Similarly, Turner et al. (2003) found that AADT was strongly associated with crashes for urban road sections in New Zealand.

EI-Basyouny and Sayed (2009) collected data from 58 arterials in Vancouver, British Columbia and found segment length, AADT, crosswalk density, business land use, unsignalized intersection density and the number of lanes were all positively associated with crash frequency. In a recent study, Gomes (2013) developed a crash prediction model for urban roads located in Lisbon, Portugal. He used a Negative Binomial (NB) model to examine crashes in relation to vehicle and pedestrian traffic flow, and highway geometric design features. The crash prediction model identified AADT, segment length, and lane-count greater than 4, as key variables associated with crash frequencies on urban roads.

Yanmaz-Tuzel and Ozbay (2010) conducted a before–after analysis on 4 urban arterials in New Jersey in which they investigated the effects of increases in lane width, installation of median barriers and guide rails, and improvements to vertical and horizontal road alignments. Using a full Bayesian approach, they observed reductions in crash rate (ranging from 23.1% to 28.6%) after adjusting the vertical and horizontal alignments (e.g., curve and grade). Increases in lane width, median barrier installations, and guide rail installations were associated with crash rate reductions of 28.1%, 14.3%, and 15%, respectively.

Das and Abdel-Aty (2011) examined the association of roadway and traffic characteristics including pavement, surface, shoulder, daylight, and street light conditions and surface width, shoulder width, speed limits, visual obstructions, presence of parking, median settings, vertical alignment, and ADT on the frequency and severity of rear-end crashes in Florida. They found higher ADTs were associated with increased crashes, and the absence of onstreet parking was associated with reduced injury severity in crashes.

Dixit et al. (2011) investigated the relationship between arterial operations and crashes in the Orlando Metro using a two-fluid model. This model assumes traffic flow consists of running and stopped vehicles, and uses maximum speed and fraction of running vehicles (ratio of running time per mile to travel time per mile) to describe running speed. Running speed and travel time data were measured using a chase-car method in which drivers followed randomly selected vehicles for about a mile or until they left the arterial. They found higher speeds were positively correlated with both rear-end and angle crash rates.

The research to date has shown the most important variable predictive of crashes is traffic volume, while some of the less important variables are segment length, number of lanes, and number of access points. The relationship of speed to arterial crashes has not received much attention in this prior work. The recent availability of FCD in Shanghai offers a unique opportunity to examine travel speed in combination with other variables that affect urban arterial safety.

2.2. Statistical modeling methods

In past decades, Generalized Linear Models (GLM) such as Poisson-lognormal (PLN) and Negative Binomial (NB) have been commonly used to predict crash frequency (Shankar et al., 1995; Vogt and Bared, 1998; Abdel-Aty and Radwan, 2000). These traditional safety models assume study units are independent. This condition, however, might not be met in the current study because segments within single arterials share similar characteristics such as geometric design, signal control, and traffic flow.

Bayesian spatial models can incorporate hierarchical data structures to correct for spatial correlations (Guo et al., 2010; Huang and Abdel-Aty, 2010), and hierarchical structures can be implemented using random effect terms in Bayesian models (Huang and Abdel-Aty, 2010). EI-Basyouny and Sayed (2009) showed that model predictions can be improved by using spatial Poisson-lognormal models to incorporate random corridor effects. Yanmaz-Tuzel and Ozbay (2010) also showed that a hierarchical structure with random effects improves the predictability of PLN models because of its ability to adjust for spatial and temporal correlations.

Some attention has been directed at the effects of informative priors on model results when adopting the Bayesian approach. Yu and Abdel-Aty (2013) showed the benefits of different informative priors including the two-stage Bayesian priors, the Maximum Likelihood (ML) priors, the Momentary priors and General Information priors in developing safety prediction models. They concluded that the two-stage Bayesian method was the best way to improve model fitting and provide the smallest credible intervals, for the reason that observed samples were treated as an extension of previous data. Miranda-Moreno et al. (2013) simulated data from prior studies using different sample sizes and years of accident data, and combined this previous experience with current data. They found model parameter estimates can be significantly improved by using informative priors based on the findings from those prior studies.

In this study we used informative priors under Bayesian framework and hierarchical model structures to reveal the role of speed and other key variables affecting urban arterial safety. Predictions from four different models, Poisson-lognormal (PLN), PLN with Maximum Likelihood priors (PLN-ML), hierarchical PLN (HPLN), and HPLN with Maximum Likelihood priors (HPLN-ML), were compared to determine if the hierarchical modeling strategy is suitable for urban arterials and if ML priors are useful for improving the efficiency of estimates.

2.3. FCD assumptions and applications

FCD collection has several advantages over fixed-based data collection including wide coverage, a large sample, and a high sampling frequency. These advantages enable the FCD method to acquire accurate and comprehensive operational data over a wide network area in a short time frame.

Currently, FCD in Shanghai can only be obtained from taxis, and the implications of this restriction need to be considered. An important assumption when using taxis to assess roadway operational conditions is that they represent the overall traffic conditions. One consideration worth noting is that traffic congestion in the Shanghai urban area limits the differences in operation between taxis and private vehicles. Nevertheless, taxis without passengers travel more slowly than taxis with passengers (Liu et al., 2009) and therefore taxis without passengers were excluded from the sample. A test of remaining speed differences between unoccupied taxis and overalltraffic flow was conducted by Hu et al. (2008). They found that error between the general traffic speed and the travel speed extracted from floating taxi data was within 4% when the sample size was larger than 2% of traffic volume. This condition was met in this study.

