Multivariate copula temporal modeling of intersection crash consequence metrics: A joint estimation of injury severity, crash type, vehicle damage and driver error

Applying the heteroskedastic ordered probit model on injury severity for improved age and gender estimation

OBJECTIVE

Driver characteristics have been linked to the frequency and severity of car crashes. Among these, age and gender have been shown to impact both the possibility and severity of a crash. Previous studies have used standard ordered probit (OP) models to analyze crash data, and some research has suggested heteroskedastic ordered probit (HETOP) could provide improved model fit. The objective of this paper is to evaluate potential improvements of the heteroskedastic ordered probit (HETOP) model compared to the standard ordered probit (OP) model in crash analysis, by examining the effect of gender across age on injury severity among drivers. This paper hypothesizes that the HETOP model can provide a better fit to crash data, by allowing heteroskedasticity in the distribution of injury severity across driver age and gender.

METHODS

Data for 20,222 crashes were analyzed for North Carolina from 2016 to 2018, which represents the state with the highest number of fatalities per 100 million vehicle miles traveled amongst available crash data from the Highway Safety Information System.

RESULTS

Darker lighting conditions, severe road surface conditions, and less severe weather were associated with increased injury severity. For driver demographics, the probability of severe injuries increased with age and for male drivers. Moreover, the variance of severity increased with age disproportionately within and across genders, and the HETOP was able to account for this.

CONCLUSIONS

The results of the two applied approaches revealed that HETOP model outperformed the standard OP model when measuring the effects of age and gender together in injury severity analysis, due to the heteroskedasticity in injury severity within gender and age. The HETOP statistical method presented in this paper can be more broadly applied across other contexts and combinations of independent variables for improved model prediction and accuracy of causal variables in traffic safety.

Analyzing the impact of curve and slope on multi-vehicle truck crash severity on mountainous freeways

Many studies examine the road characteristics that impact the severity of truck crash accidents. However, some only analyze the effect of curves or slopes separately, ignoring their combination. Therefore, there are nine types of the combination of curve and slope in this study. The combination of curve and slope factor that affected the injury severity of truck crashes on mountainous freeways was examined using a correlated random parameter logit model. This method is applied to evaluate the correlation between the random parameters and those that exhibit unobserved heterogeneity. Also, the multinomial logit model and traditional random parameter logit model are used. The study's data were collected from multi-vehicle truck crashes on mountainous freeways in China. The results showed that the correlated random parameters logit model was better than the others. In addition, they demonstrated a correlation between the random parameters. Based on the estimation coefficients and marginal effects, the combination of curve and slope has a great influence on the injury severity of truck crashes. The main finding is that curve with medium radius and medium slope will significantly increase the probability of medium severity comparing to curve with high radius and flat slope. On the other hand, the injury severity of truck accidents was significantly impacted by crash type, vehicle type, surface condition, time of day, season, lighting condition, pavement type, and guardrail. Variables such as sideswipe, head-on, medium trucks, morning, dawn or dusk and summertime reduced the probability of truck crashes. Rollover, winter, gravel, and guardrail variables increased the risk of truck crashes. Correlations were also discovered between a rollover and dry surface condition and rollover and gravel pavement type. The research findings will help traffic officials determine effective countermeasures to decrease the severity of truck crashes on mountainous freeways.

Exploring Factors Affecting Crash Injury Severity with Consideration of Secondary Collisions in Freeway Tunnels

