Accident Analysis and Prevention

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1 Accident Analysis and Prevention 50 (2013) Contents lists available at SciVerse ScienceDirect Accident Analysis and Prevention j ourna l h o mepage: Corridor-level signalized intersection safety analysis in Shanghai, China using Bayesian hierarchical models Kun Xie a, Xuesong Wang a,b,, Helai Huang c, Xiaohong Chen a a School of Transportation Engineering, Tongji University, Shanghai , China b Key Laboratory of Road and Traffic Engineering of the State Ministry of Education, Tongji University, Shanghai , China c School of Traffic and Transportation Engineering, Central South University, Changsha , China a r t i c l e i n f o Article history: Received 30 November 2011 Received in revised form 29 August 2012 Accepted 11 October 2012 Keywords: Signalized intersection Corridor Spatial correlation Safety analysis Bayesian hierarchical model Risk factors a b s t r a c t Most traffic crashes in Chinese cities occur at signalized intersections. Research on the intersection safety problem in China is still in its early stage. The recent development of an advanced traffic information system in Shanghai enables in-depth intersection safety analyses using road design, traffic operation, and crash data. In Shanghai, the road network density is relatively high and the distance between signalized intersections is small, averaging about 200 m. Adjacent signalized intersections located along the same corridor share similar traffic flows, and signals are usually coordinated. Therefore, when studying intersection safety in Shanghai, it is essential to account for intersection correlations within corridors. In this study, data for 195 signalized intersections along 22 corridors in the urban areas of Shanghai were collected. Mean speeds and speed variances of corridors were acquired from taxis equipped with Global Positioning Systems (GPS). Bayesian hierarchical models were applied to identify crash risk factors at both the intersection and the corridor levels. Results showed that intersections along corridors with lower mean speeds were associated with fewer crashes than those with higher speeds, and those intersections along two-way roads, under elevated roads, and in close proximity to each other, tended to have higher crash frequencies Elsevier Ltd. All rights reserved. 1. Introduction In China, most crashes in urban roadway networks occur at signalized intersections. To explore the effects of risk factors associated with intersection safety, crash prediction models are generally developed to relate intersection characteristics to crash frequencies. However, in China, the research using crash prediction models has not advanced very far due to limitations of both crash and operational performance data. Consequently, most studies of intersection safety in China are based on traffic conflict analysis (Cheng et al., 2004) or on trend-based crash predictions using linear regression analysis (Pei and Ma, 2005; Zhang and Jing, 1994). To further improve road safety in China, research on crash prediction models using reliable data and appropriate statistical methods is needed. Shanghai is China s largest city with a population exceeding 20 million. According to the Traffic Police Administration of Shanghai, there were 1042 traffic fatalities in Shanghai in Recently, an urban traffic information system based on a Geographic Information System (GIS) platform has been built in Corresponding author at: School of Transportation Engineering, Tongji University, Shanghai , China. Tel.: ; fax: address: wangxs@tongji.edu.cn (X. Wang). Shanghai. This new information system can provide traffic volume data as well as historical records of traffic crashes. Signalized intersections in the urban areas of Shanghai are controlled by the Sydney Coordinated Adaptive Traffic System (SCATS), from which geometric design and signal control features can be extracted. In addition to the data sources just mentioned, dynamic operational data is available from over 40,000 GPS equipped taxis in Shanghai. The GPS derived data, hereafter called Floating car data (FCD), provides continuous position data of each taxi operating in the city, and transmits this information every 10 s to a central server. This FCD system, together with the other data sources, allow the development of safety models based on accurate and comprehensive estimates of roadway operating conditions. In the urban areas of Shanghai, the distances between signals are small, averaging about 200 m. These close distances result in dependencies between adjacent intersections that need to be accounted for when performing safety analyses. However, classical crash prediction models treat signalized intersections as isolated entities, and this can lead to biased estimations. Moreover, the high densities of roadway networks in Chinese cities make it even more critical to consider the correlations among adjacent intersections. Another matter regarding research on Chinese traffic safety problems is that many of the traffic characteristics of Chinese cities including driver behaviors, traffic composition, and the traffic /$ see front matter 2012 Elsevier Ltd. All rights reserved.