Another matter of concern is the sample size needed to represent the population of moving vehicles within an acceptable level of error across the roadways of interest. Sanwal and Walrand (1995) found that if 4–6% of the cars on a road segment has a floating data collection capability, travel time error estimates would be in the 6–8% range. Other studies suggested that a floating car sample of just 3% of the vehicle population is sufficientfor a 95% confidence level in travel time and speed estimates (Chen and Chien, 2000; Cheu et al., 2002). In this study the sample represented 4–7% of the population.

Various studies using FCD have demonstrated its ability to accurately estimate travel time, speeds, and traffic conditions. FCD has also been used for forecasting (Herring et al., 2010; Zhang et al., 2007) and incident detection (Yu et al., 2007). In China, FCD collection systems have been introduced in several cities including Shanghai, Beijing, and Guangzhou. Based on 177 two-direction segments from 45 arterials in Shanghai, Wang et al. (2014) examined the influence of road geometry, traffic control, and traffic volume on urban arterial operating speeds, and found that an increased number of lanes and longer segment lengths were related to higher speeds. FCD can also be used in safety analysis. Xie et al. (2013) used FCD to calculate arterial-level travel speed and introduced speed as an explanatory variable to investigate intersection safety in Shanghai. He found higher mean speeds along arterials were associated with increased intersection crashes

Fig. 1. Road networks and selected arterials in the study area.

and speed variance was not associated with crash occurrences. However, to date, the FCD method has not been used in the safety analysis of Chinese urban arterials.

3. Data preparation

Roadway geometric design features, land use, traffic characteristics, and crash data were collected from a sample of 18 arterials located in the central parts of Shanghai.

3.1. Arterial selection

The urban arterial selection consisted of three major steps. First, all the urban arterials in the downtown areas more than 4 lanes (total, both directions) were considered, and any arterial undergoing maintenance was removed. Second, the arterials were grouped by the number of through lanes. Third, from each set, arterials were randomly selected. This stratified random sampling method ensures the selected arterials to be heterogeneously representative of urban arterials in Shanghai. Fig.1 shows the arterials used in the study.

Table 1 shows the area, length, peak and off-peak total traffic volumes, and the segment count for each selected arterial.

3.2. Computing travel speed from FCD

Vehicle ID, time, and longitude and latitude were acquired from each GPS equipped vehicle at a mean sampling frequency of once every 15 s. These FCD were sampled on each segment over 3 days (May 5th through May 7th 2009) during both peak (7:00–9:00) and off-peak (12:00–14:00) periods. Two steps, shown in Fig. 2, are needed to acquire data from an individual taxi.

In step one, GPS data points are geocoded to the road to obtain the actual path traversed by the tracked vehicle. In step two, the individual vehicle's travel time and travel speed are computed. As an example, if an individual vehicle j left N data records during its drive through a study road segment, its average travel speed through the segment can be calculated as:

$$V_j = \frac{t_1}{T} v_1 + \frac{t_2}{T} v_2 + \dots + \frac{t_i}{T} vi + \dots + \frac{t{n1}}{T} v_{n-1}$$ (1)

where Vj is the average speed of the selected vehicle j on the segment, ti is the time period between the ith position and the (i + 1)th position, vi is the travel speed for ti, and T is the total travel time the individual vehicle spent on the study segment.

If either the first or the last record from a segment did not occur at the start or end point of a segment, one more GPS record from the previous or following segment was used to calculate the travel speed for the missing part (i.e., between the start and the first record or between the last record and the end).

An example of individual-level speed profiles is shown in Fig. 3. Each speed point represents travel speed vi during ti. Typical stopand-go patterns can be recognized. Observe that most of the taxis stop before the intersections and then accelerate up in the next segment. The running speeds (excluding stops) range from 5 to 80 km/h on different arterials, depending on roadway and traffic flow characteristics. This led to the diverse speed profiles we see on the study arterials.

The average speed of the vehicles traversing the segment was then computed using the equation:

$$\overline{V} = \sum_{j=1}^{N} \frac{V_j}{N} \tag{2}$$

where V is the average travel speed during the peak or the off-peak period, Vj is the average speed of the jth vehicle, and N is the number of vehicles observed during the certain periods.

3.3. Road geometric design features and traffic characteristics

In Shanghai, most urban arterials have a constant number of lanes between consecutive signalized intersections. Given these conditions, the 18 selected arterials were divided into 176 segments, each defined by the two signalized intersections that terminated them. The study unit used is the road segment and excludes intersection approaches.

The segment length was obtained from the GIS base map. The number of lanes, median types, presence of a non-motorized lane, and the pedestrian crossing configuration were collected by field surveys along the arterials in 2009. The number of access points within each segment was determined by viewing aerial photos using Google Earth1. Traffic volume data was acquired for each lane from the loop detectors of the Sydney Coordinated Adaptive Traffic System (SCATS), and were then averaged over the month of May, 2009. The number of access points, number of lanes and the traffic volume of both directions were summed for the two-way segments.

Table 1 Summary information of selected arterials.

