--- category: literaturenote citekey: leemultilevelhotzone2015 title: Multi-level hot zone identification for pedestrian safety authors: "Lee, Jaeyoung; Abdel-Aty, Mohamed; Choi, Keechoo; Huang, Helai" year: 2015 date: 2015-00-00 2015 doi: 10.1016/j.aap.2015.01.006 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/j.aap.2015.01.006" zotero_key: R7P9HHAH zotero_storage: T454W29C collections: transpordi_planeerimine folder: 001_artiklid firstAuthor: "Lee, Jaeyoung" status: converted --- ## Accident Analysis and Prevention journal homepage: ![](_page_0_Picture_5.jpeg) # Multi-level hot zone identification for pedestrian safety ![](_page_0_Picture_7.jpeg) Jaeyoung Lee a, \*, Mohamed Abdel-Aty a , Keechoo Choi b , Helai Huang c - aDepartment of Civil, Environmental and Construction Engineering, University of Central Florida, Orlando, Florida 32816-2450, United States - bDepartment of Transportation Systems Engineering, Ajou University, Suwon 443-749, Republic of Korea - Urban Transport Research Center, School of Traffic and Transportation Engineering, Central South University, Changsha, Hunan 410075, PR China #### ARTICLE INFO Article history: Received 10 August 2014 Received in revised form 7 November 2014 Accepted 6 January 2015 Available online 17 January 2015 Keywords: Pedestrian safety Bayesian approach Spatial error modeling Gaussian conditional autoregressive CAR Screening Macroscopic analysis Poisson lognormal model Simultaneous equations modeling #### ABSTRACT According to the National Highway Traffic Safety Administration (NHTSA), while fatalities from traffic crashes have decreased, the proportion of pedestrian fatalities has steadily increased from 11% to 14% over the past decade. This study aims at identifying two zonal levels factors. The first is to identify hot zones at which pedestrian crashes occurs, while the second are zones where crash-involved pedestrians came from. Bayesian Poisson lognormal simultaneous equation spatial error model (BPLSESEM) was estimated and revealed significant factors for the two target variables. Then, PSIs (potential for safety improvements) were computed using the model. Subsequently, a novel hot zone identification method was suggested to combine both hot zones from where vulnerable pedestrians originated with hot zones where many pedestrian crashes occur. For the former zones, targeted safety education and awareness campaigns can be provided as countermeasures whereas area-wide engineering treatments and enforcement may be effective safety treatments for the latter ones. Thus, it is expected that practitioners are able to suggest appropriate safety treatments for pedestrian crashes using the method and results from this study. ã 2015 Elsevier Ltd. All rights reserved. #### 1. Introduction According to the National Highway Traffic Safety Administration (NHTSA), both fatalities and fatality rates from road traffic crashes in the United States have steadily declined from 2006 to 2011. Conversely, fatalities resulting from traffic crashes slightly increased in 2012 [\(NHTSA, 2013](#page-9-0)). Totally 33,561 lives were lost due to road traffic crashes in 2012. Among these fatalities, the proportion of pedestrian has steadily increased from 11% to 14% over the past decade [\(NHTSA, 2014](#page-9-0)). It shows the reason why we must keep focusing on the pedestrian crash issues. There are two perspectives to analyze traffic safety. The first perspective, microscopic safety analysis focuses on specific roadway entities including segments, intersections, corridors and so forth. The microscopic safety analysis aims to find out factors affecting traffic safety risk from geometric design and/or traffic characteristics of the roadway entities, and suggest specific engineering solutions to alleviate this risk. On the other hand, macroscopic safety analysis concentrates on zonal-level traffic safety with zonal characteristics. The macroscopic safety analysis can provide a broad spectrum perspective, and it suggests policy-based countermeasures including enactments of traffic rules, police enforcements, education/safety campaigns, and area-wide engineering treatments. In this study, the multi-level pedestrian safety was explored at the macroscopic level with the objective of providing guidance to policy decision makers to effectively improve pedestrian safety. Pedestrian crashes have been considered a serious issue and many researchers have conducted pedestrian crash analysis at the macroscopic level ([LaScala et al., 2000; Ng et al., 2002; Loukaitou-](#page-9-0)[Sideris et al., 2007; Wier et al., 2009; Cottrill and Thakuriah, 2010;](#page-9-0) [Ukkusuri et al., 2011; Siddiqui et al., 2012; Siddiqui and Abdel-Aty,](#page-9-0) [2012; Wang and Kockelman, 2013; Abdel-Aty et al., 2013; Lee et al.,](#page-9-0) [2013](#page-9-0)). [LaScala et al. \(2000\)](#page-9-0) examined pedestrian injury rates across 149 census tracts in the city of San Francisco. The authors found that the pedestrian injury rates were associated with traffic flow, population density, age composition of the local population, unemployment, gender and education. [Ng et al. \(2002\)](#page-9-0) revealed that the number of cinema seats, commercial area, flatted factory area, market stall, and MTR catchment area were positively related to the pedestrian crashes. Meanwhile, the greenbelt area, specialized factory area, and school places had negative relationships with pedestrian crashes in Hong Kong. [Loukaitou-Sideris et al. \(2007\)](#page-9-0) explored the pedestrian collisions based on census tracts in the city of Los Angeles. They found out that pedestrian collisions are more likely to occur in \* Corresponding author. Tel.: +1 407 823 0300. E-mail address: [jaeyoung@knights.ucf.edu](mailto:jaeyoung@knights.ucf.edu) (J. Lee). neighborhoods with high population and employment density, high traffic volumes, and a large concentration of commercial/ retail and multifamily residential land uses. Moreover, zones with high concentration of Latino population had a higher chance to have more pedestrian crashes per capita. [Wier et al. \(2009\)](#page-9-0) investigated pedestrian crashes using 176 census tracts of San Francisco. The authors showed that the traffic volume, arterials without transit, the proportion of land area zoned for commercial and residential uses, employee and resident populations, and the proportion of people living in poverty, were found significant and positively affecting pedestrian crashes. In contrast, total land area (mi2 ) and the proportion of population aged 65 or over had negative signs in the pedestrian crash model. Furthermore, [Cottrill and Thakuriah \(2010\)](#page-9-0) analyzed the pedestrian crashes in deprived areas with many low-income and minority populations. The authors corrected the underreporting problem using a Poisson model, and found that the exposure including the suitability of the area for walking and transit accessibility, crime rates, transit availability, income, and presence of children to be significant for pedestrian crashes. [Ukkusuri et al. \(2011\)](#page-9-0) used census tracts of New York City and discovered several socioeconomic and environmental factors for the frequency of pedestrian crashes using the NB (Negative Binomial) with random parameters model. [Siddiqui et al. \(2012\)](#page-9-0) found that the roadway length with 35 mph, intersections, dwelling units, population density, the percentage of households with 0 or 1 vehicle, long term parking cost, and total employment had positive relationship with the number of pedestrian crashes, whereas income reduced pedestrian crashes, from their Bayesian Poisson-lognormal model with a spatial error component. Moreover, [Siddiqui and Abdel-Aty \(2012\)](#page-9-0) estimated pedestrian crash models for zonal interior and boundary crashes, separately. The authors defined a boundary