2 26 K. Xie et al. / Accident Analysis and Prevention 50 (2013) environment are unique to a locality. For instance, in the urban areas of Shanghai, 114 km of elevated roads have been built as of 2010 (Shanghai Statistics Bureau, 2010). Elevated roads impair the sight distance of the surface roads below them and consequently, the impact of this specific environmental characteristic needs to be considered when performing analyses of Shanghai traffic safety problems. The purpose of this study is to develop an appropriate crash prediction model for signalized intersections in Shanghai that can deal with intersection correlations and can properly evaluate the specific risk factors for intersection crashes. 2. Literature review 2.1. Crash prediction models Generalized linear models (GLMs), such as Poisson models (Jones et al., 1991; Joshua and Garber, 1990; Miaou and Lum, 1993) and negative binomial (NB) models (Abdel-Aty and Radwan, 2000; Chin and Quddus, 2003; Maher and Summersgill, 2006; Miaou, 1994; Poch and Mannering, 1996; Srinivas and Venkata, 2011) have been used to investigate relationships between crash occurrence and intersection characteristics. Poisson models can accommodate the nonnegative, random and discrete features of crash frequencies, but the over-dispersion of crash data violates the Poisson distribution s assumption that the variance of the crash data is constrained to be equal to the mean (Maher and Summersgill, 2006). NB models have been proven better than Poisson models in dealing with overdispersed crash data by introducing an error term. However, both Poisson and NB models share the assumption of independent observations, and therefore do not correct for any inherent correlations of crash data. Abdel-Aty and Wang (2006) were among the first to recognize that crashes at adjacent intersections along corridors were spatially correlated and therefore not fully independent from each other. Generalized estimating equations (GEEs) which can be viewed as an extension of GLMs can deal with correlated data and have been used to model crash frequencies in previous studies (Abdel-Aty and Wang, 2006; Lord and Persaud, 2000; Wang and Abdel-Aty, 2006, 2008). Nevertheless, GEEs have the limitation of setting the same correlation matrix for different groups, and thus cannot reflect the discrepancies in correlations among different intersection groups. Another problem with GEEs is that they do not account for the potential heterogeneity attributable to unobserved characteristics across observations. In more recent research, random parameter (RP) models have been used to address this problem (Anastasopoulos and Mannering, 2009; Dinu and Veeraragavan, 2011; El-Basyouny and Sayed, 2009; Milton et al., 2008). RP models are capable of allowing some or all estimated parameters to vary across not only individual observations but also homogeneous groups, and as such, provide the necessary flexibility for handling any heterogeneity. In the study of El-Basyouny and Sayed (2009) (392) segments were clustered into 58 corridors, and then different regression curves were fitted for each corridor by including random corridor parameters. It should be noted that RP models are equivalent to random effect models if only the constant term is allowed to vary (Anastasopoulos and Mannering, 2009). Another key matter to be considered when developing crash prediction models is the need to address multilevel data structures. Signalized intersections located along the same corridor are correlated with each other since they share similar traffic flow, geometric design, land use and signal control timing (Guo et al., 2010). This data structure can be regarded as a two-level hierarchy including the intersection level and the corridor level. Hierarchical models offer an appropriate method to deal with the multilevel data (Ahmed et al., 2011; Huang et al., 2008; Huang and Abdel-Aty, 2010; Jones and Jørgensen, 2003; Kim et al., 2007; Lenguerrand et al., 2006). Compared with RP and other models, hierarchical models have greater explanatory power because they incorporate variables at the specific levels where their effects occur (Gelman and Hill, 2007). Hierarchical models for signalized intersections grouped by corridors were proposed in this paper Risk factor analysis Previous research on intersection related risk factors (e.g., Abdel-Aty and Wang, 2006; Chin and Quddus, 2003; Ma et al., 2010; Poch and Mannering, 1996; Wang and Abdel-Aty, 2008) has shown that certain variables including traffic volume (e.g., total volume and right-turn volume), geometric design (e.g., intersection type and number of lanes) and traffic control (e.g., phase number and signal control type) can all have significant impacts on signalized intersection safety. However, whether the findings from these studies can be extended to China is unknown because the traffic characteristics where these studies were conducted are different from those in China. Considering the more specific problem of corridor related risk factors, the research is limited. Guo et al. (2010) confirmed the safety effect of intersection distance by determining the magnitude of correlations with spatial distances between intersections in a conditional autoregressive model. Li and Tarko (2011) found arterial signal coordination could significantly affect the frequency and severity of rear-end and right-angle crashes for intersections. However, to properly evaluate the impacts of the key corridor-level features on safety, it is necessary to consider not only spatial distance and signal coordination, but also variables such as median treatment, speed features, and traffic volume. Recognizing the uniqueness of Shanghai s traffic characteristics, and the need to incorporate corridor-level variables into crash prediction models, this study investigated the safety effects of risk factors unique to Shanghai at both intersection and corridor levels. 