Arterial ID	Road name	Area	Length (km)	Total volume PH (pcu/h)	Total volume OPH (pcu/h)	Segment count
1	Zhaojiabang Road	W	4.934	3478	2741	14
2	Changning Road	W	6.474	3005	2187	22
3	Haining Road	W	6.943	3728	3110	25
4	Siping Road	W	5.2	1923	1565	15
5	Zhongshan Road	W	3.438	2452	2151	11
6	Caoyang Road	W	7.572	2239	1879	24
7	Middle Yanggao Road	E	6.482	4658	4258	8
8	Luoshan Road	E	4.455	5165	4765	3
9	Hengshan Road	W	1.748	2134	1770	4
10	Zhangyang Road	E	3.663	2475	2075	8
11	Longchang Road	W	0.936	1558	993	2
12	Pujian Road	E	1.28	3207	2493	3
13	West Beijing Road	W	1.775	1629	1491	5
14	Guangzhong Road	W	4.005	2020	1480	9
15	Middle Huaihai Road	W	2.175	1994	1929	5
16	Wuning Road	W	2.277	3671	2583	5
17	North Xizang Road	W	2.108	2799	2112	7
18	Xietu Road	W	2.255	1780	1378	6

Note: W represents the Puxi area and E represents the Pudong area; total volume PH represents the traffic volume of all lanes during the peak hour, and total volume OPH represents the traffic volume of all lanes during the off-peak hour.

Fig. 2. Description of FCD processing.

Fig. 3. Example of speed profile for Arterial #1.

The statistical summary of the geometric design features and traffic characteristics is shown in Table 2.

3.4. Crash data

All crashes occurring in 2009 on the selected arterials were obtained from traffic police reports. Intersection crashes were excluded because their causes are usually different from those of crashes not in proximity to an intersection. The geocoding procedure was used to locate the crashes on the GIS base map in ArcMap (2008). In order to explore the relationships under different traffic conditions, crashes in peak (7:00–9:00 am) and offpeak (12:00–14:00 pm) periods were studied separately. The total crash numbers were 1101 and 761 for peak and off-peak periods, respectively.

Table 2 Summary statistics of the geometric design features and traffic characteristics.

Explanatory variables	Description	Summary statistics
Arterial-level variable
Average segment length Segment-level variables	Average segment length on arterials (km)	Mean: 0.4640; SD: 0.2735
Segment length	Length of segment (km)	Mean: 0.384; SD: 0.269
Number of lanes	Number of through lanes in both directions	4/5 lanes: 64;
		6/7 lanes: 39;
		8 lanes: 58;
		9 lanes: 8;
		10 lanes: 7
Median separator types	Median types: 0 for no median, 1 for barrier, 2 for strip, either crossable or non-crossable	No median separator: 42;
		Median barrier: 43;
		Median strip: 91
Non-motorized lane	Presence of a non-motorized lane	Yes: 127;
		No:49
Number of accesses	Total number of access points along segment of both sides	Mean: 0.949; SD: 1.315
3-legged unsignalized intersections	Total number of 3-legged unsignalized intersections on the segment	Mean:0.574; SD: 1.031
Pedestrian crossing	Pedestrian crossing on segment: 0 for without, 1 for with	With: 28;
		Without: 148
Curve	Horizontal curve of segment: 0 for straight segment, 1 for segment with curve	Tangent segments: 126;
		Curvilinear segments: 50
Land use	Land use types: 0 for non-commercial, 1 for commercial	Non-commercial: 124;
		Commercial: 52
Average speed PH	Mean speed of segment in peak period (km/h)	Mean: 26.89; SD: 10.05
Average speed OPH	Mean speed of segment in off-peak period (km/h)	Mean: 31.70; SD: 10.09
Average volume PH	Average traffic volume per hour per lane during peak period in both directions (pcu/h/lane)	Mean: 448.88; SD: 108.484
Average volume OPH	Average traffic volume per hour per lane during off-peak period in both directions (pcu/h/lane)	Mean: 361.22; SD: 94.68

4. Statistical methods

4.1. Bayesian PLN and hierarchical PLN models

The full Bayesian approach used in this study considers parameters as random variables characterized by prior distributions, and calculates posterior distributions using both observed data and those prior distributions. Priors represent previous knowledge of the parameters, and this knowledge changes after taking into account the observed sample and the relationship between explanatory and response variables.

The theoretical framework for Bayesian inference is defined as:

$$\pi(\theta|\mathbf{y}) = \frac{L(\mathbf{y}|\theta)\pi(\theta)}{\int L(\mathbf{y}|\theta)\pi(\theta)d\theta}$$ (3)

where y is the vector of observed data, u is the vector of parameters required for the likelihood function, ^Lðyju^Þ is the likelihood function, pðu^Þ is the prior distribution of u, R ^LðyjuÞpðuÞdu is the marginal distribution of observed data, and pðujy^Þ denotes the posterior distribution of u given y. The posterior distribution pðujy^Þ combines information from both the observed data and the prior distribution.

Rare events such as crashes have been found to conform to a Poisson distribution. Therefore Poisson models are frequently used in traffic safety studies to model these random, discrete, nonnegative data (Abdel-Aty and Radwan, 2000). However, because the classic Poisson model assumes that the mean of the dependent variable should be equal to its variance, it cannot handle the overdispersion problem typically observed in crash data. Under the Bayesian framework, Poisson-lognormal models express the model as a typical Poisson model and can incorporate random effects of the linear predictor to address overdispersion for unobserved or unmeasured heterogeneity (EI-Basyouny and Sayed, 2009).

