A Joint Analysis of Secondary Collisions and Injury Severity Levels Using Structural Equation Models

Transcription

1 A Joint Analysis of Secondary Collisions and Injury Severity Levels Using Structural Equation Models Kun Xie, Ph.D. Candidate *Corresponding author Graduate Research Assistant Department of Civil and Urban Engineering Center for Urban Science and Progress Urban Mobility and Intelligent Transportation Systems (UrbanMITS) Laboratory New York University MetroTech Center, Brooklyn, NY 0, USA kun.xie@nyu.edu Phone: Kaan Ozbay, Ph.D. Professor Department of Civil and Urban Engineering Center for Urban Science and Progress Urban Mobility and Intelligent Transportation Systems (UrbanMITS) Laboratory New York University MetroTech Center, Brooklyn, NY 0, USA kaan.ozbay@nyu.edu Phone: Hong Yang, Ph.D. Assistant Professor Department of Modeling, Simulation & Visualization Engineering Old Dominion University 00 Elkhorn Ave, Norfolk, VA, USA hyang@odu.edu Phone: +--- Word Count: 00 (Text) + Figures+ Tables=00 words Abstract: Submission Date: Aug., 0 Prepared for Presentation at the th TRB Annual Meeting

2 0 0 ABSTRACT This study aims to investigate the contributing factors to secondary collisions and the effects of secondary collisions on injury severity levels. Manhattan, which is the most densely populated urban area of New York City, is used as a case study. In Manhattan, about.% of crash events get involved with secondary collisions and as high as.% of those secondary collisions lead to incapacitating and fatal injuries. Structural equation models (SEMs) are proposed to jointly model the presence of secondary collisions and injury severity levels. This study contributes to the literature by fully exploring the determinants of secondary collisions such as speeding, alcohol, fatigue, brake defective, limited view and rain. To assess the temporal effects, we use time as a moderator in the proposed SEM framework and results indicate that it is more likely to sustain secondary collisions and severe injuries at night. The parameter estimates of the proposed SEM are further compared with those of the standard probit models which estimate the presence of secondary collisions and injury severity independently. Results show that standard probit models overestimate the safety effects of confounding variables (i.e. variables that can affect both secondary collision occurrence and injury severity) by mixing the direct and indirect effects. In addition, it is found that the standard probit models significantly overestimate the effects of secondary collisions on injury severity propensity by.% for daytime crashes and by.% for nighttime crashes, since the endogeneity of the presence of secondary collisions is ignored in the estimation. Understanding the causes and impacts of secondary collisions can help the transportation agencies and automobile manufacturers develop effective injury prevention countermeasures. Keywords: Safety Analysis, Secondary Collisions, Injury Severity, Endogeneity, Structural Equation Model, Urban Area

3 INTRODUCTION A secondary collision in this study is defined as any collision or non-collision event (e.g. overturn) that occurs after the initial collision in a traffic crash event. It should be distinguished that the secondary collisions are different from the secondary crashes defined in the previous studies such as (, ). A secondary crash is an induced crash event that occurs due to influence of the previous one, whereas a secondary collision along with the initial collision can be regarded as different phases of a single crash event. Common examples of secondary crashes include the ones which occur as a consequence of the queues induced by the primary crashes. Examples of secondary collisions include, but are not limited to, one vehicle striking another two vehicles consecutively, one vehicle hitting another vehicle first and then a pedestrian/bicyclist/fixed object and one vehicle overturning after striking another vehicle. Secondary collisions are not rare events and are among the most injurious phases in crash events (, ). For instance, in Manhattan, New York City, about.% of crash events include secondary collisions and as high as.% of those secondary collisions lead to incapacitating and fatal injuries according to the historical crash data we collected. New York City mayor launched the Vision Zero Action Plan in 0, which targets at reducing injuries and fatalities caused by traffic crashes. To improve traffic safety, the investigation of contributing factors to secondary collisions and safety impacts of secondary collisions are both of great importance to transportation agencies. It is expected that rational and effective injury prevention countermeasures could be developed by understanding the causes and impacts of secondary collisions. Manhattan, the most densely populated urban area of New York City, is used as a case study. New York City s open data policy makes detailed crash data available to the public and enables data-driven safety analysis. The objectives of this study are to explore the determinants of secondary collisions and to investigate the effects of secondary collisions on injury severity using a robust quantitative method. Statistical models are proposed to capture the structural relationship between the contributing factors, presence of secondary collisions and injury severity levels. LITERATURE REVIEW There are a few studies on secondary collisions in the literature. Bryden and Fortuniewicz () () examined a total of,0 barrier crashes in New York State, and found that secondary collisions were present in about % of all cases and accounted for nearly 0% of the fatalities. Ray et al. () () collected the barrier crash data from the New York State and North Carolina State and investigated the impacts of secondary collisions on injury severity. They found that occupants often suffered from severe injuries in secondary collisions after their vehicles being redirected from the longitudinal barriers and the risks of severe injuries were nearly three times greater when second collisions were present. More recently, Gabauer (00) () examined the risk of secondary collisions following an initial barrier impact, based on -year crash data from National Automotive Sampling System and Crashworthiness Data System. Two binary logistic regression model were used to predict the presence of secondary collisions and severe injuries, respectively. Vehicle type and barrier penetration were found to be significantly associated with the involvement of secondary collisions, and secondary collisions were expected to increase the risk of severe injuries by a factor of., close to the safety effect of seat belt use. In a following study by Gowat and Gabauer (0) () which used a similar data source and statistical methods, barrier lateral stiffness, post-impact vehicle trajectory, vehicle type and pre-impact tracking condition were found to influence the occurrence of secondary collisions significantly, and secondary collisions were predicted to raise the likelihood of severe injuries by a factor of. versus crashes without secondary collisions.