3. Data preparation Corridors and intersections were selected based on criteria listed in Section 3.1, and their characteristics (e.g., geometric design and signal control) were stored in a database. Crash data for the year of 2009 were geocoded on a GIS map using the crash location descriptions and then were linked to the selected intersections according to the records in crash reports. The Sydney Coordinated Adaptive Traffic System (SCATS) provided the intersection signal information. Traffic volume data was acquired from loop detectors, and speed data was obtained from the floating cars Intersection and corridor selection The GIS was used to identify selected intersections and their corridors in the urban areas of Shanghai. To simplify the analysis of geometric features, intersections were limited to either 3-legged or 4-legged designs. To ensure the independence of intersections across corridors, efforts were made to avoid choosing intersecting corridors. In hierarchical models, each signalized intersection must be categorized into one group. However, a few signalized intersections belonged to more than one corridor, and so we adopted a rule that assigned such intersection to the corridor with the greater traffic volume. This was based on the assumption that crash occurrence at adjacent intersections tended to be more highly correlated when they share greater traffic volumes. Fig. 1 shows the locations of the 195 intersections and 22 corridors selected in the urban areas of Shanghai for this study.

3 K. Xie et al. / Accident Analysis and Prevention 50 (2013) Mean speed and speed variance of each corridor as mentioned were acquired from the FCD. The six corridor-level variables with brief descriptions and their descriptive statistics are listed in Table Floating car data (FCD) collection and processing The percentage of taxis in the traffic stream is around 20% for the selected arterials. The speed data obtained from taxis are representative of all vehicles on the selected arterials. There are studies in China comparing speeds from taxis carrying passengers to other privately owned vehicles and the results showed no significant differences between these categories (Chen, 2008; Li, 2009). However, taxis without passengers did perform differently than privately owned vehicles, and so were removed from our samples of speed data. The FCD for one week between the hours of 13:00 14:00 was used to determine the mean speed and speed variance for each corridor. The locations of taxis were matched using the Shanghai GIS road network, and only taxi samples that passed through the study corridors were chosen. As mentioned above, the positions of taxi samples equipped with GPS devices were recorded every 10 s. So, for taxi sample i, the speed V i can be defined as: m i S ij V i = V S ij (1) i j=1 Fig. 1. Shanghai road network and selected corridors and intersections Intersection related variables A total of 17 intersection related variables were used in development of the models. Different sources were used to collect the data for these variables. Traffic volumes were acquired from loop detectors, and geometric design and traffic control data were obtained from the SCATS in Shanghai. For each intersection, the presence or absence of an elevated road over the intersection, and its distance to adjacent intersections were determined from the projected coordinates of each intersection. One variable, the number of signal phases, was preprocessed before being entered into the model. It was treated as a binary variable with one level for 2 3 phase signals and a second level for 4 6 phase signals. This was done because the average number of crashes at intersections with 2 3 phases is lower than the average number of crashes at those with 4 6 phases. It should be noted that several variables known to affect crash frequencies were not considered in this study because they are not relevant for Shanghai. For example, the presence of trucks was not considered because trucks are not allowed to enter Shanghai s downtown areas in the day time, and their percentage in the traffic stream is less than 1% even in the night time. The percentage of buses for the selected corridors is also low at less than 5%, and so their presence was not judged to have a significant impact. Other variables not considered were lane width, the absence of shoulders, and pavement conditions, as these were all relatively uniform for the selected