The Poisson-lognormal model can be defined as follows:

$$Y_i | \theta_i \sim \text{Poisson}(\theta_i)$$ (4)

where Yi is the crash frequency on the arterial segmenti. To address overdispersion for unobserved or unmeasured heterogeneity, it assumed that:

$$\theta_i = \mu_i \exp(\varepsilon_i) \tag{5}$$

$$Log(\mu_i) = \beta_0 + \beta X_i \tag{6}$$

where Xi represents the risk factors (e.g., mean speed, number of lanes) and b is a vector of regression parameters. The term exp(ei) represents a random effect and is expressed in the following equation:

$$\exp(\varepsiloni) \sim \text{Lognormal}(0, \sigma{\varepsilon}^2), \text{ or } \varepsiloni \sim N(0, \sigma{\varepsilon}^2)$$ (7)

where the variance parameter 1=s² ^e is specified as Gamma prior distribution (0.001, 0.001).

In this study, the segments belong to 18 different urban arterials, and segments within an arterial share spatial correlations and different arterials have spatial heterogeneities, a condition requiring a hierarchical structure of Bayesian inference to model the inherent multilevel data structure of the arterials. A two-level structure with a varying-intercept proposed by Huang and Abdel-Aty (2010) was adopted in this study for PLN models. This hierarchical PLN model can be defined as follows:

Segment-level (Level 1) model:

$$Log(\theta_i) = \beta_0^{L1} + \beta^{L1} X^{L1} + \varepsilon^{L1}$$ (8)

Arterial-level (Level 2) model:

$$\beta0^{L1} = \beta{00}^{L2} + \beta_0^{L2} X^{L2} + \varepsilon^{L2} \tag{9}$$

The combined model (below) is obtained by substituting the Arterial-level model into the Segment-level model:

$$Log(\thetai) = \beta{00}^{L2} + \beta_0^{L2} X^{L2} + \beta^{L1} X^{L1} + \varepsilon^{L1} + \varepsilon^{L2}$$ (10)

where bL2 ⁰⁰ is the intercept represents the main effect on the average values of covariates, bL2 ⁰ is the main-effect coefficient of level 2 covariates XL2 on the dependent variable, bL1 is the maineffect coefficient of level 1 covariates XL1 on the dependent variable. eL1 is the random effect of level 1 equation, and exp eL1 - follows a Lognormal distribution, and eL2 is the random effect of level 2 equation. In particular, eL1 explains the within-arterial (between-segment) variation and eL2 explains the betweenarterial variation. The variance parameters for eL1 and eL2 are specified as Gamma prior distributions (0.001, 0.001).

4.2. Informative priors

Informative priors that incorporate extra information and experience about the data can be used to make model estimates more robust. There are different methods to obtain such informative priors. Yu and Abdel-Aty (2013) investigated four approaches of developing informative priors. The two-stage Bayesian updating method needs historical data gathered from previous work, which is unavailable in this study. ML priors, derived using Maximum Likelihood estimation, have been shown to perform better at improving model fitting than the other two methods such as method of moments and expert experience. To acquire a ML prior for a parameter, a statistical model (e.g., NB model) is first established, and the parameter is estimated by the classical Maximum Likelihood method. The mean and variance of this estimate are then used to formulate a normal distribution. In comparison, the non-informative prior used in this study followed a normal distribution with the mean of 0 and the variance of 100,000. This prior utilized little information of sample data. While it is convenient for computing, it is less helpful for remaining estimates unbiased.

4.3. Goodness-of-fit test for Bayesian estimations

Spiegelhalter et al. (2003) introduced the Deviance Information Criterion (DIC) as a means to compare the adequacy and complexity of models. It is given by the expression:

$$DIC(m) = 2\overline{D(\theta_m, m)} - D(\overline{\theta}, m) = D(\overline{\theta_m, m}) + 2p_m$$ (11)

where ^D um; ^m^Þ is the usual deviance measure, and is equal to minus twice the log-likelihood ^D um; ^m^Þ ^¼ 2logfðyjum; ^m^Þ and ^Dðum; ^m^Þ is its posterior mean, pm can be interpreted as the number of effective parameters for the model as given by pm ^¼ ^Dðum; ^m^Þ ^Dðu; ^mÞ, and u is the posterior mean of the parameters involved in the model. Smaller DIC values indicate a better-fitting model.

5. Model results

Crashes in both peak and off-peak periods were modeled as a function of geometric design features, land use, and traffic characteristics. Four Bayesian models, PLN, PLN-ML, HPLN, and HPLN-ML, were developed and results were compared to reach the best modeling solution.

5.1. Bayesian model estimates

The independent variables were geometric design features, land use, and the traffic characteristics of average volume and average travel speed. The dependent variables were the peak and the off-peak period crashes. When fitting the models, the total traffic volume of segments were highly correlated with number of lanes, and therefore average volume per lane was used instead. It should also be noted that average segment length of an arterial manifests the hierarchical structure, and has a different meaning in comparison to segment length at the segment-level, because it accounts for the effects of arterials' roadway features on crashes.

In order to obtain the ML priors, classical NB models were first developed for each independent variable using ML estimation in SAS (2002). The mean and variance of output estimates were then used to formulate the ML priors. The ML priors are summarized in Table 3. Please note that the number of lanes was recoded into five categories and represented by four dummy variables with the baseline as "4/5 lanes". The presence of a non-motorized lane and commercial land use were also treated as categorical variables.