4 However, these previous studies are limited to the cases where secondary collisions occurred after striking longitudinal barriers as the first objects. Contributing factors to other types of secondary collisions (e.g. one vehicle hitting another two vehicles consecutively or one vehicle hitting another vehicle and then a pedestrian) haven t been fully explored. In addition, previous studies didn t account for the endogeneity of the presence of secondary collisions in explaining injury severity. In econometrics, the endogeneity occurs when an explanatory variable is correlated with the error term (). Endogeneity can arise as a result of various causes such as omitted variable, measurement error and simultaneity (). In this study, the presence of secondary collisions is likely to be endogenous to the injury severity due to the possible existence of confounding variables (e.g. speeding, alcohol and fatigue) which can impact both secondary collisions and injury severity levels. Ignoring the endogeneity may lead to an overestimated effects of secondary collision on injury severity. Addressing the endogeneity issue is gaining increased attention in studies on traffic safety modeling. Rana et al. (00) presented a detailed literature review on a variety of crash injury severity models with consideration of endogeneity. In this study, we focus on the case that endogeneity is caused by uncontrolled confounding variables (either observed or unobserved). To account for this type of endogeneity, a structural model specification is generally suggested. Kim et al. () () treated crash type as an exogenous variable when modeling injury severity. Ye et al. (00) (0) advanced the joint model of crash type and injury severity by including random variables representing unobserved heterogeneity. Their results confirmed the presence of unobserved variables that influenced both crash type and injury severity. In the study by Eluru and Bhat (00) (), the endogeneity effects of seat belt use on severity were examined, since unbelted drivers are likely be intrinsically unsafe drivers, who are prone to a high risk of severe injuries. It was found that observed variables such as gender, alcohol and vehicle type and unobserved variables could significantly affect both seat belt use and injury severity. In a recent study by Abay et al. (0) (), the joint model of seat belt use and injury severity was extended in a multivariate response structure. A different finding was presented on the endogeneity effects of seat belt use that belted driers tended to drive more aggressively due to the increased safety they perceived by belting up. Additionally, the endogeneity effects of aggressive driving behavior (), passenger characteristics () and the use of airbags and antilock brakes () were investigated in safety literature. In this study, to address the endogeneity issue, we jointly model the presence of secondary collisions and severity injury levels using structural equation models (SEMs), which haven t found widespread use among transportation research. CRASH DATA AND DESCRIPTIVE ANALYSIS Three-year crash record data (0/0/00~0/0/0) was obtained from the New York State Department of Transportation (NYSDOT). Information pertaining to crashes is recorded in three related files. The first file provides event information such as location, time, and weather. The second file presents the information of crash parties (including vehicles, pedestrians and bicyclists) such as the vehicle type, age and gender. Contributing factors to crashes such as speeding, alcohol and fatigue can be obtained from the third file. All crashes which result in death, injury or property damage over one thousand dollars are considered as reportable. Reportable crashes have complete Another common cause of endogeneity simultaneity - at least one explanatory variables are simultaneously influenced by the response variable is not discussed in this study. Source:

5 information on events, parties and contributing factors, and thus a total of, reportable crashes were selected and used for safety analysis in this study., crash events (involving, parties) got involved with secondary collisions, accounting for about.% of the total. Secondary collisions recorded include collisions with motor vehicles, bicyclists, pedestrians and fixed objects after the initial ones, and non-collision events such as overturned. Figure presents the frequencies by secondary collision type. Secondary collisions with motor vehicles (,) and fixed objects (,0) account for about.% of the total. 0 Figure Frequencies by secondary collision type. Regarding injury severity, crashes were classified into five types: no injury (.0%), possible injury (.%), non-incapacitating injury (.%), incapacitating injury (.0%) and fatality (0.%). From Figure, the proportion of serious crashes (including incapacitating injuries and fatalities) is.0% when secondary collisions are not present, and the proportion increases sharply to.% when secondary collisions are present. Empirically, secondary collisions tend to raise the likelihood of severe injuries in crash events. 0 (a) (b) Figure Proportions of serious crashes for (a) without secondary collisions present and (b) with secondary collisions present.