crash if the crash was located within 100 feet from the boundary line, and otherwise the crash was defined as an interior crash. The authors assumed that interior crashes are influenced solely by the characteristics of the zone within which they are spatially located. On the hand, boundary crashes are hypothesized that they are affected by not only the crash zone but also neighboring zones. They pointed out that the models could capture several unique explanatory variables explicitly related to interior and boundary crashes. For instance, total roadway length with 35 mph speed limit and long term parking cost were not significant in the interior pedestrian crash model but they were significant in the boundary model. It was also found that hotel units were positively associated with interior crashes whereas it had a negative sign in the boundary crash model. Recently, [Wang and Kockelman \(2013\)](#page-9-0) studied the relationship between pedestrian crash frequency and land use, network and demographic attributes at the census tract level. They revealed that the higher shares of residences near transit stops are associated with pedestrian crash risks. In addition, the provision of sidewalk is Table 1 Descriptive statistics of the prepared data. | Category | Variable | Mean | Stdev | Min | Max | |---------------------|-----------------------------------------------------------------------------|---------|---------|-------|---------| | Target | Pedestrian crashes per crash location ZIP | 17.411 | 22.849 | 0 | 227 | | | Crash-involved pedestrians per residence ZIP | 23.779 | 26.843 | 0 | 224 | | Demographic | Population | 19126.5 | 14561.8 | 0 | 72257 | | | Proportion of children (5–14 years) | 0.112 | 0.037 | 0.000 | 0.222 | | | Proportion of adolescents (15–19 years) | 0.065 | 0.054 | 0.000 | 0.974 | | | Proportion of young people (20–24 years) | 0.063 | 0.049 | 0.000 | 0.643 | | | Proportion of elderly people (65–74 years) | 0.189 | 0.116 | 0.000 | 1.000 | | | Proportion of very elderly people (75 years or older) | 0.085 | 0.063 | 0.000 | 0.788 | | Socioeconomic | Proportion of workers in the tertiary sector | 0.780 | 0.138 | 0.000 | 1.000 | | | Proportion of households without available vehicle | 0.027 | 0.034 | 0.000 | 0.462 | | | Proportion of unemployed people | 0.102 | 0.053 | 0.000 | 0.545 | | | Proportion of households below poverty level | 0.169 | 0.189 | 0.000 | 1.000 | | | Median household income (in \$1,000) | 50.023 | 18.796 | 9.979 | 250.000 | | | Whether median year of structure built is before 1984 (yes = 1, no = 0) | 0.507 | 0.500 | 0.000 | 1.000 | | Commute | Proportion of commuters using public transportation | 0.017 | 0.046 | 0.000 | 1.000 | | | Proportion of commuter using non-motorized modes | 0.026 | 0.052 | 0.000 | 1.000 | | | Proportion of commuters by walking | 0.019 | 0.036 | 0.000 | 0.444 | | | Proportion of people working at home | 0.054 | 0.070 | 0.000 | 1.000 | | | Proportion of workers whose commute time is 15 min or shorter | 0.263 | 0.143 | 0.000 | 1.000 | | | Proportion of workers whose commute time is 45 min or longer | 0.157 | 0.108 | 0.000 | 1.000 | | Roadway/traffic | VMT | 391498 | 334027 | 0 | 2426838 | | | Proportion of trucks | 0.080 | 0.051 | 0.000 | 0.405 | | | Proportion of low-speed roads (speed limit: 35 mph or lower) | 0.227 | 0.253 | 0.000 | 1.000 | | | Proportion of medium-speed roads (speed limit: 40–45 mph) | 0.402 | 0.268 | 0.000 | 1.000 | | | Proportion of high-speed roads (speed limit: 55 mph or higher) | 0.350 | 0.311 | 0.000 | 1.000 | | | Proportion of roads with poor pavement condition | 0.003 | 0.016 | 0.000 | 0.220 | | | Number of traffic signals per miles | 0.542 | 0.801 | 0.000 | 8.903 | | | Number of intersections per miles | 10.732 | 29.699 | 0.000 | 908.265 | | Facility/attraction | Number of rail and bus stations per mi2 | 0.058 | 0.774 | 0.000 | 19.766 | | | Number of retail stores (grocery, home improvement, pharmacy, etc.) per mi2 | 4.936 | 9.448 | 0.000 | 165.540 | | | Number of restaurants per mi2 | 4.270 | 11.830 | 0.000 | 284.136 | | | Number of banks per mi2 | 0.840 | 4.297 | 0.000 | 128.479 | | | Number of hotels, motels, and guest houses per mi2 | 0.791 | 3.061 | 0.000 | 54.2714 | | | Number of K–12 schools per mi2 | 0.610 | 1.078 | 0.000 | 20.342 | | | Number of gas stations per mi2 | 0.553 | 0.726 | 0.000 | 4.726 | | | Number of parks and recreation areas per mi2 | 0.375 | 0.777 | 0.000 | 6.510 | | | Number of department stores and shopping malls per mi2 | 0.325 | 0.738 | 0.000 | 9.883 | | | Number of tourist attractions per mi2 | 0.310 | 0.950 | 0.000 | 19.766 | | | Number of colleges and universities per mi2 | 0.072 | 0.362 | 0.000 | 7.412 | | | Number of marinas/ferry terminals per mi2 | 0.066 | 0.256 | 0.000 | 4.536 | | | Number of hospitals per mi2 | 0.046 | 0.176 | 0.000 | 3.506 | associated with lower pedestrian crash rates. [Abdel-Aty et al.](#page-9-0) [\(2013\)](#page-9-0) compared the pedestrian crash models based on different spatial units as census tracts, block groups and traffic analysis zones. It was found that VMT (Vehicle-Miles-Traveled) and the number of intersections, the number of workers commuting by public transportation, the workers commuting by walking and the proportion of minority population were significant in all models Moreover, roadways with relatively lower speed limits were positively associated with the pedestrian crashes in block group/ traffic analysis zone based models. Furthermore, the roadways with high speed limit (65 mph) variable was significant and negatively associated with pedestrian crashes solely in the census tract based model. In addition, the population of children aged from 0 to 15 was negatively related to pedestrian crashes in the block group/traffic analysis zone based models whereas the density of children (K–12th grade) was positively associated with pedestrian crashes only in the traffic analysis zone based model. Workers with commute time 15–19 min was significant only in the traffic analysis zone based model. Furthermore, the number of home workers had a negative relationship with pedestrian crashes for the block group/traffic analysis zone based models. [Lee et al.](#page-9-0) [\(2013\)](#page-9-0) investigated the residential characteristics of pedestrians who are involved in the traffic crash using the NB model formulation. The authors discovered that people living in the ZIP code area with lower median age, larger number of Hispanic population, more workers commuting by public transportation, shorter travel time to work, lower income, older buildings, smaller number of workers in the primary industry field were more likely to be involved in pedestrian crashes. Although many pedestrian crashes have been analyzed at the macroscopic level, there are still unanswered research questions: (1) What are the contributing factors for the number of pedestrians per crash location zone and factors per residence zone? (2) Do the two targets have common unobserved factors and spatial autocorrelations? (3) How are the hot zones for both targets spatially distributed? (4) Is there a way to analyze the hot zones for the two targets simultaneously? Therefore, the main objectives of this study are to identify the contributing factors both for 'Pedestrian crashes per crash location ZIP code area' and 'Crash-involved pedestrians per residence ZIP' and compare them. It was hypothesized that these two targets have commonly shared factors but have unique factors. The common factors may include unobserved shared factors and spatial autocorrelation across the two targets. Subsequently, PSI (potential for safety improvement) was selected for the screening performance measure and calculated for the two targets. PSI is the difference between the expected (or adjusted observed) and predicted number of crashes. If the PSI is positive in an area, the area is experiencing