Markov Chain Monte Carlo (MCMC) methods are used in Bayesian inference to obtain posterior distributions, which consist of two parts—Markov Chain algorithms and Monte Carlo simulations (Lunn et al., 2000). Gibbs sampling algorithm, one of the Markov Chain algorithms, was used to generate two chains for each parameter in this study. It started with initializing a parameter of interest, and then updating the parameter using its last value until an equilibrium distribution was reached. This condition required the first 5000 iterations of each chain to be treated as burn-in and excluded from this study. Convergence tests such as MC error and trace plots were then conducted. Once the two chains were converged, the Monte Carlo simulation generated 10,000 samples that were drawn from each chain, and a posterior distribution of each parameter was plotted. Finally, posterior summaries (e.g., mean, standard errors) were calculated. Tables 4 and 5 show the posterior summaries for the peak period and off-peak period models.

Table 3 ML prior distributions for Bayesian models.

Explanatory variables	Peak period	Off-peak period
Average segment length of arterial	(2.8848, 3.1899)	(1.6955, 3.7398)
Segment length	(2.4737, 6.4125)	(1.8028, 7.2457)
6/7 lanes vs. 4/5 lanes	(0.572, 15.4878)	(0.0135, 16.8518)
8 lanes vs. 4/5 lanes	(0.8965, 19.596)	(0.3627, 21.7749)*
9 lanes vs. 4/5 lanes	(0.5091, 4.6149)	(0.1335, 5.0408)
10 lanes vs. 4/5 lanes	(1.1992, 4.3133)	(0.2064, 4.5212)
Non-motorized lane	(0.487, 21.0227)	(0.5461, 24.2905)
Number of accesses	(0.0634, 1089.2178)	(0.0749, 1351.6436)
Commercial land use	(0.1881, 22.0622)	(0.602, 28.0541)
Average traffic volume	(1.3859, 5.3238)	(0.7227, 6.7290)*
Average travel speed	(0.0288, 11562.0303)	(0.0075, 16436.5549)

Note: Prior distributions are normal distributions with N (mean, 1/variance). Variables bolded were statistically significant with 95% certainty; variables bolded and noted by * were statistically significant with 90% certainty.

Table 4 Posterior summary for the peak period Bayesian models.

Explanatory variables	PLN	PLN-ML	HPLN	HPLN-ML
Intercept	2.703 (2.258)	5.342 (1.725)	4.861 (1.14)	5.679 (1.192)
Arterial-level variable
Average segment length			9.386 (3.926)	2.856 (0.5529)
Segment-level variable
Segment length	2.463 (0.2722)	2.285 (0.2297)	2.15 (0.322)	2.17 (0.2287)
Number of lanes
6/7 lanes vs. 4/5 lanes	0.5 (0.2391)	0.5739 (0.1608)	0.1623 (0.2588)	0.4351 (0.172)
8 lanes vs. 4/5 lanes	0.8095 (0.2131)	0.8111 (0.1411)	0.7567 (0.2742)	0.8908 (0.1608)
9 lanes vs. 4/5 lanes	0.3514 (0.4186)	0.4258 (0.3012)	0.2176 (0.4253)	0.4339 (0.2964)
10 lanes vs. 4/5 lanes	0.05247 (0.52)	0.5492 (0.3298)	0.06942 (0.5283)	0.636 (0.3411)
Non-motorized lane
Yes vs. No	0.856 (0.1969)	0.6906 (0.146)	0.621 (0.2359)	0.6015 (0.1586)
Number of access points	0.0852 (0.0248)	0.0779 (0.0189)	0.0348 (0.030)	0.0510 (0.0224)
Volume in log form	0.2928 (0.3724)	0.6967 (0.2846)	0.2646 (0.2341)	0.6357 (0.1928)
Average speed	0.0100 (0.0088)	0.0041 (0.0059)	0.0188 (0.0094)	0.0029 (0.0065)*
s2 s			0.4116 (0.2634)	0.2776 (0.1931)
s2 0			0.5062 (0.1019)	0.5521 (0.1086)
DIC	788.176	790.866	778.484	782.147

Note: Posterior distributions are summarized as mean and standard error. Standard error is placed within the bracket. Variables bolded were statistically significant with 95% certainty; variables bolded and noted by * were statistically significant with 90% certainty.

Table 5 Posterior summary for the off-peak period Bayesian models.

Explanatory variables	PLN	PLN-ML	HPLN	HPLN-ML
Intercept	1.969 (2.521)	2.855 (1.017)	1.536 (2.961)	2.407 (1.409)*
Arterial-level variable
Average segment length			5.583 (5.8)*	1.645 (0.5227)
Segment-level variable
Segment length	2.043 (0.3259)	1.792 (0.2311)	1.944 (0.3391)	1.717 (0.2317)
Number of lanes
6/7 lanes vs. 4/5 lanes	0.0208 (0.2556)	0.0321 (0.1652)	0.2908 (0.291)	0.0828 (0.1746)
8 lanes vs. 4/5 lanes	0.3854 (0.2225)	0.3382 (0.1392)	0.5068 (0.303)*	0.4362 (0.1594)
9 lanes vs. 4/5 lanes	0.0129 (0.4301)	0.0531 (0.2995)	0.0492 (0.4476)	0.0628 (0.2911)
10 lanes vs. 4/5 lanes	0.8522 (0.5557)	0.3167 (0.3425)	0.5877 (0.584)	0.2076 (0.3452)
Non-motorized lane
Yes vs. No	0.8034 (0.2003)	0.6788 (0.1423)	0.6858 (0.2454)	0.6178 (0.1517)
Commercial land use
Yes vs. No	0.6619 (0.1894)	0.6495 (0.129)	0.3296 (0.2062)	0.5278 (0.1357)
Volume in log form	0.2784 (0.4314)	0.4028 (0.1735)	0.0044 (0.3129)	0.2561 (0.2365)*
Average speed	0.0149 (0.0100)	0.0033 (0.0058)	0.0288 (0.0112)	0.0044 (0.0062)
s2 s			0.4417 (0.26)	0.2851 (0.1716)
s2 0			0.5415 (0.1138)	0.5593 (0.1111)
DIC	737.34	738.18	726.953	728.279