Although there have been several studies conducted exploring the factors affecting injury severity in tunnel crashes, most studies have focused on identifying factors that directly influence injury severity. In particular, variables related to crash characteristics and tunnel characteristics affect the injury severity, but the inconvenient driving environment in a tunnel space, characterized by narrow space and dark lighting, can affect crash characteristics such as secondary collisions, which in turn can affect the injury severity. Moreover, studies on secondary collisions in freeway tunnels are very limited. The objective of this study was to explore factors affecting injury severity with the consideration of secondary collisions in freeway tunnel crashes. To account for complex relationships between multiple exogenous variables and endogenous variables by considering the direct and indirect relationships between them, this study used a structural equation modeling with tunnel crash data obtained from Korean freeway tunnels from 2013 to 2017. Moreover, based on high-definition closed-circuit televisions installed every 250 m to monitor incidents in Korean freeway tunnels, this study utilized unique crash characteristics such as secondary collisions. As a result, we found that tunnel characteristics indirectly affected injury severity through crash characteristics. In addition, one variable regarding crashes involving drivers younger than 40 years old was associated with decreased injury severity. By contrast, ten variables exhibited a higher likelihood of severe injuries: crashes by male drivers, crashes by trucks, crashes in March, crashes under sunny weather conditions, crashes on dry surface conditions, crashes in interior zones, crashes in wider tunnels, crashes in longer tunnels, rear-end collisions, and secondary collisions with other vehicles.

Spatial influence of engineering construction on traffic accidents, a case study of Jinan

Due to urban construction, engineering transport vehicles are gradually increased on roads, which might speed up traffic accident risks. To investigate the influence of urban construction on traffic accidents, this paper adopted 1977 traffic accidents of engineering transport vehicles and 220 engineering construction projects for correlation analysis. First, considering three degrees (Major, Ordinary and Minor) of accidents, the spatial autocorrelation test of engineering transport vehicle accidents is carried out by using spatial econometric. Then to further evaluate and analyze the spatial regression model, the optimal model is selected to analyze the spatial influence of the floor area of different types of engineering construction projects on the accidents of engineering transport vehicles. The results show that the accident of engineering transport vehicles itself is spatially dependent, that is, the higher the severity of the accident, the more concentrated it is in space, and there is a significant spatial positive correlation with engineering construction projects. And the floor areas of synthetic land, residential land, commercial land and land for roads and transportation facilities have significant spatial effects on engineering transport vehicle accidents, and the indirect effects are also concerned. The increase of floor area of roads and transportation facilities is more likely to induce accidents of engineering transport vehicles. For every 10,000 square meters of the floor area of roads and transportation facilities, there are 12.66 accidents of engineering transport vehicles in the region and its neighboring areas.

An integrated text mining, literature review, and meta-analysis approach to investigate pedestrian violation behaviours

The goal of this study is to provide an overview of previous research that investigated pedestrian violation behaviour, with a focus on identifying the contributing factors of such behaviour, its impact on pedestrian safety, the mitigation strategies, the limitations of current studies, and the future research directions. To that end, the Latent Dirichlet Allocation (LDA) text mining method was applied to extract a comprehensive list of studies that were conducted during the past 21 years related to pedestrian violation behaviours. Using the extracted studies, a multi-sectional literature review was developed to provide a comprehensive understanding of the different aspects related to pedestrian violations. Afterward, a meta-analysis was undertaken, using the studies that reported quantitative results, in order to obtain the average impact of the different contributing factors on the frequency of pedestrian violations. The study found that pedestrian violations are one of the hazardous behaviours that contribute to both the frequency and severity of pedestrian-vehicle collisions. According to the literature, the waiting time at the curbside, traffic volume, walking speed, pedestrian distraction, the presence of bus stops and schools, and the presence of on-street parking are among the key factors that increase the likelihood of pedestrian violations. The study has also reviewed a wide range of strategies that can be used to mitigate violations and reduce the safety consequences of such behaviour, including simple engineering-based countermeasures, enforcement, solutions that rely on advanced in-vehicle technologies, and infrastructure connectivity features, educational programs, and public campaigns.