more crashes than other areas with similar features. In contrast, if the area is experiencing less crashes compared to other similar areas its PSI is negative. PSI and other terms will be explained in detail in Section [6](#page-6-0). Then, hot zones were identified for both targets separately and then integrated. It is expected that this integrated screening method can provide a more comprehensive perspective by location and residence zonal factors for pedestrian safety. #### 2. Data preparation Data from 983 ZIP areas in Florida were used for the analysis. Pedestrian crashes occurring between 2009 and 2011 were collected from Florida Department of Transportation (FDOT). Demographic, commute pattern, and socio–economic data were obtained from the U.S. Census Bureau and the roadway/traffic data were acquired from FDOT Roadway Characteristics Inventory. Lastly, the facility/attraction data were obtained from FDOT Unified Basemap Repository. Overall 40 candidate explanatory variables and 2 target variables were processed. The prepared data are summarized in [Table 1.](#page-1-0) #### 3. Distance analysis In this study, both 'Pedestrian crashes per crash location ZIP' and 'Crash-involved pedestrians per residence ZIP' were analyzed ![](_page_2_Figure_10.jpeg) Fig. 1. Descriptive statistics of distance between crash location ZIP and pedestrian residence ZIP. simultaneously. Some may argue that most of pedestrians are involved in traffic crashes at the same or very close to their residence ZIP area, and it is not necessary to separate these two targets. In order to justify the objectives of this study, the distance between pedestrian crash location and pedestrians' residence were explored. Both crash location ZIP and pedestrians' residence ZIP information were collected from each pedestrian crash and the coordinate information of the ZIP centroids were obtained using GIS. After that, the distance between crash location ZIP and crashinvolved pedestrians' residence ZIP was calculated for each pedestrian crash. [Fig. 1](#page-2-0) exhibits the distribution of these distances. It was shown that actually the distance between pedestrian crashes and their residence zones are quite close. About 90% of pedestrian crashes occur within 14 miles within the pedestrians' residence zone and approximately 50% of pedestrian crashes happened in the pedestrians' residence zones; however still other 50% occur in zones other than their residence. Thus, it can be justified to separately explore 'Pedestrian crashes per crash location ZIP' and 'Crash-involved pedestrians per residence ZIP'. #### 4. Statistical modeling Bayesian Poisson lognormal simultaneous equations spatial error model (BPLSESEM) was adopted in this study. Different from the classical models, Bayesian models do not depend on the assumption of asymptotic normality. Sampling based methods of Bayesian estimation focus on estimating the entire density of parameters as compared to the traditional classical estimation methods which are intended for finding a single point estimate using the maximum likelihood approach [\(Congdon, 2006](#page-9-0)). Of course, sometimes point estimates may be more convenient for the practical application since it clearly suggest a single point. However, the Bayesian approach has a significant advantage over the maximum likelihood estimation. The Bayesian estimation determines posterior density for each parameter under consideration. This density estimation is the outcome of a process where a long run or a series of long runs of samples are taken from the posterior density based on the prior information about the parameter and data. Accordingly a Bayesian approach provides a considerable interpretive advantage since posterior estimates reflect the probabilities that the analyst is primarily interested in, the probability of the null hypothesis being true called a Bayesian credible interval (BCI). On the other hand, classical confidence intervals on parameter estimates provide the probability of observing data given that a parameter takes on a specific value. This distinction of the Bayesian approach provides a substantial philosophical and practical advantage ([Mitra and](#page-9-0) [Washington, 2007](#page-9-0)). Therefore, the Bayesian approach is thought to be more suitable compared to the classical likelihood based inference methods and thus have been popular in recent traffic safety research. Furthermore, the Bayesian approach is more practical especially when handling complicated models such as the BPLSESEM in this study compared to the classical estimation methods (i.e. maximum likelihood approach). The Poisson regression models have played a key role in analyzing crash frequency data. The Poisson regression model has been broadly used by many researchers since it can cope with nonnegative integers. This study also adopted the Poisson regression based model because Poisson distribution approximates rare event frequency data such as the number of pedestrian crashes or the number of crash-involved pedestrians, which were used as the response variables in this study. The probability of ZIP i having yi the number of pedestrian crashes aggregated based on their crash location zone (or the number of crash-involved pedestrians aggregated based on their residence zone) per time period is given by: $$P(y_i) = \frac{\exp(-\lambda_i)\lambda_i^{y_i}}{y_i!} \tag{1}$$ where P(yi) is the probability of entity i having yi pedestrian crashes (or crash-involved pedestrians) per given time period, and li is the Poisson parameter, which shows the expected number of pedestrian crashes (or crash-involved pedestrians) per period, Poisson regression models are estimated by specifying li (Poisson parameter) as a function of explanatory variables, the most widely used functional form is: $$\lambda_i = \exp(\beta X_i) \tag{2}$$ where Xi is a row vector of explanatory variables of entity i, and b is a coefficient estimate of model covariates bXi. Nevertheless, the Poisson models cannot manage both overand under-dispersion in the data since it assumes mean and variance are equal. Hence, the Poisson lognormal model was suggested as one of the alternative models to Poisson models to account for the over-dispersion of crash data ([Lord and Mannering,](#page-9-0) [2010](#page-9-0)). Furthermore, simultaneous equations and random parameters shared by two equations for the two targets were used to account for unobserved factors between the two targets ([Ye et al.,](#page-9-0) [2009](#page-9-0)). The expected number of pedestrian crashes (or crashinvolved pedestrians) is formulated as follows: $$\lambda_{i1} = \exp(\beta_1 X_{i1} + \theta_{i1} + \varphi_i) = \exp(\beta_1 X_{i1} + \delta_1 u_{i1} + \varphi_i)$$ (3) where, li1 is the expected number of pedestrian crashes per crash location ZIP i, Xi1 is a row vector of explanatory variables showing characteristics of ZIP i, b1 is a coefficient estimate of model covariates Xi1, ui1 is a random error term representing normal heterogeneity of ZIP i, ui1 follows normal distribution (0, tu) for ZIP i, tu is the precision parameter that is the inverse of the variance; it follows prior gamma (0.5, 0.005), di is the coefficient for ui1, and 'i is a shared spatial autocorrelation error term. $$\lambda_{i2} = \exp(\beta_2 X_{i2} + \theta_{i2} + \varphi_i) = \exp(\beta_2 X_{i2} + \delta_2 u_{i1} + \delta_3 u_{i2} + \varphi_i)$$ (4) Table 2 Selection of exposure variables for each target variable. | Target | Exposure variable | b0
(intercept) | | | | b1
(exposure variable) | | | | DIC | |----------------------------------------------|-----------------------------------|-------------------|-------------|-------------------------------|-----------|---------------------------|--------------------------------------------|-------|-------|---------| | | | Mean | s.d. | Bayesian credible
interval | | | Mean s.d.