6 0 Driver, vehicle, road and environmental features with the potential to affect the occurrence of secondary collisions and injury severity were extracted from the crash record files. Driver features mostly describe the risky driving behaviors such as speeding, following closely, driving under the influence of alcohol, and using cell phones while driving. Vehicle features include the brake defective, oversized vehicle and the vehicle types get involved in collisions. Road features provide the information mainly about the pavement, traffic control and the location where each crash occurred. Environmental features include the weather (e.g. cloudy, rain and snow) and the time period (e.g. nighttime or daytime). The descriptions and descriptive statistics of data are listed in Table.

7 Table Descriptions and Descriptive Statistics of Key Variables (N=, Crashes) Variable Description Mean S.D. Injury severity for no injury; for possible injury; for non-incapacitating injury; for incapacitating injury; for fatality. 0. Secondary collision for crashes involving secondary collisions; 0 for others Driver Alcohol for crashes with drivers involving alcohol; 0 for others Drugs for crashes with drivers involving drugs; 0 for others Backing for crashes caused by backing unsafely; 0 for others Inattention for crashes caused by driver inattention; 0 for others Inexperience for crashes caused by driver inexperience; 0 for others Yield for crashes caused by failure to yield right of way; 0 for others Sleep for crashes caused by drivers asleep; 0 for others Follow closely for crashes caused by following too closely; 0 for others Illness for crashes caused by driver illness; 0 for others Passenger distraction for crashes caused by passenger distraction; 0 for others Passing improperly for crashes caused by passing improperly; 0 for others Pedestrian error for crashes caused by pedestrian errors; 0 for others Control disregarded for crashes caused by disregarding the traffic control devices; 0 for others Turning improperly for crashes caused by turning improperly; 0 for others Speeding for crashes caused by speeding; 0 for others Lane changing for crashes caused by unsafe lane changing; 0 for others Fatigue for crashes caused by driver fatigue; 0 for others Cell phone for crashes caused by using cell phones; 0 for others Failure right for crashes caused by failure to keep right; 0 for others Rage for crashes caused by aggressive driving; 0 for others Vehicle Brake defective for crashes involving vehicles with brake defects; 0 for others Oversized vehicle for crashes involving oversized vehicles; 0 for others Pedestrian involved for crashes involving pedestrians; 0 for others Bike involved for crashes involving bikes; 0 for others Motorcycle involved for crashes involving motorcycles; 0 for others Truck involved for crashes involving trucks; 0 for others Bus involved for crashes involving buses; 0 for others Road Pavement defective for crashes occurring at roads with pavement defects; 0 for others Road surface for crashes occurring at roads with adverse surface condition; 0 for others Limited view for crashes occurring at roads with limited view; 0 for others Intersection for crashes occurring at intersections; 0 for others Traffic signal for crashes occurring at roads with traffic signal; 0 for others Stop sign for crashes occurring at roads with stop sign; 0 for others Environmental Cloudy for crashes occurring during cloudy days; 0 for others Rain for crashes occurring during rain; 0 for others Snow for crashes occurring during snow; 0 for others Glare for crashes caused by sun glare; 0 for others Time for crashes occurring during nighttime ( pm- am); 0 for crashes occurring during daytime ( am- pm) 0. 0.

8 0 STRUCTURAL EQUATION MODEL (SEM) Model Specification The conceptual framework of the proposed SEM is shown in Figure. Secondary collision propensity is a function of driver, vehicle, road and environmental features. A secondary collision is predicted to occur once the secondary collision propensity is over a certain threshold. The presence of secondary collisions as well as driver, vehicle, road and environmental features are used to estimate the injury severity propensity which is associated with injury severity outcome. To assess the temporal effects, the variable time (0 for daytime and for nighttime) is used as a moderator in the proposed SEM framework. Crash events are classified into the daytime and nighttime groups. The model parameters including the coefficients of explanatory variables and thresholds can be constrained to be the same or allowed to vary between groups. The types of constraints we used are described in the section of Modeling Results. 0 Figure Conceptual framework of the proposed structural equation model (SEM). The formulation for the proposed SEM is expressed as: * ' sc αz i i i sc if sc sc otherwise y * i, i, i 0, * ' i i i i k y k, if y i βx sc k * i * where i ( i,,..., N) is an index for crashes, sc i is the latent secondary collision propensity in crash sc is the secondary collision indicator with indicating the presence of secondary i, i collisions, z i is a (M ) vector of exogenous variables that explains the presence of secondary collisions in crash i, α is a (M ) vector of coefficients corresponding to z i, i is a normally ()