corridors. The 17 intersection-level variables with brief descriptions and their descriptive statistics are listed in Table Corridor related variables A total of six corridor related variables were collected for model development. The presence of a median was obtained from Google Earth and the traffic volumes (average daily traffic and average daily traffic per lane along corridors) were obtained using loop detectors. The GIS data allowed us to classify roads into either one or two-way. where V ij is the speed between two FCD points for taxi sample i, S ij the distance between two FCD points, m i the number of FCD points for taxi sample i on a corridor, S i the total passing distance along a certain corridor. V i is actually the weighted mean speed over the known distance. Fig. 2 presents an example of FCD processing for a single taxi sample Calculations of speed characteristics The mean speed V and speed variance D(V) of a corridor can be expressed as follows: V = n V n i=1 D(V) = n (V i V) 2 i=1 n 1 where n is the number of taxi samples passing through the corridor. The mean speed (V) and speed variance (D(V)) for each corridor were acquired from the FCD. 4. Methodology 4.1. Bayesian hierarchical models Hierarchical models are regression models with parameters that can vary (Gelman and Hill, 2007). As shown in Fig. 3, the data structure used in this study can be viewed as a two-level hierarchy with level 1 being the intersection level, and level 2 being the corridor level. In the hierarchical model proposed in this paper, parameters at the intersection level will be expressed by probability models at the corridor level. Where within-group correlations exist (as they do in this case), hierarchical models are able to make more reliable estimations than traditional GLMs, because hierarchical models can accommodate the heterogeneity among different groups (Huang and Abdel-Aty, 2010; Lenguerrand et al., 2006). In addition, hierarchical models are capable of including covariates at the intersection and corridor levels, thus allowing the effects of intersection and corridor variables to be independently evaluated (Gelman and Hill, 2007). (2) (3)

4 28 K. Xie et al. / Accident Analysis and Prevention 50 (2013) Table 1 Intersection related variables with their descriptions and descriptive statistics. Variables Description Min Max Mean S.D. Intersection type 0 for 4-legged, 1 for 3-legged Minimum angle Minimum angle of intersecting roadways Maximum angle Maximum angle of intersecting roadways Total number of lanes Total number of lanes for all entering approaches Number of through lanes Number of through lanes for all entering approaches Number of right-turn lanes Number of right-turn lanes for all entering approaches Number of left-turn lanes Number of left-turn lanes for all entering approaches Number of through-right lanes Number of through-right mixed use lanes for all entering approaches Number of through-left lanes Number of through-left mixed use lanes for all entering approaches Ratio of turning lanes The ratio of the total number of turning lanes to the total number of lanes Under elevated roads or not 1 for intersection under elevated roads, 0 for not Proximity of intersections Distance to the nearest intersection along corridors (km) Total number of phases 0 for 2 3 phases, 1 for 4 6 phases Cycle length Cycle length (s) Saturation degree Saturation degree of intersections Intersection ADT Average daily traffic of entering the entire intersection (in 10 4 vehicles) Intersection ADTPL Average daily traffic per lane of entire intersection (in 10 4 vehicles) Table 2 Corridor related variables with their descriptions and descriptive statistics. Variables Description Min Max Mean S.D. Presence of a median 0 for without median, 1 for with median One-way road or not 0 for two-way road, 1 for one-way road, ADT along corridor Average daily traffic volume along corridors in two directions (in 10 4 vehicles) ADTPL along corridor Average daily traffic volume per lane in two directions along corridors (in 10 4 vehicles) Mean speed Mean speed of taxi samples for corridors (km/h) Speed variance Speed variance of taxi samples for corridors Fig. 2. Illustration of FCD processing for one taxi sample. Several researchers have shown the advantages of Bayesian methods (Andrew et al., 2011; Huang et al., 2009; Mitra and Washington, 2007; Persaud et al., 2010; Troung et al., 2011) over classical statistical methods in achieving valid results using smaller samples, and in accommodating complex model structures. Bayesian methodology combines prior distributions with a likelihood function obtained from the observed data to create posterior distributions as estimates. The prior distributions can be either non-informative or achieved from the history record and experts. The theoretical framework for Bayesian inference (Carlin and Louis, 2009) can be expressed as: ( y) = L(y )() (4) L(y )()d where y is the vector of observed data, the vector of parameters required for the likelihood function, L(y ) the likelihood function, () the prior distribution of, L(y )() d the marginal Fig. 3. The hierarchical structure of the correlated intersections along corridors.