Bayesian credible
interval | | | | | | 2.5%
97.5% | | | | | 2.5% | 97.5% | | | | | Pedestrian crash per crash location ZIP | Log of population | 7.374
| 0.254 | 7.739
| 6.833
| 0.999 | 0.026 | 0.943 | 1.036 | 5437.23 | | | Log of VMT | 3.671
| 0.192 | 4.029
| 4.003
| 0.049 | 0.002 0.046 | | 0.051 | 5424.98 | | | (Log of population) (Log of VMT) | 7.693 | 0.373 | 8.378
| 7.063
| 0.786 | 0.029 | 0.736 | 0.840 | 5360.89 | | Crash-involved pedestrians per residence ZIP | Log of population | | 6.836 0.242 | 7.283
| 6.387
| 0.989 | 0.025 | 0.943 | 1.035 | 5877.91 | | | Log of VMT | | 4.240 0.161 | 4.572
| 3.940
| 0.547 | 0.013 | 0.523 | 0.573 | 6046.88 | | | (Log of population) (Log of VMT) | | 2.895 0.151 | 3.151
| 2.553
| 0.046 | 0.001 | 0.043 | 0.048 | 5883.75 | Table 3 Bayesian poisson lognormal simultaneous equations spatial error modeling result. | Variable | | | Pedestrian crashes per crash location ZIP | | | | Crash-involved pedestrians per residence ZIP | | |------------------------------------------------------|-----------|-------|-------------------------------------------|-----------|-----------|-------|----------------------------------------------|-----------| | | Mean | s.d. | Bayesian credible interval | | Mean | s.d. | Bayesian credible interval | | | | | | 2.5% | 97.5% | | | 2.5% | 97.5% | | Intercept | 2.210
| 0.254 | 2.599
| 1.733
| 3.902
| 0.630 | 4.860
| 2.560
| | (Log of population) (Log of VMT) | 0.036 | 0.002 | 0.032 | 0.038 | | | | | | Log of population | | | | | 0.760 | 0.062 | 0.634 | 0.854 | | Proportion of children (5–14 years) | | | | | 1.804 | 0.495 | 0.982 | 2.877 | | Proportion of people working at home | | | | | 1.930
| 0.492 | 2.940
| 1.012
| | Proportion of households without available vehicle | | | | | 1.849 | 0.529 | 0.719 | 2.760 | | Proportion of households below poverty level | 2.820 | 0.192 | 2.479 | 3.174 | | | | | | Median household income
(in \$1,000) | | | | | 0.013
| 0.001 | 0.016
| 0.011
| | Proportion of high-speed roads
(55 mph or higher) | 1.161
| 0.089 | 1.329
| 0.989
| 0.598
| 0.088 | 0.767
| 0.441
| | Number of rail and bus stations per mi2 | 0.035 | 0.017 | 0.001 | 0.068 | | | | | | Number of hotels, motels, and guest houses per mi2 | 0.022 | 0.004 | 0.013 | 0.029 | | | | | | Number of marina/ferry terminals per mi2 | 0.222 | 0.062 | 0.093 | 0.332 | | | | | | Number of K–12 schools per mi2 | 0.084 | 0.017 | 0.047 | 0.115 | | | | | | d1,d2 | 2.018 | 0.739 | 1.090 | 3.764 | 0.810 | 0.342 | 0.354 | 1.538 | | d3 | | | | | 0.645
| 0.356 | 1.540
| 0.192
| | s.d. of 'i | 0.544 | 0.060 | 0.424 | 0.664 | Same | | | | | DIC | 11101.8 | | | | | | | | where, li2 is the expected number of crash-involved crashes per residence ZIP i, Xi2 is a row vector of explanatory variables presenting features of ZIP i, b2 is a coefficient estimate of model covariates Xi2, ui2 is a random error term representing normal heterogeneity of ZIP i, ui1 and ui2 follow normal distribution (0, tu) for ZIP i, tu is the precision parameter that is the inverse of the variance; it follows prior gamma (0.5, 0.005), d2 and d3 are the coefficients for ui1 and ui2, and 'i is a shared spatial autocorrelation error term. WinBUGS was used to estimate the model parameters and their posterior distributions in this study. The model was run considering a non-informative normal (0,10000) prior for both dm and bk. In the case of the univariate model structure, d2, d4 and d5 are set to zero because the univariate model do not account for correlations between heterogeneities of crashes by different modes. Spatial autocorrelation is a technical term for the fact that spatial data from near sites are more likely to be similar to data from distant sites (O'[sullivan and Unwin, 2002](#page-9-0)). The existence of the spatial autocorrelation in the crash data may invalidate the assumption of the random distribution ([LeSage and Pace, 2004](#page-9-0)). In order to control for the spatial autocorrelation, a spatial error term ('i) was included in the model specification. Spatial distribution was implemented by specifying intrinsic Gaussian conditional autoregressive (CAR) prior with normal ('i , t2 i ) distribution as recommended by [Besag \(1974\)](#page-9-0). Mean of 'i is calculated as follows: $$\overline{\varphi}_{i} = \frac{\left(\sum_{i \neq j} \varphi_{j} \times w_{ij}\right)}{\left(\sum_{i \neq j} w_{ij}\right)} \tag{5}$$ where, wij is the element of adjacency matrix with a value of 1 if i and j are adjacent or 0 otherwise. Among the benefits of the Bayesian approach are a more natural interpretation of parameter intervals, termed Bayesian credible interval (BCI) and the freedom of obtaining true parameter density ([Congdon, 2006](#page-9-0)). On the other hand, likelihood based estimates depend on normality approximations based on large sample asymptotics [\(Congdon, 2006](#page-9-0)). In this study, only variables whose 90% BCI of the posterior parameter estimates showing the same sign were included in the final model. Furthermore, DIC (deviance information criterion) was computed. The following equation is used to calculate DIC ([Spiegelhalter et al., 2002](#page-9-0)). Models with smaller DIC are preferred to models with larger DIC. Therefore, the model with the smallest DIC was chosen as a final model. $$DIC = 2 \times \overline{D} - \hat{D} \tag{6}$$ where D: posterior mean of deviance, D;D^ ¼ 2 ð Þ p yð Þ ju , and u: posterior mean of u, respectively. Regarding the exposure variable, it was thought that both population and traffic volume can be used as exposure variables for the two targets. Initially, both 'Log of population' and 'Log of VMT' were attempted at the same time in the model; however, these two variables are highly correlated with each other (r = 0.720) and thus cannot be used simultaneously. We calculated the product of 'Log of population' and 'Log of VMT' and tried it as an exposure variable, since it was believed that this new variable can reflect both population and traffic volume at the same time. 'Log of population', 'Log of VMT', and the product of 'Log of population' and 'Log of VMT' were attempted one by one, and all of these variables were found to be significant at the 5% level. Nevertheless, it was uncovered that the product of 'Log of population' and 'Log of VMT' was the best exposure variable for 'Pedestrian crashes per crash location ZIP', whereas 'Log of population' was the best exposure variable for 'Crash-involved pedestrians per residence ZIP' ([Table 2](#page-3-0)). It implies that the number of pedestrian crashes is largely affected both by population and traffic volume because a pedestrian crash is a collision between pedestrian and motor vehicle. When it comes to the number of crash-involved pedestrian per their residence, the populations plays a more important role because traffic volume is not directly related to crash-involved pedestrians aggregated based on their residence whereas the population is a direct exposure measure for the pedestrian crashes. For example, consider a zone with many pedestrians who were involved in crashes but with low car-ownership. More than likely, the zone have lower traffic volume but they are likely to have large population exposed to traffic crashes. #### 5. Modeling results The modeling results are summarized in Table 3. It is shown that two target variables: 'Pedestrian crashes per crash location ZIP' and 'Crash-involved pedestrians per residence ZIP' have different significant variable sets. For the first target variable, ![](_page_5_Figure_2.jpeg) Fig. 2. Summary of significant factors for the two targets. 