Spatiotemporal analysis of crash severity on rural highway: A case study in Anhui, China

Traffic crashes are the result of the interaction between human activities and different socio-economic, geographical, and environmental factors, showing a temporal and spatial relationship. The temporal and spatial correlations must be characterized in crash severity studies, for which the geographically and temporally weighted ordered logistic regression (GTWOLR) model is an effective approach. However, existing studies using the GTWOLR model only subjectively selected a type of kernel function and kernel bandwidth, which cannot determine the best expression of the spatiotemporal relationship between crashes. This paper explores the optimal kernel function and kernel bandwidth considering the aforementioned problem to obtain the best GTWOLR model to analyze the crash data based on the crash data of rural highways in Anhui Province, China, from 2014 to 2017. First, the GTWOLR models with Gaussian or Bi-square kernel function and fixed (the spatiotemporal distance remains constant of local sample) or adaptive (the quantity of the local sample is constant) bandwidth are compared. Second, the log-likelihood and Akaike information criterion are used to compare the GTWOLR model with the ordered logistic regression (OLR) model. Finally, the spatial and temporal characteristics of the contributing factors in the best GTWOLR model are analyzed, and corresponding countermeasures for improving traffic safety on rural highways are proposed. Model comparison results reveal that although the difference was insignificant, the Bi-square kernel function with fixed bandwidth (BF)- GTWOLR model has a better goodness of fit than the GTWOLR models with other types of kernel function and bandwidth and the OLR model. The BF-GTWOLR model estimation results showed that eight factors, including pedestrian-vehicle crash, middle-aged driver, hit-and-run, truck, motorcycle, curve, slope and mountainous, passed the non-stationary test, indicating their varying effects on the crash severity across space and over time. As a crash severity modeling approach that effectively quantifies the spatiotemporal relationships in crashes, the BF-GTWOLR model, which adapts to crash data, may have implications for future research. In addition, the findings of this paper can help traffic management departments to propose progressive and targeted policies or countermeasures, so as to reduce the severity of rural highway crashes.

Developing a grouped random parameter beta model to analyze drivers' speeding behavior on urban and suburban arterials with probe speed data

Speeding is one of the major contributing factors to traffic fatalities. Various speed management strategies have been proposed to encourage drivers to select more appropriate speeds. This study aims to explore the different effects of the speed management strategies on the speeding proportions at urban and suburban arterials. Probe speed data was used to calculate the speeding proportions. To overcome the variability of probe speed data caused by the signalized intersections, a new method was suggested to calculate the speeding proportion, and a fractional split model was estimated to adjust the probe speed data. A Beta regression model was developed to analyze the speeding proportion. A grouped random parameter modeling structure was adopted to realize the different effects of speed management strategies and other road attributes on speeding proportions by different road types. Besides, a fixed beta model was developed for the comparison. The results suggested the grouped random parameter model could provide better performance over the counterpart and could realize the different effects of road features and other contributing factors on the speeding of different roads. It is expected that the findings could help inform more appropriate road design in order to reduce speed limit violations on urban and suburban arterials.

An integrated clustering and copula-based model to assess the impact of intersection characteristics on violation-related collisions

The main goal of this study is to investigate the impact of a variety of factors on the frequency and the severity of pedestrian-vehicle collisions that involve pedestrian violations. To that end, the collision dataset of the City of Hamilton between 2010 and 2017 was reviewed to filter out pedestrian collisions that involved pedestrian violations. A Latent Class Analysis (LCA) method was applied to divide the dataset into a set of homogeneous clusters, based on traffic and intersection characteristics. A copula-based multivariate model was then developed for each cluster in order to study the impact of the different factors on collisions under the prevailing conditions of each cluster. The results showed that the number of bus stops within the intersection area is directly associated with the frequency and the severity of collisions involving pedestrian violations. A reduction in collisions was observed with the increase in the frequency of buses at intersections that are located along main transit routes. Moreover, the presence of schools near the intersection tends to increase the frequency of collisions involving pedestrian violations, especially at large intersections. The results also revealed that the presence of central refuge islands, despite their overall safety benefits, increases the likelihood of collisions involving pedestrian violations in large intersections. The results of this study provide valuable insights for a better understanding of the safety consequences of pedestrian violations. Such understanding assists engineers and planners to design intersections that reduce the frequency of pedestrian violations and mitigate their negative safety consequences.