5 K. Xie et al. / Accident Analysis and Prevention 50 (2013) distribution of observed data, and ( y) the posterior distribution of given y Model specifications A hierarchical negative binominal (HNB) model was proposed in a Bayesian framework for this study. To account for the over-dispersion, crash occurrence was assumed to follow the NB distribution. The specific structure of the HNB model can be expressed as follows: Base model: y ij Negbin ( ij, r) (5) Level 1 model: log ( ij ) = ˇ0j + P ˇpj X pij (6) p=1 Level 2 model: ˇ0j = 00 + Q q=1 ˇ1j = 10 ˇ2j = ˇPj = P0 0q W qj + ε 0j where y ij is the crash number in a certain intersection, ij the expectation of y ij, r an over-dispersion coefficient, X pij the intersection-level variables, W qj the corridor-level variables, 00, 10, 20,... p0 the regression coefficients to be estimated, and ε 0j is the random effect at the corridor level where ε 0j N(0, 2 ε ) Model assessment The Deviance Information Criterion (DIC) can be used to compare complex models, because it offers a Bayesian measure of model fitting and complexity (Speigelhalter et al., 2003). Specifically, DIC is defined as: DIC = D() + p D (9) where D() is the Bayesian deviance of the estimated parameter and D() denotes the posterior mean of D(). D() can be taken as a measure of model fitting. p D is the effective number of parameters and indicates complexity of models. Models with smaller DIC are preferred. Another two common measures, Mean Absolute Deviance (MAD) and Mean Squared Predictive Error (MSPE) can be used to test goodness of fit of models. MAD and MSPE are expressed as: n MAD = 1 y pred y obs n i i (10) i=1 MSPE = 1 n n i=1 (7) (y pred y obs ) 2 (11) i i where y obs is the observed crash number for intersection i and y pred i i is the expected crash number obtained by the three crash prediction models. Models associated with less MAD and MSPE fit better to the data. 5. Modeling results Bayesian inference is usually implemented using a Markov Chain Monte Carlo (MCMC) algorithm (Gilks et al., 1995). Open source software, WinBUGS, was used to provide a computing approach for calibration of Bayesian models using MCMC (Spiegelhalter et al., 2003). Without credible prior information, uninformative priors were assumed for all regression coefficients with the Normal distributions (0, 10 5 ). The variance of the random effect and the over-dispersion coefficient for the NB distribution were assumed with the Inverse-Gamma distribution (10 3, 10 3 ). Considering convergence and time of updating, two MCMC chains of 20,000 iterations were run, and the first 2000 samples were discarded as burn-in. The proposed HNB model for safety performance of signalized intersections was developed, including intersection and corridor-level variables. A negative binomial (NB) model and a Random Parameter (RP) model allowing the constant terms and the coefficients of intersection ADT to vary randomly from one corridor to another were calibrated using the Bayesian method as comparisons. Like the HNB model, the RP model can account for the heterogeneity across corridors. Nevertheless, one important difference between them is that the RP model does not include corridor-level variables. The posterior summary of the three Bayesian models is reported in Table 3. In this study, for a variable to be considered significant, it had to reach the 95% Bayesian Credible Interval (95% BCI). Variable estimations can be regarded as not significant at the 95% level if 95% of BCIs cover 0 and vice versa (Gelman et al., 2003). Intersection type in the NB, RP and HNB models and proximity of intersections in the NB and RP models were not found to be significant. The corridor-level random effect variances (0.17 in the RP model, and 0.11 in the HNB model) were statistically significant and affirmed the presence of between-corridor heterogeneity. The estimated dispersion values (0.89 in the NB model, 0.81 in the RP model, and 0.65 in the HNB model) provided strong evidence of over-dispersion. This over-dispersion would have resulted in the underestimation of the standard errors in the Poisson model formulation. Table 4 shows comparisons of the three Bayesian models. The HNB model has the lowest DIC, MAD and MSPE, and therefore performs better than the others. Compared with the NB model, the HNB model shows substantial improvement although it is penalized by higher p D values which reflect the increasing complexity of hierarchical models. The less MAD and MSPE values of the HNB model indicate that it has a better model fitting than the NB model. This result further affirms the existence of the intrinsic correlation of crash data. By allowing the effects of variables to vary across corridors, the RP model is superior to the NB model. Referring to DIC, MAD and MSPE values, the HNB model yields a better result than the RP model by including variables at the corridor level. 