'Pedestrian crashes per crash location ZIP', overall 7 explanatory variables were significant at 5%. As stated earlier, the product of 'Log of population' and 'Log of VMT' were used as exposure variables for the first target variable. As expected, the exposure variable is positively associated with the first target variable. It was shown that 'Proportion of households below poverty level' has a positive effect on the first target. It implies that pedestrians are more likely to be involved in traffic crashes in the economically deprived areas because pedestrian facilities in such area may be insufficient or poorly maintained. Moreover, it was uncovered that the 'Proportion of high-speed roads (55 mph or higher)' was negatively associated with the first target variable. It shows that pedestrians in areas with dense high-speed roads experience less crashes. In other words, pedestrian crashes are more likely to occur in areas with many low-speed local roads. Furthermore, it was revealed that four facility related variables have positive effects on the first target variable. First, 'Number of rail and bus stations per mi20 infer that public transportation facilities may lead to increased pedestrian volume and thus more pedestrian crashes. 'Number of hotels, motels, and guest houses per mi20 may be surrogate measures of visitors and tourists. If this is the case, the areas with many visitors and tourists experience more pedestrian crashes compared to other areas with less number of visitors and tourists. At first glance, 'Number of marina/ferry terminals per mi20 variable is not directly relevant to pedestrian crashes. However, it can show that the area has many tourists and it is located in the coastal area. It may infer that tourists in the coastal areas have higher chance to be involved in the pedestrian crashes. Lastly, 'Number of K– 12 schools per mi20 implies that school-aged children are more vulnerable to pedestrian crashes. Concerning the second target variable, 'Crash-involved pedestrian per residence ZIP', a total of 6 explanatory variables were significant at the 5% level. The exposure variable of the second target is 'Log of population' as mentioned earlier and it positively influences the second target variable. 'Proportion of children (5–14 years)' is positively related to the second target. This variable is similar as 'Number of K–12 schools per mi20 in the first target model. It shows that young children between 5 and 14 are more likely to be involved in pedestrian crashes. Moreover, 'Proportion of people working at home' has a negative effect on the second target. It is thought that people working at home are less exposed to traffic because they do not need to commute and it may lead to decreased pedestrian crashes. In addition, it was shown that 'Proportion of households without available vehicle' has a positive effect on the second target variable. Individuals in households with no available vehicle need to travel by public transportation or by walking. Both of these alternative modes result in more exposure to pedestrian crashes. In addition, 'Median household income (in \$1,000)' was found to have a negative relationship with the second target variable. It is possible that people from lower socio– economic status households may prefer to walk or use public transportation even if they have vehicles. Also, the people from deprived areas might have difficulty to obtain enough information regarding traffic safety [\(Martinez and Veloz, 1996](#page-9-0)). 'Proportion of high-speed roads (55 mph or higher)' is commonly significant for the first and second target variables. As in the first target model, it is also negatively associated with the second target variable. It infers that pedestrian crashes are less frequent in the area with more high-speed roads. With regards to the random parameters (d1, d2, and d3) that reflect the unobserved common components between 'Pedestrian crashes per crash location ZIP' and 'Crash-involved pedestrians per residence ZIP', d1, d2, and d3 are significant at 5%. It implies the existence of common factors between the two targets although they are unobserved. Furthermore, the standard deviation of the shared spatial error term, 's.d. of 'i ' is statistically significant at 5%. It suggests that both targets are spatially correlated among adjacent zones and the spatial autocorrelation is controlled by the spatial error term included in the model. In summary, 'Pedestrian crashes per crash location ZIP' has more physical variables (i.e. facility density) while 'Crash-involved pedestrians per residence ZIP' has more demographic and socioeconomic variables. Nevertheless, the two targets have three common significant variables, 'Proportion of high-speed roads (speed limit: 55 mph or higher)', 'Spatial autocorrelation', and 'Unobserved shared factors' as shown in Fig. 2. Table 4 Pearson correlation matrix for the pedestrian crashes per cash location ZIP model. | Variable | (Log of
population) (Log
of VMT) | Proportion of
households below
poverty level | Proportion of high
speed roads (55 mph
or higher) | Number of rail
and bus stations
per mi2 | Number of hotels,
motels, and guest
houses per mi2 | Number of
marina/ferry
terminals per mi2 | Number of K–
12 schools per
mi2 | |----------------------------------------------------------|-----------------------------------------|----------------------------------------------------|---------------------------------------------------------|-----------------------------------------------|----------------------------------------------------------|------------------------------------------------|---------------------------------------| | (Log of
population) (Log
of VMT) | 1.000 | | | | | | | | Proportion of
households below
poverty level | 0.039
| 1.000 | | | | | | | Proportion of high
speed roads
(55 mph or higher) | 0.102
| 0.064 | 1.000 | | | | | | Number of rail and
bus stations per mi2 | 0.005
| 0.058 | 0.054
| 1.000 | | | | | Number of hotels,
motels, and guest
houses per mi2 | 0.031 | 0.025
| 0.215
| 0.255 | 1.000 | | | | Number of marina/
ferry terminals per
mi2 | 0.047
| 0.056
| 0.203
| 0.026 | 0.348 | 1.000 | | | Number of K–
12 schools per mi2 | 0.214 | 0.095 | 0.362