Correlated mixed logit modeling with heterogeneity in means for crash severity and surrogate measure with temporal instability

This study employs the correlated mixed logit models with heterogeneity in means by accounting for temporal instability to estimate both injury severity and vehicle damage. Two years of intersection crash data from Connecticut were analyzed based on driver characteristics, highway and traffic attributes, environmental variables, vehicle and crash types. These elements were used as independent variables to explore the contributing factors to crash outcome. The likelihood ratio test highlights that the temporal instability exists in both injury severity and vehicle damage models. The model estimation results illustrate that the means of some random parameters are different among crashes. The correlation coefficients of random parameters verify that these random parameters are not always independent, and their correlations should be considered and accounted for in crash severity estimation models. The investigation and comparison between injury severity models and vehicle damage models verify that the injury severity and vehicle damage are highly correlated, and the effects of contributing factors on vehicle damage are consistent with the results of injury severity models. This finding demonstrates that vehicle damage can be used as a potential surrogate measure to injury severity when suffering from a low sample of severe injury crashes in crash severity prediction models. It is anticipated that this study can shed light on selecting appropriate statistical models in crash severity estimation, identifying intersection crash contributing factors, and help develop effective countermeasures to improve intersection safety.

Factors associated with consecutive and non-consecutive crashes on freeways: A two-level logistic modeling approach

A consecutive crash consists of a primary crash and one or more secondary crashes that occur subsequently in a short period of time within a certain distance. It often affects a relatively large area of road space and the traffic disruption created can be difficult for traffic managers to control and resolve. This study identifies the factors delineating a primary crash that results in secondary crashes within a minute from a regular crash that does not result in any secondary crashes. Random-effects, random-parameter and two-level binary logistic regression models are applied to data collected on 8779 crashes on the freeway network of the Guizhou Province, China in 2018, of which 299 are consecutive crashes. According to the AIC values, the two-level logistic model outperforms the other two models. Rear-end primary crashes have a significant random effect varying across road segments on the occurrence of consecutive crashes. Various crash types (rear-end, roll-over and side-swipe), tunnel crash and foggy weather are positively associated with the possibility to cause subsequent consecutive crashes, whereas single-vehicle crash, truck involvement and the time periods with poorer natural lighting are less likely to incur consecutive crashes. Recommendations are provided to minimize the possibility of the occurrence of consecutive crashes on a freeway.

An accelerated hierarchical Bayesian crash frequency model with accommodation of spatiotemporal interactions

Although spatial and temporal correlations of crash observations have been well addressed in the literature, the interactions between them are rarely studied. This study proposes a Bayesian spatiotemporal interaction (BSTI) approach for crash frequency modeling with an integrated nested Laplace approximation (INLA) method to greatly expedite the Bayesian estimation process. Manhattan, which is the most densely populated urban area of New York City, is selected as the study area. Hexagons are used as the basic geographic units to capture crash, transportation, land use, and demo-economic data from 2013 to 2019. A series of Bayesian models with various spatiotemporal specifications are developed and compared. The BSTI model with Type II interaction, which assumes that the structured temporal random effect interacts with the unstructured spatial random effect is found to outperform the others in terms of goodness-of-fit and the ability to reduce the dependency of residuals. It is also found that the unobserved heterogeneity is mostly attributed to the spatial effects instead of temporal effects. In addition, the BSTI Type II model also yields the lowest predictive error when the last year's data are used as the test set. The proposed BSTI approach can potentially advance safety analytics by achieving high prediction accuracy and computational efficiency while maintaining its interpretability on the effects of contributing factors and the unobserved heterogeneity.

Highway safety assessment and improvement through crash prediction by injury severity and vehicle damage using Multivariate Poisson-Lognormal model and Joint Negative Binomial-Generalized Ordered Probit Fractional Split model

INTRODUCTION

Predicting crash counts by severity plays a dominant role in identifying roadway sites that experience overrepresented crashes, or an increase in the potential for crashes with higher severity levels. Valid and reliable methodologies for predicting highway accidents by severity are necessary in assessing contributing factors to severe highway crashes, and assisting the practitioners in allocating safety improvement resources.