9 0 0 0 distributed error term with mean 0 and variance * y i, is the threshold corresponding to the presence of secondary collisions, is the latent injury severity propensity for crash i, is the observed injury severity level ( for no injury, for possible injury, for non-incapacitating injury, for incapacitating injury, and for fatality) for crash, is a (N ) vector of exogenous variables that affects the injury severity propensity, β is a (N ) vector of coefficients corresponding to x i i x i, is the effect of the presence of secondary collisions on the injury severity, is a normally distributed error term with mean 0 and variance represent injury severity outcome, and k 0, k ( k,,..., K) is an index to is the upper threshold corresponding to the injury severity 0 outcome k (with...,, ). Mean- and variance- adjusted weighted least squares (WLSMV) estimator is robust for the estimation of models with ordered-categorical response variables (). Therefore, we used the WLSMV estimator to estimate the parameters of the proposed SEMs. Model Assessment A set of statistical indices can be used to assess the performance of the SEMs. Chi-square ( ) tests are widely used to indicate the model goodness of fit. The null hypothesis of a chi-square test is that the proposed model can fit the data, so insignificant results are desired. However, the chi-square tests always tend to be statistically significant for models with large sample size (). The chi-square difference statistic ( ) measures the statistical significance of the decrement/improvement in model overall fit as free parameters are eliminated/added (). It is appropriate to use chi-square difference statistics to compare two hierarchical SEMs estimated with the same data, even if the sample size is large. Another widely-used measure of model fit is the root mean square error of approximation (RMSEA). The RMSEA is computed based on the chi-square statistic, but it considers the model complexity by including degrees of freedom. The RMSEA is given by: M D RMSEA M dfm df ( N ) M where is the chi-square statistic for the proposed model M, indicates the degrees of freedom and N is the number of samples. The RMSEA ranges from 0 to, with smaller value indicating a better fit. Generally, a model with RMSEA less than 0.0 is favored (). The comparative fit index (CFI) and Tucker Lewis index (TLI) measure the relative improvement in the fit of the proposed model over that of a baseline model (null model with no explanatory variables) (). The CFI and TLI penalize model complexity using df and M / df M, respectively. The CFI and TLI are given by: CFI df M M B dfb / df / df TLI B B M M B / dfb df M M y i () M () () i

10 0 0 0 B df B where and are the chi-square statistics and degrees of freedom for the baseline model, respectively. A CFI/TLI above 0. indicates a good fit to the data (). MODELING RESULTS The SEM framework in Figure is used to model the presence of secondary collisions and injury severity levels. To test parameter constraints over groups, three SMEs were developed with equal thresholds (the threshold estimates are constrained to be the same for the daytime crash model and the nighttime crash model), equal regressions (the regression coefficients are constrained to be the same for the daytime crash model and the nighttime crash model) and no constraint (the thresholds and regression coefficients of the daytime and nighttime crash models are set to be different). Only the explanatory variables with statistically significant effects are used in the final models. Each SEM has the same selection of explanatory variables so effective model comparison can be performed. Statistical indices of those three SEMs are reported in Table. Table Statistical Indices of Structural Equation Models (SEMs) with Equal Thresholds, Equal Regressions and No Constraint Structural Equation Models (SEMs) Equal Thresholds Equal Regressions No Constraint Chi-square statistics Chi-square.0.. Degrees of freedom 0 P-value RMSEA CFI TLI Considering the great number of samples (N=,) used for model development, the significant results of chi-square tests can be ignored. All the SEMs have RMSEAs less than 0.0, suggesting a good fit to the data. Additionally, the CFIs and TLIs of all the SEMs are greater than 0., except the TLI for the SEM with equal thresholds (0.) which is slightly lower than the acceptance criteria. Chi-square difference tests were conducted to compare the three SEMs developed. The SEM with no constraint can result in a smaller chi-square at the expense of lower degrees of freedom. The chi-square of the SEM with no constraint is. (.0-.) less than that of the SEM with equal thresholds, with degrees of freedom decreasing by (-0). The p- value of the chi-square difference statistic is greater than 0. ( (., ) 0. ), and it indicates that the SEM with no constraint has a significantly smaller chi-square and a better fit than the SEM with equal thresholds. Similarly, it is found that the SEM with no constraint outperforms the SEM with equal regressions by presenting a significantly lower chi-square (p-value= (., ) 0. ). Due to its better performance, the SEM with no constraint is used for variable interpretation and its estimates of parameters are presented in Table. To evaluate the endogeneity effects, standard probit models were also developed and the estimation results are reported in Table. Statistic indicator p-value was used to test the significance of explanatory variables. All the explanatory variables were regarded as statistically significant at % level (p-values<0.0) in the