| 0.186 | 0.158 | 0.060 | 1.000 | Any variables that have potential correlation with other variables were not included simultaneously in the final model, and careful consideration of the correlated variables separately was attempted before reaching the final model. We checked the possible correlations between all explanatory variables included in the final model using Pearson correlation coefficients. Tables 4 and 5 present the correlation coefficient matrices for the first and second target models, respectively. In the first target model, the strongest correlation was found between 'Proportion of highspeed roads (55 mph or higher)' and 'Number of K–12 schools per mi20 (r = -0.362). The strongest correlation in the second target model was observed between 'Proportion of households without available vehicle' and 'Median household income (in \$1,000)' and its Pearson correlation coefficient is -0.302. None of the variables in the final model have evident correlations. ## 6. Hot zone identification analysis In order to identify hot zones, the performance measure should be determined. A variety of performance measures have been used in previous screening studies. They include crash frequency, EPDO (equivalent property damage only) crash frequency, crash rate, proportion by crash types, empirical bayes (EB), PSI, and so forth. In this study, PSI was selected as the performance measure. PSI, or excess crash frequency, shows whether a zone is experiencing more or less number of crashes compared to other zones with similar characteristics. PSI is calculated by the difference between the expected and predicted number of crashes The expected number of crashes, or the adjusted observed number of crashes, is the estimate of long-term average crash frequency of an area under a given set of zonal characteristics in a given time period. Because crashes are random events the observed number of crashes at an area naturally fluctuates over time. Thus, the observed crash frequency over a short time period is not a reliable indicator of what crash frequency is expected under the same conditions over a long period of time ([HSM, 2010](#page-9-0)). Instead, the Bayesian expected number of crashes was used to account for the regression-to-themean problem for the more reliable expected crash frequency. On the other hand, the predicted number of crashes is the average number of crashes in zones with similar characteristics. Therefore, PSI can effectively identify those zones experiencing more pedestrian crashes or having more crash-involved pedestrians than other zones with similar characteristics. Therefore, if a zone has PSI greater than zero, the zone is considered hazardous whereas a zone is regarded as safe if its PSI is smaller than zero. The predicted number of pedestrian crashes (or crash-involved pedestrians) for each zone was calculated from the model [\(Table 3\)](#page-4-0). PSIs were calculated by the following equations Table 5 Pearson correlation matrix for the crash-involved pedestrian per residence ZIP model. | Variable | Log of
population | Proportion of
children (5–
14 years) | Proportion of people
working at home | Proportion of household
without available vehicle | Median household
income (in \$1,000) | Proportion of high-speed
roads (55 mph or higher) | |------------------------------------------------------|----------------------|--------------------------------------------|-----------------------------------------|------------------------------------------------------|-----------------------------------------|------------------------------------------------------| | Log of population | 1.000 | | | | | | | Proportion of children (5–
14 years) | 0.232 | 1.000 | | | | | | Proportion of people
working at home | 0.172
| 0.230
| 1.000 | | | | | Proportion of household
without available vehicle | 0.115 | 0.012
| 0.072
| 1.000 | | | | Median household income
(in \$1,000) | 0.019 | 0.125 | 0.244 | 0.302
| 1.000 | | | Proportion of high-speed
roads (55 mph or higher) | 0.215
| 0.218 | 0.044
| 0.163
| 0.084
| 1.000 | ![](_page_7_Figure_2.jpeg) Fig. 3. Definition of zonal screening categories. ### ([Aguero-Valverde and Jovanis, 2009\)](#page-9-0): $$PSI = N_{\text{expected}} - N_{\text{predicted}} \tag{7}$$ $$= \exp(\beta_0 + \beta X_i + \theta_i + \varphi_i) - \exp(\beta_0 + \beta X_i)$$ (8) $$= \exp(\beta_0 + \beta X_i)(\exp(\theta_i + \varphi_i) - 1)$$ (9) All zones in the study area were classified into three categories based on their PSIs: hot ('H'), warm ('W'), and cold ('C') zones. Hot zones are defined as zones with a top 10% PSI, warm zones refer to zones with a PSI between 0 and top 10%, and cold zones are those with PSI less than 0, as shown in Fig. 3. Thus, 'H' have much more pedestrian crashes (or crash-involved pedestrians) compared to other zones with similar characteristics. 'W' zones also have some room for pedestrian crash reduction (or crash-involved pedestrians); however the pedestrian safety is not much risky as in 'H' zones. In case of cold zones, it has less pedestrian crashes (or crashinvolved pedestrians) compared to other similar zones. Although 10% was used as the hot zone threshold in this study, the threshold is flexible. It can be decreased to 5% or 1% if researchers want to focus on very high risk sites. On the other hand, the threshold can be increased to 20% when researchers wish to address more areas with higher traffic crash risk. Moreover, there is no clear threshold to identify hot zones (or hotspots) even in the Highway Safety Manual [\(HSM, 2010](#page-9-0)). Table 6 exhibits a part of the screening results of 'Pedestrian crashes per crash location ZIP'. In case of ZIP code 33311, its PSI is 137.1 and ranked number 1 based on the PSI. Because it is in the top 0.1% PSI, this zone was categorized as 'H', which shows that the zone has serious pedestrian safety problems, compared to other similar zones. The PSI of ZIP code 32817 is 5.0 and it is in the top 52.2% PSI, this zone was categorized as 'W', which has a pedestrian safety problem in the location but it is not severe as much as in 'H'. On the other hand, ZIP code 33563 has a negative PSI, -13.4, and thus it is classified as 'C', which is relatively safe for pedestrian crashes. Fig. 4 displays the screening result based on the PSI of pedestrian crashes per crash location ZIP (upper figure) and that based on PSI of crash-involved pedestrians per residence ZIP (lower figure). As shown in the figures, the locations of 'H' zones of the two targets are quite comparable but not exactly the same. The general trend of 'H' zones of the targets shows that most of them are concentrated in the urban area. In case of 'W' and 'C' zones, they Table 6 Example of screening result: pedestrian crashes per crash location ZIP. | ZIP | Rank | PSI | Percent | Category | |-------|------|----------|---------|----------| | 33311 | 1 | 137.1 | 0.1% | H | | 33139 | 2 | 122.0 | 0.2% | H | | 33142 | 3 | 96.5 | 0.3% | H | | : | : | : | : | : | | 32817 | 265 | 5.0 | 27.0% | W | | : | : | : | : | : | | 33563 | 983 | 13.4