METHODS

This paper uses urban and suburban intersection data in Connecticut, along with two sophisticated modeling approaches, i.e. a Multivariate Poisson-Lognormal (MVPLN) model and a Joint Negative Binomial-Generalized Ordered Probit Fractional Split (NB-GOPFS) model to assess the methodological rationality and accuracy by accommodating for the unobserved factors in predicting crash counts by severity level. Furthermore, crash prediction models based on vehicle damage level are estimated using the same two methodologies to supplement the injury severity in estimating crashes by severity when the sample mean of severe injury crashes (e.g., fatal crashes) is very low.

RESULTS

The model estimation results highlight the presence of correlations of crash counts among severity levels, as well as the crash counts in total and crash proportions by different severity levels. A comparison of results indicates that injury severity and vehicle damage are highly consistent.

CONCLUSIONS

Crash severity counts are significantly correlated and should be accommodated in crash prediction models. Practical application: The findings of this research could help select sound and reliable methodologies for predicting highway accidents by injury severity. When crash data samples have challenges associated with the low observed sampling rates for severe injury crashes, this research also confirmed that vehicle damage can be appropriate as an alternative to injury severity in crash prediction by severity.

Hierarchical binary logit model to compare driver injury severity in single-vehicle crash based on age-groups

Most of the previous single-vehicle crash analysis studies ignored the effect of road-segments level at higher plan that could probably be unobserved heterogeneity and vary among crash-level factor from one road-segment to next and possibly could lead to a potential biased estimated result. This study developed a hierarchical binary logit model which have the ability to account for both unobserved heterogeneity and correlation within road-segment, to investigate and compare the impact of significant factors influencing fatal single-vehicle crash between young, mid-age and old driver model. A seven-years from 2011 to 2017 crash data, Department of Highway (DOH), Thailand were used in this study. The Intra-Class-Correlation values indicate the importance of road-segment level that 10.1%, 12.2% and 12.8% of the total variation were accounted by random effect from road-segment heterogeneity for young, mid-age and old driver model, respectively. The estimated result of this study shows that influence of alcohol and fatigue increase risk of fatal crash among young and old driver, seatbelt-usage reduce risk of being fatal among mid-age and old driver, roadside safety feature (guardrail) significantly reduce fatality risk among young and mid-age driver, and night time driving without light increase probability of fatal crash for mid-age driver. This study recommends the need to enforce the law on driver under influence of alcohol and seatbelt usage, educational campaign on driving, and installation of guardrail on curve road.

Investigating exposure measures and functional forms in urban and suburban intersection safety performance functions using generalized negative binomial - P model

Selecting an appropriate exposure measure and functional form for Safety Performance Functions (SPFs) is critical in precisely predicting crash counts by different crash types for intersections. This study proposes a new approach, namely Generalized Negative Binomial-P (GNB-P) model, to model the complex relationship between crashes and different exposure measures by crash type for intersections, which helps not only identify the most reliable exposure measure for intersection SPFs, but also explore the most appropriate functional form of the NB models. To this end, three types of SPF functional forms, namely Power function, Hoerl function 1 and Hoerl function 2 with different exposure measures including major road AADT, minor road AADT and total AADT were estimated by crash type for stop-controlled and two types of signalized intersections. The over-dispersion of the SPF models was estimated using the exposure measures to account for crash data variation across different intersections. The SPF estimation results highlighted that the mean-variance structure of NB models is not consistent and varies by crash data. The over-dispersion of SPFs by crash type is not constant and varies across different intersections. The minor road AADT is shown to be positively correlated with the over-dispersion of SPFs in estimating crash counts for Same-Direction Crashes (SDC), Intersecting-Direction Crashes (IDC) and Single-Vehicle Crashes (SVC). Estimating the over-dispersion using exposure measures results in more reliable SPF results. Furthermore, it is found that the Power function with major road and minor road AADT as the exposure measure performs the best in estimating SPFs for Opposite-Direction Crashes (ODC). The Hoerl function 2 with total AADT and the proportion of minor road AADT over the total as the exposure measure performs the best in estimating SVC SPFs for intersections. The Hoerl function 1 with major road and minor road AADT as the exposure measure is more accurate in estimating SPFs for both SDC and IDC.