6. Interpretation of variables Six variables at the intersection level and two variables at the corridor level were significant predictors of crashes. These intersection and corridor related variables will be considered separately below Intersection-level variables The risk factors at the intersection level can be grouped into four categories: traffic volume, location feature, geometric design, and traffic control. Estimates for each risk factor category are presented in Table 3 above, and are discussed separately below.

6 30 K. Xie et al. / Accident Analysis and Prevention 50 (2013) Table 3 Posterior summary of Bayesian model fitting. Variable NB Random parameter (RP) Hierarchical NB (HNB) Mean (SD) 95% BCI Mean (SD) 95% BCI Mean (SD) 95% BCI Fixed effect Intercept 3.3(0.22) (2.87,3.72) 3.58(0.25) (3.05,4.06) 1.99(0.52) (1.03,2.94) Intersection level Under elevated roads or not 0.43(0.18) (0.08,0.77) 0.25(0.12) (0.02,0.43) 0.46(0.2) (0.07,0.86) Proximity of intersections 0.77(0.45) ( 1.61,0.15) 0.45(0.31) ( 1.21,0.26) 0.86(0.41) ( 1.63, 0.02) Intersection type 0.18(0.19) ( 0.54,0.20) 0.15(0.17) ( 0.49,0.17) 0.29(0.17) ( 0.61,0.05) Ratio of turning lanes 1.15(0.44) (0.28,2.01) 0.43(0.2) (0.05,0.72) 0.93(0.4) (0.11,1.70) Total number of phases 0.3(0.16) (0.04,0.64) 0.15(0.08) (0.02,0.33) 0.37(0.16) (0.05,0.69) Intersection ADT 0.04(0.02) (0.02,0.07) 0.03(0.03) (0.01,0.06) 0.04(0.01) (0.02,0.07) (SD of parameter distribution) 0.14(0.04) (0.06,0.20) Corridor Level One-way road or not 0.64(0.32) ( 1.23, 0.02) Mean speed 0.06(0.02) (0.01,0.09) Random effect ε (0.15) (0.03,0.59) 0.11(0.07) (0.01,0.27) Dispersion r 0.89(0.09) (0.72,1.08) 0.81(0.09) (0.64,1.00) 0.65(0.08) (0.50,0.81) Table 4 Model comparisons using DIC, MAD and MSPE. Model D() p D DIC MAD MSPE NB Random parameter (RP) Hierarchical NB (HNB) Traffic volume ADT was found to be positively associated with crash occurrence at intersections. This finding agrees with several prior studies (Abdel-Aty and Abdalla, 2004; Abdel-Aty and Wang, 2006; Chin and Quddus, 2003; Poch and Mannering, 1996; Wang and Abdel- Aty, 2006, 2008). The reason for the finding is that greater traffic volumes provide more opportunities for exposure to conflicts. The HNB model showed the mean of the ADT coefficient to be 0.04, and therefore, assuming other factors do not change, each increase in 10,000 vehicles predicts an increase in expected crash frequency of about 4% (e ) Location feature According to the HNB model, intersections under elevated roads have a 58% (e ) greater crash rate than intersections not under elevated roads, keeping other variables constant. There are only a few studies on the safety impact of elevated roadway presence, but it is important for traffic safety managers in Shanghai to consider, given that 114 km elevated roads have been built, and more are planned. Possible reasons for the higher crash rates at intersections under elevated roadways are limitations in sight distance, and disruptions in traffic flows caused by cars entering and leaving on- and off-ramps. Another location feature variable to consider is the proximity of intersections to each other. Its negative coefficient ( 0.86) predicts that as the distance between intersections decreases, crashes at these intersections will increase. Wang and Abdel-Aty (2006) also found this effect in their study of intersection crashes in Florida. This finding may attribute to the waving sections between intersections being too short for vehicles to change lanes, with the result of an increase in conflicts. The finding is important for Chinese cities which have high road network densities. As shown in Fig. 4, compared with U.S. cities, the road network density in the urban areas of Shanghai is higher than in most U.S. cities Geometric design It was found that 3-legged intersections had 25% (1 e 0.29 ) lower crash rate than 4-legged intersections. Unsurprisingly, Fig. 4. Road network density in a 10 km radius from the city center. (The road network density of U.S. cities is calculated from the models developed in a separate paper (Quinn and Fern andez, 2010).)