| 100.0% | C | also have similar spatial distributions between the two target variables. #### 7. Integrated screening In the preceding section, hot zones for two targets: 'Pedestrian crashes per crash location ZIP' and 'Crash-involved pedestrians per residence ZIP' are identified individually. In this section, the hot zone identification results of the two targets are combined to ![](_page_7_Picture_17.jpeg) ![](_page_7_Figure_18.jpeg) Fig. 4. Screening results based on PSI of pedestrian crashes per crash location ZIP (upper) and that based on PSI of crash-involved pedestrians per residence ZIP (lower). ![](_page_8_Picture_2.jpeg) Fig. 5. Integrated screening result. provide a broad spectrum perspective for both locations with higher risk for pedestrians and residences with many pedestrians vulnerable to crashes. All zones were again categorized according to the two scopes: location and residence, and 3 traffic safety levels: 'H', 'W', and 'C'. Therefore, there are overall 9 combination classifications: 'HH', 'HW', 'HC', 'WH', 'WW', 'WC', 'CH', 'CW', and 'CC'. The initial letter of the classifications represents the locationbased pedestrian safety risk, and the latter character symbolizes the residence-based pedestrian safety risk. However, 'HC' and 'CH' cases, which have extremely different pedestrian safety levels between location and residence, are not observed in the screening result. The integrated screening result is summarized in Fig. 5 and Table 7 with seven screening categories. Overall, 73 'HH' zones (7.4%) were identified, which is top priority for pedestrian safety treatments because they have serious pedestrian problems in their locations and also many pedestrians vulnerable to traffic crashes. Furthermore, there are 25 'HW' (2.5%) zones and 25 'WH' (2.5%) zones, the next highest priority for pedestrian treatments. 'HW' zones have very high risk for pedestrians in their zones; but pedestrians from the zones are not particularly exposed to crashes at other zones. Pedestrians in 'WH' zones are very vulnerable to traffic crashes whereas their locations are not exceptionally dangerous for pedestrians. More than one-third of zones (35.0%) are classified as 'WW' zones. These 344 'WW' zones have moderate risks in their physical locations and their pedestrians vulnerable to crashes. There are 38 'WC' zones (3.9%), which are with intermediate risk in their locations but their pedestrians are less likely to be involved in crashes. 47 'CW' zones (4.8%) have little pedestrian problems in their locations but their pedestrians are a little vulnerable to crashes. Lastly, nearly half of zones (43.8%) were classified as 'CC'. In these 431 'CC' zones, pedestrians are relatively safe for the two targets. Engineering, education, and enforcement (3E) are traditional but still valid treatments to reduce traffic crashes effectively. We Table 7 Zones by integrated screening categories. | Category | HH | HW | WH | WW | WC | CW | CC | Sum | |------------|------|------|------|-------|------|------|-------|--------| | Counts | 73 | 25 | 25 | 344 | 38 | 47 | 431 | 983 | | Percentage | 7.4% | 2.5% | 2.5% | 35.0% | 3.9% | 4.8% | 43.8% | 100.0% | can implement different 3E treatment strategies for different screening categories. If zones have higher pedestrian crash risks (i.e. HH, HW, etc.), both area-wide engineering treatments and enforcement can effectively reduce pedestrian crashes in these zones. Education and/or safety campaigns for pedestrians may be a good way to reduce the number of crash-involved pedestrians aggregated based on their residence zone, if the residence has more crash-involved pedestrians (i.e. HH, WH, etc.). All 3E general countermeasures need to be implemented for 'HH' zones. Of course specific treatments would need to be tailored to the specific problem and location. #### 8. Summary and conclusions In this study, two targets: 'Pedestrian crashes per crash location ZIP' and 'Crash-involved pedestrians per residence ZIP' were comprehensively analyzed. In the preliminary analysis, it was shown that pedestrian crashes do not necessarily occur in the pedestrians' residence zone. Of course, the distance between pedestrian crashes and their residence zones are close. About 90% of pedestrian crashes occur within 14 miles within the pedestrians' residence zone. Approximately 50% of pedestrian crashes happened in the pedestrians' residence zones; however the other 50% occurred in zones other than their residence. Thus, it can be justified to separately explore 'Pedestrian crashes per crash location ZIP' and 'Crash-involved pedestrians per residence ZIP'. Different exposure variables were applied for the two targets. 'Log of population', 'Log of VMT', and the product of 'Log of population' and 'Log of VMT' were attempted one by one, and all of these variables were found to be significant at the 5% level. Nevertheless, it was uncovered that the product of 'Log of population' and 'Log of VMT' was the best exposure variable for 'Pedestrian crashes per crash location ZIP', whereas 'Log of population' was the best exposure variable for 'Crash-involved pedestrians per residence ZIP'. BPLSESEM (Bayesian poisson lognormal simultaneous equations spatial error model) was adopted in this study to account for unobserved common factors between the two targets and spatial autocorrelation among adjacent zones. The BPLSESEM revealed that two targets have different contributing factors. The first target, 'Pedestrian crashes per crash location ZIP', has 7 significant factors whereas the second target, 'Crash-involved pedestrians per residence ZIP' has 6 significant factors. It was shown that the first target has more variables related to location factors such as facility related factors. In contrast, the second target is associated with more sociodemographic factors. It is probable that there are common factors between two target variables although the shared factors are unobserved. Moreover, both the spatial autocorrelations among adjacent zones are detected in the both targets but they are controlled by the spatial error term included in the model. Subsequently, hot zones for 'Pedestrian crashes per crash location ZIP' and 'Crash-involved pedestrians per residence ZIP' were identified, separately, using PSI measures. It was shown that the screening results for the two targets are similar but not exactly the same. After that, the screening results for the two targets were integrated to provide a more comprehensive perspective for pedestrian safety problems. A novel hot zone identification method was suggested to combine both hot zones with many pedestrian crash occurrences and hot zones with many crashinvolved pedestrians in the residence. For the former zones, areawide engineering treatments and enforcement can be provided as general countermeasures whereas targeted safety education and campaigns may be effective safety treatments for the latter ones. In conclusion, it is expected that practitioners are able to suggest appropriate safety treatments for pedestrian crashes using the screening method and results from this study. #### Acknowledgements The authors wish to thank the Florida Department of Transportation for funding this study. Some of the research for this paper was conducted as part of the efforts of the Southeastern Transportation Center (STC) at the University of Tennessee. The primary sponsor for the STC is the United States Department of Transportation through grant number DTRT13-G-UTC34. #### References - [Aguero-Valverde, J., Jovanis, P.P., 2009. Bayesian multivariate Poisson lognormal](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0005) [models for crash severity modeling and site ranking. Transp. Res. Record: J.](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0005) [Transp. Res. Board 2136, 82](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0005)–91. - [Besag, J., 1974. Spatial interaction and the statistical analysis of lattice systems. J. R.](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0010) [Stat. Soc. Series B \(Stat. Methodol.