11 proposed SEM, whereas the variables sleep and limited view were found to be insignificant in the standard probit model for the nighttime secondary collisions. Table Estimates of the Structural Equation Model (SEM) with No Constraint Daytime Nighttime Secondary Collision Injury Severity Secondary Collision Injury Severity Estimate P-value Estimate P-value Estimate P-value Estimate P-value Secondary collision Driver Alcohol Drugs Inattention Inexperience Yield Sleep Illness Control disregarded Speeding Fatigue Cell phone Vehicle Brake defective Motorcycle involved Bike involved Pedestrian involved Road Pavement defective Intersection Limited view Environmental Rain Threshold

12 0 Table Estimates of the Standard Probit Models Daytime Nighttime Secondary Collision Injury Severity Secondary Collision Injury Severity Estimate P-value Estimate P-value Estimate P-value Estimate P-value Secondary collision Driver Alcohol Drugs Inattention Inexperience Yield Sleep Illness Control disregarded Speeding Fatigue Cell phone Vehicle Brake defective Motorcycle involved Bike involved Pedestrian involved Road Pavement defective Intersection Limited view Environmental Rain Threshold

13 DISCUSSION Variable Interpretation The contributing factors to severe injuries have been fully explored in the literature, but limited studies are available on the determinants of the secondary collisions. According to Table, explanatory variables are found to contribute to the presence of secondary collisions and affect the injury severity of crashes. The effects of driver, vehicle, road and environmental features on secondary collisions and severe injuries are discussed in the following paragraphs. Drivers under the influence of alcohol are more likely to get involved with secondary collisions relative to those who are sober, presumably because the alcohol would affect the judgment, reasoning and reaction of drivers. It is also found that drinking alcohol may lead to aggressive driving and thus severe injuries, consistent with the earlier studies such as (,,, ). Similar to the impact of alcohol, taking drugs would make drivers lose consciousness and result in more secondary collisions and severe injuries. Consistent results have been obtained in the previous studies such as (, ). For crashes caused by driver inattention, the likelihoods of secondary collisions and severe injuries are expected to be higher. David and Linda (00) () found a higher likelihood of severe injuries for passengers of teenage drivers when their drivers were distracted by devices or passengers. Zhu and Srinivasan (0) (0) also found driver distraction was associated with higher severity levels. Inexperienced drivers are prone to a higher risk of secondary collisions, possibly due to their inability to control the vehicles after the initial collisions. Injury severity levels rise substantially for drivers who suffer from illness, since they are in vulnerable situations. The impact of illness was considered in the study by Zhu and Srinivasan (0) (0), but no significant relation were found between illness and severe injuries because of the missing data issue. If drivers fail to yield the right of way, the risk of getting severely injured would increase. It is intuitive that drivers who fall asleep can lead to more chances of secondary collisions since they couldn t react in time even after the initial collisions. If the drivers disregard the traffic control devices, more likely the secondary collisions and severe injuries would occur. Speeding is predicted to increase the likelihood of secondary collisions, presumably because speeding vehicles couldn t be slowed down immediately and have higher possibility to strike multiple objects. Speeding is also found to be associated with greater severe injury propensity, a result observed in the previous studies such as (, ). Fatigued drivers are prone to higher risks of secondary collisions and severe injuries, possibly because they are unable to make a quick reaction. The safety effect of fatigue was investigated in the study by Zhu and Srinivasan (0) (0). Although variables related to the fatigue turned out to be insignificant predictors of injury severity, they stated the possible reason that the effect of fatigue could be partially captured by variables such as time of day and crash type. In addition, the use of cell phone would lead to a high risk of severe injuries. According to the study by McEvoy et al. (00) (), cell phone use caused a fourfold increase in crash injuries resulting in hospitalization. David and Linda (00) () found that teenage drivers had an increased likelihood of severe injuries if distracted by cell phones. Vehicles with brake defects tend to be exposed to secondary collisions and severe injuries, since those vehicles couldn t stop fast enough. Khattak et al. (00) () and Chen and Chen (0) () found defective truck brakes were significantly associated with severe injuries. It is found that pedestrian crashes are less likely to have secondary collisions. Crashes involving motorcycles, bikes and pedestrians are prone to a higher risk of severe injuries, since motorcyclists, bicyclists and pedestrians are vulnerable road users relative to vehicle occupants. Chang and Wang (00) () stated that motorcyclists, bicyclists and pedestrians received less protection and were expected to have a greater likelihood of severe injuries compared with the automobile drivers. Valent et al. (00)