7 K. Xie et al. / Accident Analysis and Prevention 50 (2013) Fig. 5. The box-plot of crash rate for each corridor ordered by (a) mean speed and (b) speed variance. compared with 4-legged intersections, the traffic organization of 3- legged intersections will result in less potential conflicts between pedestrians and vehicles and thus less crashes. Another geometric variable predictive of crashes is the ratio of turning lanes to the total lanes and it shows that having more turning lanes promotes the likelihood of crash occurrence. It is obvious that greater turning traffic volumes increase the frequency of conflicts. For instance, increasing right-turn vehicles could bring forth more conflicts with pedestrians and non-motorized vehicles and increasing left-turn vehicles would result in more left-through conflicts. A study by Ma et al. (2010) found that intersection angle was another geometric feature predictive of the safety level, because the sight distance of intersections was relevant to angle. Intersection angle was included, but did not show a significant effect. This is likely because most of the intersections selected for this study were regular Traffic control An important finding was that increases in the number of signal phases were accompanied by increases in the number of intersection crashes. This finding is also consistent with previous research (Poch and Mannering, 1996; Chin and Quddus, 2003). Although more phases can separate traffic flow temporally, e.g., a left-turn signal can keep left-turn and opposing through traffic flow apart, there is a possibility that more rear-end crashes may result (Roess et al., 2003). Furthermore, many crashes occur during the period of signal switching when traffic regulation violations such as red light running usually happen. Frequent signal changes mean more

8 32 K. Xie et al. / Accident Analysis and Prevention 50 (2013) opportunities for red light running and thus can contribute to an elevated crash risk. The effect of another important variable of traffic control cycle length was not found to be significant in these models Corridor-level variables As shown in Table 3 above, two variables at the corridor level were found to be predictive of intersection crashes: whether a road was one-way or two-way, and operating speed. The effects of these two variables are described below One-way road versus two-way road The HNB model results show intersections along one-way roads with 47% (1 e 0.64 ) fewer crashes than two-way roads, when other factors are the same. This is not surprising because intersections along one-way roads have less turning traffic than do intersections on two-way roads, and consequently it is much easier for traffic to avoid conflicts Operating speed Operating speed is an important indicator of traffic operations. There are several studies that consider the impact of speed limit on safety (Abdel-Aty and Wang, 2006; Guo et al., 2010; Wang and Abdel-Aty, 2006), but fewer consider the effects of mean speed and speed variance on safety, because it is more difficult to obtain those measures. It was found that the HNB model made improved predictions of crash probability when the mean speed was included. Keeping other variables constant, one unit increase of mean speed was associated with about 6% (e ) increase in crash occurrence. Somewhat unexpectedly, we did not find speed variance to be significantly related to crashes. Box-plots of the intersection crash rate for the 22 corridors, ordered by mean speed and speed variance, are presented in Fig. 5a and b. In both box-plots, crash rate values more than three interquartile ranges from the end of a box are denoted with asterisks (*), and values more than 1.5 interquartile ranges but less than 3 interquartile ranges with circles ( ). In Fig. 5a, more outlying values