As stated in Spiegelhalter et al. (2003), when comparing two Bayesian models' goodness-of-fit, differences in DIC values of more than 10 rule out the model with higher DIC. Differences less than 5 are not substantial enough to judge for better model fitting. Consequently, there was no statistically significant difference in goodness-of-fit between the PLN and the PLN-ML models. Likewise, close DIC values were found between the HPLN and the HPLN-ML models. However, when comparing the PLN-ML with the HPLN-ML, the differences of the DIC values were significant. This suggested that hierarchical model specification significantly benefited goodness-of-fit. In addition, the Standard Error (S.E.) of HPLN models' estimations were all larger than those of the HPLN-ML models, except for the constant terms during the peak period.

Considering the example of the segment length, the standard errors of the HPLN-ML model were 29.0% and 31.7% less than those of HPLN model for peak and off-peak periods, respectively. This suggested that the use of the ML prior helped to improve the efficiency of the estimates. Moreover, the between-arterial variations of total variations (calculated as s² ^s = s² ^s ^þ s² ) are about 33.5% and 33.8% for peak and off-peak periods respectively, indicating the existence of unobserved spatial heterogeneities among selected arterials and the necessity of using a hierarchical model structure. Consequently, the HPLN-ML models were determined to be the best for exploring the effects of the independent variables on crash frequencies for both the peak and off-peak periods.

5.2. Variable interpretation

5.2.1. Roadway geometric design features

Average segment length was introduced as an arterial-level variable in the HPLN-ML models. With each increase of 1 km in average segment length, crash frequencies increased by a factor of 17.39 for peak periods and by a factor of 5.18 for off-peak periods.

Segment length was positively related to crash frequency. Each 1 km increase in segment length was associated with an increase in crash frequency by a factor of 8.76 for peak and 5.57 for off-peak periods. This is consistent with Griebe's (2003) findings that longer segment lengths are associated with higher crash frequencies.

Number of lanes ranged from 4 to 10, and increases of number of lanes were positively associated with increases in crash frequencies during both peak and off-peak periods. This finding is consistent with previous studies (EI-Basyouny and Sayed, 2009; Gomes, 2013).

Non-motorized lane segment crash frequencies were 82% and 85% higher than segments without non-motorized lanes for peak and off-peak periods, respectively. Non-motorized traffic is forbidden on segments without non-motorized lanes, and this confirms that conflicts between motorized and non-motorized traffic contribute to increased crashes on urban arterials.

Number of access points had a statistically significant although small, association with crash frequency during the peak periods only. Each unit increase in the number of access points was associated with an increase in crash frequency of 5%, a finding that is also consistent with an earlier study by Greibe (2003).

5.2.2. Land use

Commercial land use in the off-peak period had a 70% higher crash frequency than non-commercial land use (i.e., residential, mixed). An explanation could be that commercial land use has more traffic than non-commercial land use, resulting in increased conflicts. In the peak period, traffic volume was saturated, so the difference of traffic volume between commercial land use and noncommercial land use was minimal, and therefore no relationship to crash frequency was observed in the peak models.

5.2.3. Traffic characteristics

Average traffic volume was positively correlated with crash frequencies during both peak and off-peak periods, although the relationship was stronger during the peak periods. This finding is probably attributable to increased interactions in the traffic flow associated with increased volume, a finding that was also shown in earlier studies (Greibe, 2003; EI-Basyouny and Sayed, 2009; Das and Abdel-Aty, 2011; Gomes, 2013).

Average travel speed was not significantly related to crash frequency during the off-peak period, however, during the peak period, an increase of 10 km/h in speed was associated with an increase in crash frequency of 3%, a finding consistent with some previous studies (Nilsson, 1982; Elvik, 2009). However, other studies (Bruya, 1989; Garber and Gadiraju, 1989) found an inverse speed-crash relationship on rural roads. Bruya (1989) explained this negative relationship by attributing it to interactions among variables, while Garber and Gadiraju (1989) attributed itto a strong negative correlation between speed deviation and average speeds.

6. Summary and discussion

The objective of this study was to examine the relationships among geometric design features, land use, traffic volume, average travel speed and urban arterial safety. Data from over 15,000 individual-level speed samples were acquired from taxis running through Shanghai's central urban network. These data were used to calculate segment-level speeds on 18 urban arterials and allowed speed to be included as an explanatory variable in arterial safety models for the first time at the network level. The FCD method adopted in this study has two advantages over fixed based speed assessment methods that have been used previously (see e.g., Baruya, 1998; Garber and Gadiraju, 1989). First, sampling at a 15-s rate simultaneously from numerous vehicles equipped with GPS makes it possible to comprehensively assess the nature of speed profiles along the entire length of the selected segments. Second, FCD can be collected across an entire urban road network over any time period of interest.

Four different Bayesian models, PLN, PLN-ML, HPLN, and HPLN-ML, were developed for both peak and off-peak periods to compare the efficiency of their predictions. HPLN had better goodness-of-fit than PLN, and this implies that a multilevel data structure exists in urban arterials. This data structure accommodates the fact that segments from the same arterial share spatial correlations and that different arterials are distinguished by spatial heterogeneities. ML priors helped to obtain more efficient estimates than noninformative priors because such priors better matched the nature of the data and thereby improved the predictability of the models. This finding is consistent with the findings of Yu and Abdel-Aty (2013).