14 () found crashes involving motorcyclists, bicyclists and pedestrians were associated with high death risk. Regarding the road features found significant, secondary collisions are more likely to happen at the roads with pavement defects and limited view. Pavement defects can also increase the risk of severe injuries. Chang and Wang (00) () found injury severity had a serious correlation with the pavement condition. Milton et al. () found increasing pavement friction leaded to more severe injuries. However, opposite finding is stated in the study by Clifton et al. (00) (). Furthermore, crashes occurring at intersections tend to be involved with severe injuries in comparison with those occurring at road mid-blocks. The study by Yamamoto and Shankar (00) () suggested a lower driver injury risk at intersections for vehicle-fixed object crashes, because of the lower driving speed and more attention by drivers when approaching the intersections. However, in this study which considers all types of crashes, head-on and right-angle crashes are far more likely to occur at intersections than mid-blocks, and these crash types are associated with a high risk of severe injuries (0). Furthermore, in rainy days, more secondary collisions are found to happen due to the slippery roadway and affected view. However, no weather feature is found to significantly impact the injury severity in this study. Different results were obtained in the literature on the safety impacts of weather. Eluru (00) (0) found crashes occurring under adverse weather conditions increased the likelihood of fatally injured. On the contrary, Abdel-Aty (00) () found drivers were less likely to experience severe injuries under adverse weather condition, because drivers tended to slow down and kept a safe distance from other vehicles. Considering the temporal effects, the parameter estimates of the daytime and nighttime models are compared. Explanatory variables including sleep, control disregarded, fatigue, brake defective and pedestrian involved have greater impacts on the secondary collision propensity during the nighttime compared with the daytime. On the other hand, the effects of explanatory variables including alcohol, inattention, yield and pavement defective on the severity injury propensity are found to be greater during the nighttime compared with the daytime. According to the threshold parameters ( ) which map the secondary collision propensity to the observed secondary collision occurrence, the smaller threshold value in the nighttime secondary collision model implies that secondary collision are more likely to occur during the nighttime. Similarly, the threshold for each injury severity level ( ) is lower for nighttime crashes than that of the daytime crashes, indicating that it is more likely to sustain severe injuries at night. The study by Abdel-Aty (00) () also revealed an increased severity risk for crashes occurring at night. Kockelman and Kweon (00) () found later-night driving on Friday, Saturday and Sunday exhibited a high likelihood of severe injuries. k Comparison of the SEM and the Probit model The parameter estimates of the SEM with no constraint (presented in Table ) are further compared with those of the standard probit models (presented in Table ) which estimate the presence of secondary collisions and injury severity independently. The percentage difference of parameter estimates are presented in Table. According to Table, most coefficient estimates of secondary collision determinants in the proposed SEM are similar to those in the standard probit models, except a few variables such as control disregarded and limited view. On the other hand, the effects of confounding variables including the variables alcohol, inattention, speeding, fatigue and pavement defective on injury severity are estimated quiet differently in the SEM and the standard probit

15 0 models. The standard probit models overestimate the safety effects of those confounding variables by mixing the direct effects and indirect effects which are mediated by the presence of secondary collisions in the SEM. For instance, according to SEM estimates in Table, the direct effects of drinking alcohol on injury severity propensity during daytime is 0.0, and meanwhile drinking alcohol contributes to severe injures indirectly by increasing the secondary collision propensity by 0.. However, according to Table, the effects of drinking alcohol on severity propensity during daytime is estimated to be 0. by the standard probit models which cannot distinguish the direct and indirect effects of drinking alcohol. Most importantly, the standard probit models significantly overestimate the effects of secondary collisions on injury severity propensity by.% for daytime crashes and by.% for nighttime crashes because endogeneity effects are ignored in the estimation. The endogeneity issue is caused by the fact that secondary collisions are associated with risk factors such as speeding, alcohol and fatigue which contribute to severe injuries. On the other hand, the estimates of the SEM present the pure effects of secondary collisions on injury severity by accounting for its endogeneity effects. Table Percentage Difference of Parameter Estimates between the Structural Equation Model (SEM) with No Constraint and the Standard Probit Models Daytime Nighttime Secondary Collision Injury Severity Secondary Collision Injury Severity Estimate Difference Estimate Difference Estimate Difference Estimate Difference Secondary collision -.% -.% Driver Alcohol -.%.% -0.%.% Drugs.%.% -.%.% Inattention 0.%.% -.%.% Inexperience.% - -.% - Yield - -.% - -.% Sleep -0.% - -.% - Illness - -.% - -.% Control disregarded -.%.% -.0%.% Speeding.%.% *.%.% Fatigue.%.% *.%.0% Cell phone - -.0% - -.% Vehicle Brake defective.%.0% -0.%.0% Motorcycle involved -.% -.% Pedestrian involved.% -.% -0.% -.% Bike involved -.% -.% Road Pavement defective.0%.%.%.% Intersection -.% -.% Limited view -.% - -.% - Environmental Rain.% -.% -