\) 36 \(2\), 192](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0010)–236. - [Congdon, P., 2006. Applied Bayesian Modelling, 2nd edition John Wiley and Sons,](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0015) [West Sussex, England](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0015). - [Cottrill, C.D., Thakuriah, P., 2010. Evaluating pedestrian crashes in areas with high](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0020) [low-income or minority populations. Accid. Anal. Prev. 42 \(6\), 1718](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0020)–1728. - Highway Safety Manual, 2010. American Association of State Highway and Transportation Officials (AASHTO), Washington, DC. - [LaScala, E.A., Gerber, D., Gruenewald, P.J., 2000. Demographic and environmental](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0030) [correlates of pedestrian injury collisions: a spatial analysis. Accid. Anal. Prev. 32](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0030) [\(5\), 651](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0030)–658. - [Lee, J., Abdel-Aty, M., Choi, K., Siddiqui, C., 2013. Analysis of residence characteristics](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0035) [of drivers, pedestrians, and bicyclists involved in traf](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0035)fic crashes. Transportation [Research Board 92nd Annual Meeting. Transportation Research Board of the](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0035) [National Academics, Washington, D.C.](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0035) - [LeSage, J.P., Pace, R.K., 2004. Models for spatially dependent missing data. J. Real](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0040) [Estate Finan. Econ. 29 \(2\), 233](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0040)–254. - [Lord, D., Mannering, F., 2010. The statistical analysis of crash-frequency data: a](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0045) [review and assessment of methodological alternatives. Transp. Res. Part A:](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0045) [Policy Pract. 44 \(5\), 291](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0045)–305. - [Loukaitou-Sideris, A., Liggett, R., Sung, H.-G., 2007. Death on the crosswalk: a study](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0050) [of pedestrian-automobile collisions in Los Angeles. J. Educ. Res. 26 \(3\),](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0050) [338](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0050)–351. - [Martinez, R., Veloz, R.A., 1996. A challenge in injury prevention](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0055) the hispanic [population. Acad. Emerg. Med. 3 \(3\), 194](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0055)–197. - [Mitra, S., Washington, S., 2007. On the nature of over-dispersion in motor vehicle](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0060) [crash prediction models. Accid. Anal. Prev. 39 \(3\), 459](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0060)–468. - [Ng, K., Hung, W., Wong, W., 2002. An algorithm for assessing the risk of traf](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0065)fic [accident. J. Saf. Res. 33 \(3\), 387](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0065)–410. - NHTSA, 2013. 2012 Motor vehicle crashes: overview, U.S. Department of Transportation, National Highway Traffic Safety Administration. - NHTSA, 2014. Traffic safety facts 2012 data: pedestrians, U.S. Department of Transportation, National Highway Traffic Safety Administration. - O'[sullivan, D., Unwin, D., 2002. Geographic Information Analysis. John Wiley and](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0080) [Sons, Hoboken, New Jersey.](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0080) - [Siddiqui, C., Abdel-Aty, M., Choi, K., 2012. Macroscopic spatial analysis of pedestrian](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0085) [and bicycle crashes. Accid. Anal. Prev. 45, 382](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0085)–391. - [Siddiqui, C., Abdel-Aty, M., 2012. On the nature of modeling boundary pedestrian](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0090) [crashes at zones. Transportation Research Board 91th Annual Meeting.](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0090) [Transportation Research Board of the National Academics, Washington, D.C](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0090). - [Spiegelhalter, D.J., Best, N.G., Carlin, B.P., Van Der Linde, A., 2002. Bayesian measures](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0095) of model complexity and fi[t. J. R. Stat. Soc. Series B \(Stat. Methodol.\) 64 \(4\),](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0095) [583](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0095)–639. - [Ukkusuri, S., Hasan, S., Aziz, H.M.A., 2011. Random parameter model used to explain](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0100) [effects of built-environment characteristics on pedestrian crash frequency.](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0100) [Transp. Res. Rec. J. Trans. Res. Board 2237, 98](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0100)–106. - [Wang, Y., Kockelman, K.M., 2013. A Poisson-lognormal conditional-autoregressive](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0105) [model for multivariate spatial analysis of pedestrian crash counts across](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0105) [neighborhoods. Accid. Anal. Prev. 60, 71](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0105)–84. - [Wier, M., Weintraub, J., Humphreys, E.H., Seto, E., Bhatia, R., 2009. An area-level](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0110) [model of vehicle-pedestrian injury collisions with implications for land use and](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0110) [transportation planning. Accid. Anal. Prev. 41, 137](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0110)–145. - [Ye, X., Pendyala, R.M., Washington, S.P., Konduri, K., Oh, J., 2009. A simultaneous](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0115) [equations model of crash frequency by collision type for rural intersections. Saf.](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0115) [Sci. 47 \(3\), 443](http://refhub.elsevier.com/S0001-4575(15)00017-2/sbref0115)–452.