The use of prior distributions for making predictions goes to the heart of Bayesian analysis because it allows the researcher to take advantage of previous knowledge when making predictions based on new data. The previous knowledge can be acquired from earlier studies, experts' opinions, or even preliminary analyses of current data. The Bayesian approach also enables prior information to be updated, and this helps to overcome the subjective concerns of Bayesian approach. Advocates of classical approaches have criticized the Bayesian approach for the subjectivity inherent in the selection of prior distributions. Indeed, priors vary from one experimenter to another and different methods for determining priors may be used. However, considering that random sampling does not lead to sufficient sample sizes in these types of field studies, it seems advantageous to use the Bayesian approach.

Quantification of the associations among geometric design features, land use, traffic characteristics and crash frequencies is useful for traffic planners and engineers as they seek to improve urban arterial safety. The finding, for example, that segments with non-motorized lanes have higher crash frequencies than those without such lanes is important for any cities where mixed traffic flows commonly exist on urban arterials. Such a finding suggests non-motorized traffic should not be permitted on some arterials. Also, the finding that increases in the number of lanes are associated with increased crashes suggests that careful consideration be given on whether to add lanes, while the finding that increased access points are correlated to increased crashes suggests better access management needs to be considered. Other variables including average segment length, segment length, and commercial land use suggest more attention needs to be paid to road network planning.

The relationship of average travel speed was relatively weak in this study—an increase of 10 km/h in speed was associated with just a 3% increase in crashes. Aarts and Schagen (2006) pointed out that the interactions among many variables including road geometric properties, intersection density, and traffic flow affect the relationship between speed and safety, and this could explain why consistent speed–crash relationships have not been routinely found. In addition, inconsistent findings of speed–crash relationships may be attributable to measurement inaccuracies of prevailing speeds and speed distributions at the moment of the crash. Such inconsistencies may be also explained by the way the question is asked. In this study we looked at average speed over arterial segments, whereas some of the other research (e.g., Solomon, 1964; Cirillo, 1968) focused on the speeds and variability of individual vehicles at the moment of the crash. Using speed data from crash involved vehicles for modeling may be more predictive of crash frequencies. However, most engineering measures including speed limits affect the population of traffic, and therefore it is necessary to examine the relationship between speed and crash frequency at the road segment level. Compared to previous fixed based methods, FCD may be used in the future to help unravel some of these inconsistencies because of its potential for acquiring precise pre-crash average speeds of segments, as well as the variability of segment speeds occurring at the moment of crashes.

Research on urban arterial safety is in early stage in China, and various problems need to be further considered. This study was an attempt to exploit the FCD method to measure travel speed, and to introduce this new technique in combination with Bayesian hierarchical modeling strategies to reflect relationships between operational conditions and traffic safety from a macroscopic perspective.

Acknowledgements

This study was jointly sponsored by the Chinese National Science Foundation (51138003), Science and Technology Commission of Shanghai Municipality (15DZ1204800), and the Fundamental Research Funds for the Central Universities. The authors would like to thank Shanghai YOOTU Cooperation for providing the Floating Car Data.