of crash rates appear for corridors with higher mean speeds. It can also be seen that increases in mean speed are accompanied by an overall increase in the trend of the crash rate. Nevertheless, since crash occurrence is affected by many variables, certain inconsistencies also appear. For instance, the corridor with a mean speed of km/h has a much higher crash rate than expected. A possible explanation is that 60% of the intersections of this corridor have more than three phases, a proportion much higher than that of the other intersections (30% it was earlier confirmed that signalized intersections with more phases were associated with higher crash rates.). Consider the unexpectedly high crash rate for the corridor with a mean speed of km/h. In this case the reason may be that the corridor lies under an elevated road, and as discussed earlier the sight distances of intersections along such corridors are limited. Considering speed variance (Fig. 5b), this study does not find a clear relationship with crash rate. Speed variance is usually regarded as a significant variable that has positive effects on crash rate (Aarts and Schagen, 2005; Cirillo, 1968; Garber and Gadiraju, 1989; Solomon, 1964; Taylor et al., 2000). However, most of the previous research on variance and crash rate looked at the relationship for uninterrupted traffic flows. In this study traffic flow of the selected corridors was continuously interrupted by signal controls occurring at close intersection spacing, and by congestion. These interrupted traffic flows could explain why there was no observed relationship between speed variance and crashes in this study. 7. Summary and conclusions This study developed a crash prediction model for signalized intersections that can account for intersection correlations and can be used to evaluate the effects of risk factors at both intersection and corridor levels using data from the city of Shanghai, China. Recognizing the unique traffic characteristics of Chinese cities, the findings of this study can serve as useful compliments to the pervious intersection safety analyses. A total of 195 signalized intersections clustered into 22 corridors in the urban areas of Shanghai were selected for this study. Crash frequency data, 17 variables at the intersection level, and 6 variables at the corridor level were used for model development. In order to capture the inherent multilevel structure of the data, a Bayesian hierarchical negative binomial (HNB) model incorporating intersection and corridor-level variables was developed. A Bayesian negative binomial (NB) model and a Bayesian random parameter (RP) model were also developed as comparison models. The Deviance Information Criterion (DIC), Mean Absolute Deviance (MAD) and Mean Squared Predictive Error (MSPE) were used for model assessment. It was found that the HNB model yielded a better result than the NB model most likely because of the within-corridor correlations between signalized intersections. Furthermore, compared with the RP model, the performance of the HNB model was superior due to the HNB model s incorporation of corridor-level variables. It is important for traffic planners and managers to be able to have quantified data on risk factors that accompany different designs and different operational conditions. When considering risk factors at the intersection level, the finding that intersections under the elevated roads have much higher crash frequencies (58% higher) than those not under elevated roads is very important for Chinese cities, because such roads have become so common in recent years. It was also confirmed that closer distances between intersections increased the likelihood of crashes. Thus when planning and rebuilding urban road networks, it is recommended that intersections should located as far apart as is feasible. In addition, the role of intersection type, phase number and ratio of turning lanes suggest more attention needs to be paid to these variables, particularly when 4-legged intersections, intersections with more phases and more turning lanes are under consideration. At the corridor level, it was confirmed that intersections along one-way roads were associated with less crash occurrence. 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