16 SUMMARY AND CONCLUSIONS This study investigates the contributing factors to secondary collisions and the effects of secondary collisions on injury severity levels using the crash data from Manhattan. Structural equation models (SEMs) are proposed to jointly model the presence of secondary collisions and injury severity levels. To assess the temporal effects, the variable time is used as a moderator in the proposed SEM framework. Three SMEs were developed with equal thresholds, equal regressions and no constraint for the daytime and nighttime crash groups. The results of chi-square difference test indicate that the SEM with no constraint outperforms the others by presenting a significantly lower chi-square statistic. Due to its better performance compared with other models, the SEM with no constraint is used to investigate the effects of driver, vehicle, road and environmental features on secondary collisions and severe injuries. explanatory variables are found to contribute to the presence of secondary collisions, including alcohol, drugs, inattention, inexperience, sleep, control disregarded, speeding, fatigue, brake defective, pedestrian involved, pavement defective, limited view and rain; while were expected to increase the risk of severe injuries, including the presence of secondary collision, alcohol, drugs, inattention, yield, illness, control disregarded, speeding, fatigue, cell phone, brake defective, motorcycle involved, bike involved, pedestrian involved, pavement defective and intersection. Considering the temporal effects, the parameter estimates of the daytime and nighttime models are compared, and the results indicate that it is more likely to sustain secondary collisions and severe injuries at night. In addition, the parameter estimates of the proposed SEM are further compared with those of the standard probit models which estimate the presence of secondary collisions and injury severity independently. The standard probit models are found to overestimate the safety effects of confounding variables by mixing the direct and indirect effects. It is found that the standard probit models significantly overestimate the effects of secondary collision on injury severity propensity by.% for daytime crashes and by.% for nighttime crashes because endogeneity effects are ignored in the estimation. This study contributes to the literature by fully investigating the contributing factors to secondary collisions and estimating the safety effects of secondary collisions after adjusting for the endogeneity effects. Understanding the causes and impacts of secondary collisions can help the transportation agencies and automobile manufacturers develop effective injury prevention countermeasures. In addition, this study shows the potential of using SEMs in exploring the structural relationship between risk factors and safety indicators, regarding that SEMs haven t been widely exploited in the traffic safety research. For future study, we will attempt to use multilevel SEMs to accommodate the hierarchy of crash data (e.g. with crash characteristics being the first level of dataset, vehicle characteristics being the second level and driver characteristics being the third level). ACKNOWLEDGMENTS The work is partially funded by Urban Mobility & Intelligent Transportation Systems (UrbanMITS) laboratory, Center for Urban Science and Progress (CUSP) and Department of Civil and Urban Engineering at New York University (NYU). The authors would like to thank the New York State Department of Transportation for providing data for the study. The contents of this paper reflect views of the authors who are responsible for the facts and accuracy of the data presented herein. The contents of the paper do not necessarily reflect the official views or policies of the agencies.