References

Aarts, L., Schagen, I.V., 2006. Driving speed and the risk of road crashes: a review. Accid. Anal. Prev. 38 (2), 215–224.
Abdel-Aty, M., Radwan, E., 2000. Modeling traffic accident occurrence and involvement. Accid. Anal. Prev. 32 (5), 633–642.
ArcMap1, Version 9.3, 2008. Environmental Systems Research Institute (ESRI) Inc. Bayes, T., Price, R., 1763. An essay towards solving a problem in the doctrine of chances. Philos. Trans. R. Soc. 53, 370–418.
Baruya, B., 1998. Speed-accident relationships on European roads. Proceedings of the Conference 'Road Safety in Europe', Bergisch Gladbach, Germany,
September 21–23, VTI Konferens No.10A, Part 10, pp. 1–17. Bonneson, J.A., McCoy, P.T.,1997. Effect of median treatment on urban arterial safety an accident prediction model. Transp. Res. Rec.: J. Transp. Res. Board 1581 (1),
27–36. Cirillo, J.A., 1968. Interstate system crash research; study II, interim report II. Public Roads 35 (3), 71–76.
Cheu, R.L., Xie, C., Lee, D.H., 2002. Probe vehicle population and sample size for arterial speed estimation. Comput. Aided Civ. Infrastruct. Eng. 17, 53–60.
Chen, M., Chien, S., 2000. Determining the number of probe vehicles for freeway travel time estimation using microscopic simulation. Proceedings of the
Transportation Research Board 79th Annual Meeting, Washington, D.C.. Das, A., Abdel-Aty, M.A., 2011. A combined frequency–severity approach for the analysis of rear-end crashes on urban arterials. Saf. Sci. 49, 1156–1163.
Dixit, V.V., Pande, A., Abdel-Aty, M., Das, A., Radwan, E., 2011. Quality of traffic flow on urban arterial streets and its relationship with safety. Accid. Anal. Prev. 43 (5), 1610–1616.
EI-Basyouny, K., Sayed, T., 2009. Accident prediction models with random arterial parameters. Accid. Anal. Prev. 41 (5), 1118–1123.
Elvik, R., 2009. The Power Model of the relationship between speed and road accidents. TØI Report 1034/2009. Institute of Transport Economics TOI, Oslo.
Garber, N.J., Gadiraju, R., 1989. Factors affecting speed variance and its influence on accidents. Transp. Res. Rec. (1213), 64–71.
Gomes, S.V., 2013. The influence of the infrastructure characteristics on urban road accidents occurrence. Accid. Anal. Prev. 60, 289–297. Greibe, P., 2003. Accident prediction models for urban roads. Accid. Anal. Prev. 35
(2), 273–285. Herring, R., Hofleitner, A., Abbeel, P., Bayen, A., 2010. Estimating arterial traffic
conditions using sparse probe data. Proceedings of the 13th International IEEE Conference Intelligent Transportation Systems 929–936.
Hu, Z.W., Wen H.M., Sun, J.P., Chen, F., 2008. Study on Floating Car Data System Based on Vehicle License Plate Recognition Data.
Huang, H., Abdel-Aty, M., 2010. Multilevel data and Bayesian analysis in traffic safety. Accid. Anal. Prev. 42 (6), 1556–1565.
Guo, F., Wang, X., Abdey-Aty, M., 2010. Modeling signalized intersection safety with arterial-level spatial correlations. Accid. Anal. Prev. 42 (1), 84–92.
Liu, B., Liu, K., Mizuta, H., 2009. Study on impact of taxi status to probe car system performance. Intelligent Transport Systems Telecommunications (ITST), 9th International Conference on IEEE 136–137.
Lord, D., Miranda-Moreno, L.F., 2008. Effects of low sample mean values and small sample size on the estimation of the fixed dispersion parameter of Poissongamma models for modeling motor vehicle crashes: a Bayesian perspective. Saf. Sci. 46 (5), 751–770.
Lunn, D.J., Thomas, A., Best, N., Spiegelhalter, D., 2000. WinBUGS—a Bayesian modelling framework: concepts, structure, and extensibility. Stat. Comput. 10, 325–337.
Miranda-Moreno, L.F., Heydari, S., Lord, D., Fu, L., 2013. Bayesian road safety analysis: incorporation of past evidence and effect of hyper-prior choice. J. Saf. Res. 46, 31–40.
Mountain, L., Fawaz, B., Jarrett, D., 1996. Accident prediction models for roads with minor junctions. Accid. Anal. Prev. 28 (6), 695–707.
Nilsson, G., 1982. The effects of speed limits on traffic crashes in Sweden. 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.
Ntzoufras, I., 2011. Bayesian Modeling Using WinBUGS, vol. 698. John Wiley & Sons. Solomon, D., 1964. Crashes on main rural highways related to speed, driver and vehicle. Bureau of Public Roads. U.S. Department of Commerce. United States Government Printing Office, Washington, D.C.
Sanwal, K.K., Walrand, J., 1995. Vehicle as probes. California PATH Working Paper UCB-ITS-PWP-95-11. Institute of Transportation Studies, University of California, Berkley.
Shankar, V., Mannering, F., Barfield, W., 1995. Effects of roadway geometrics and environmental factors on rural freeway accident frequencies. Accid. Anal. Prev. 27 (3), 371–389.
SAS, 2002. Version 9.3 of the SAS System for Windows. SAS Institute Inc..
Spiegelhalter, D., Thomas, A., Best, N., Lunn, D., 2003. WinBUGS User Manual. MRC Biostatistics Unit, Cambridge.
Taylor, M.C., Lynam, D.A., Baruya, A., 2000. The effects of drivers' speed on the frequency of road accidents. TRL Report, No. 421. Transport Research Laboratory TRL, Crowthorne, Berkshire.
Turner, S., Durdin, P., Bone, I., Jackett, M., 2003. New Zealand accident prediction models and their applications. Transport: Our Highway to a Sustainable Future: Proceedings of the 21st ARRB and 11th REAAA Conference, Cairns, Queensland, Australia.
Vogt, A., Bared, J., 1998. Accident models for two-lane rural segments and intersections. Transp. Res. Rec.: J. Transp. Res. Board 1635 (1), 18–29.
Wang, X., Liu, H., Yu, R., Deng, B., Chen, X., Wu, B., 2014. Exploring operating speeds on urban arterials using floating car data: case study in Shanghai. J. Transp. Eng. 140 (September (9)), 04014044.
Xie, K., Wang, X., Huang, H., Chen, X., 2013. Corridor-level signalized intersection safety analysis in Shanghai, China using Bayesian hierarchical models. Accid. Anal. Prev. 50, 25–33.
Yanmaz-Tuzel, O., Ozbay, K., 2010. A comparative full Bayesian before-and-after analysis and application to urban road safety countermeasures in New Jersey. Accid. Anal. Prev. 42 (6), 2099–2107.
Yu, R., Abdel-Aty, M., 2013. Formulating informative priors and the effects on Bayesian hierarchical crash models. Proceedings of Transportation Research Board 92nd Annual Meeting, Washington, D.C..
Yu, L., Yu, L., Qi, Y., Wang, J.Q., Wen, H.M., 2007. Traffic incident detection algorithm for urban expressways based on probe vehicle data. J. Transp. Syst. Eng. Inf. Technol. 8 (4), 36–41.
Zhang, W., Xu, J., Wang, H., 2007. Urban traffic situation calculation methods based on probe vehicle data. J. Transp. Syst. Eng. Inf. Technol. 1, 43–49.

wangsafetymodelingurbanarterials2015.md 69 KB Cronologia Originale