17 REFERENCES. Yang, H., K. Ozbay, and K. Xie, 0. Assessing the risk of secondary crashes on highways. Journal of safety research, pp.. e-.. Yang, H., E. Morgul, B. Bartin, and K. Ozbay, 0. Development of an on-line scalable approach for identifying secondary crashes. Transportation Research Record: Journal of the Transportation Research Board, Accepted February, pp. 0.. Gabauer, D.J., 00. Secondary collisions following a traffic barrier impact: frequency, factors, and occupant risk. In: Proceedings of the Annals of Advances in Automotive Medicine/Annual Scientific Conference, pp... Ray, M.H., J. Michie, W. Hunter, and J. Stutts,. An analysis of the risk of occupant injury in second collisions.. Bryden, J.E. and J.S. Fortuniewicz,. Traffic barrier performance related to vehicle size and type.. Gowat, R.C. and D.J. Gabauer, 0. Secondary collisions revisited: real-world crash data and relationship to crash test criteria. Traffic injury prevention (), pp. -.. Wooldridge, J.M., 00. Econometric analysis of cross section and panel data, MIT press.. Greene, W.H., 00. Econometric analysis, Pearson Education India.. Kim, K., L. Nitz, J. Richardson, and L. Li,. Personal and behavioral predictors of automobile crash and injury severity. Accident Analysis & Prevention (), pp Ye, X., R.M. Pendyala, F.S. Al-Rukaibi, and K. Konduri, 00. Joint Model of Accident Type and Severity for Two-Vehicle Crashes. In: Proceedings of the Transportation Research Board th Annual Meeting.. Eluru, N. and C.R. Bhat, 00. A joint econometric analysis of seat belt use and crash-related injury severity. Accident Analysis & Prevention (), pp Abay, K.A., R. Paleti, and C.R. Bhat, 0. The joint analysis of injury severity of drivers in two-vehicle crashes accommodating seat belt use endogeneity. Transportation Research Part B: Methodological 0(0), pp. -.. Paleti, R., N. Eluru, and C.R. Bhat, 00. Examining the influence of aggressive driving behavior on driver injury severity in traffic crashes. Accident Analysis & Prevention (), pp. -.. Lee, C. and M. Abdel-Aty, 00. Presence of passengers: Does it increase or reduce driver's crash potential? Accident Analysis & Prevention 0(), pp Winston, C., V. Maheshri, and F. Mannering, 00. An exploration of the offset hypothesis using disaggregate data: The case of airbags and antilock brakes. Journal of Risk and Uncertainty (), pp. -.. Markus, K.A., 0. Principles and Practice of Structural Equation Modeling by Rex B. Kline. Structural Equation Modeling: A Multidisciplinary Journal (), pp Hu, L.-t. and P.M. Bentler,. Evaluating model fit.. Khattak, A.J., R.J. Schneider, and F. Targa, 00. Risk factors in large truck rollovers and injury severity: analysis of single-vehicle collisions. Transportation Research Record.. Neyens, D.M. and L.N. Boyle, 00. The influence of driver distraction on the severity of injuries sustained by teenage drivers and their passengers. Accident Analysis & Prevention 0(), pp Zhu, X. and S. Srinivasan, 0. A comprehensive analysis of factors influencing the injury severity of large-truck crashes. Accident Analysis & Prevention (), pp. -.

18 0 0. Chang, L.-Y. and F. Mannering,. Analysis of injury severity and vehicle occupancy in truck-and non-truck-involved accidents. Accident Analysis & Prevention (), pp. -.. Abdel-Aty, M., 00. Analysis of driver injury severity levels at multiple locations using ordered probit models. Journal of Safety Research (), pp McEvoy, S.P., M.R. Stevenson, A.T. McCartt, M. Woodward, C. Haworth, P. Palamara, and R. Cercarelli, 00. Role of mobile phones in motor vehicle crashes resulting in hospital attendance: a case-crossover study. bmj (), pp... Chen, F. and S. Chen, 0. Injury severities of truck drivers in single-and multi-vehicle accidents on rural highways. Accident Analysis & Prevention (), pp. -.. Chang, L.-Y. and H.-W. Wang, 00. Analysis of traffic injury severity: An application of nonparametric classification tree techniques. Accident Analysis & Prevention (), pp Valent, F., F. Schiava, C. Savonitto, T. Gallo, S. Brusaferro, and F. Barbone, 00. Risk factors for fatal road traffic accidents in Udine, Italy. Accident Analysis & Prevention (), pp. -.. Milton, J.C., V.N. Shankar, and F.L. Mannering, 00. Highway accident severities and the mixed logit model: An exploratory empirical analysis. Accident Analysis & Prevention 0(), pp Clifton, K.J., C.V. Burnier, and G. Akar, 00. Severity of injury resulting from pedestrian vehicle crashes: What can we learn from examining the built environment? Transportation Research Part D: Transport and Environment (), pp. -.. Yamamoto, T. and V.N. Shankar, 00. Bivariate ordered-response probit model of driver s and passenger s injury severities in collisions with fixed objects. Accident Analysis & Prevention (), pp Eluru, N., C.R. Bhat, and D.A. Hensher, 00. A mixed generalized ordered response model for examining pedestrian and bicyclist injury severity level in traffic crashes. Accident Analysis & Prevention 0(), pp Kockelman, K.M. and Y.-J. Kweon, 00. Driver injury severity: an application of ordered probit models. Accident Analysis & Prevention (), pp. -. 0