Examining driver injury severity in left-turn crashes using hierarchical ordered probit models

OBJECTIVE

Few existing studies in the literature devoted efforts to examine the driver injury severity in left-turn crashes. To fill this research gap, this paper aims to provide a comprehensive study of the contributing factors of left-turn crashes and the corresponding injury severities.

METHODS

The hierarchical ordered probit (HOPIT) model is first applied to study driver injury severity in left-turn crashes. The HOPIT model can overcome the limitations of traditional ordered probit models since its thresholds are always positive and ordered. It is a function of unique explanatory parameters that do not necessarily affect the ordered probability outcomes directly. Considering the driving condition during the wintertime could be significantly different from other seasons, this study divided the overall crash dataset into "winter" and "other-season" subsets based on the temperature, snowing condition, and other factors.

RESULTS

With the "other-season" dataset, results demonstrated that contributing factors, such as young drivers, male drivers, clear, light, and ramp intersection with crossroad, are associated with a decrease in injury severity. On the contrary, factors like drug, alcohol, disregard traffic control device, high-speed limit, the protected left-turn signal, etc., are related to an increase in injury severity. In winter, results revealed that only nine contributing factors are significant to the left-turn crash. Alcohol, disregard traffic control device, nighttime, high-speed limit, head-on collision, and state road are associated with an increase in injury severity. Also, two-vehicle involved, snow, ramp intersection with crossroad are related to a decrease in injury severity.

CONCLUSIONS

The HOPIT model is applied to examine contributing factors of left-turn crashes and the corresponding injury severity, based on left-turn crash records from 2010 to 2017 in Utah. Eighteen significant factors of left-turn crash injury severity are identified in the overall dataset. In seasons rather than winter, the significant factors are almost the same as that of the entire year. In the winter, less significant factors and different patterns are found compared with the overall crashes.

A copula-based approach for jointly modeling crash severity and number of vehicles involved in express bus crashes on expressways considering temporal stability of data

The consequences of crashes, including injury, loss of lives, and damage to properties, are further worsened when buses plying expressways are involved in the crash. Previous studies have separately analyzed crash severity in terms of monetary cost, injuries and loss of lives, and the size of crashes in terms of the number of vehicles involved. However, as both outcome variables are correlated, it is imperative to perform a combined analysis using an appropriate econometric model to achieve a better model fit. This study contributes to the literature by jointly exploring the factors influencing the severity and size of express bus-involved crashes that occur on expressways and characterizes the dependence between both outcome variables by employing a more plausible copula regression framework. Likelihood ratio tests were also conducted to investigate the temporal stability of the factors that affect both crash severity and size. Based on the goodness-of-fit statistics, the Frank copula model proved superior to the independent ordered probit model. The estimate of the underlying dependence between the outcome variables provided a better comprehension of the correlation between them. Temporal instability was detected for the individual parameters in the models and is attributed to the changing driving behavior due to the heightened road safety campaigns. The results suggest that traffic exposure measures are significantly associated with a higher propensity of observing increased bus crash severity and size. Insights into the factors influencing the size and severity of express bus crashes are discussed, and appropriate engineering, enforcement, and education-related countermeasures are proposed.

A Bayesian spatial Poisson-lognormal model to examine pedestrian crash severity at signalized intersections

Reducing nonmotorized crashes requires a profound understanding of the causes and consequences of the crashes at the facility level. Generally, existing literature on bicyclists and pedestrian crash models suffers from two distinct problems: lack of exposure/volume data and inadequacy in capturing potential correlations across various crash aspects. To develop a robust framework for pedestrian crash analysis, this research employed a multivariate model across multiple pedestrian crash severities incorporating a crucial piece of information: pedestrian exposure. A multivariate spatial (conditional autoregressive) Poisson-lognormal model in a Bayesian framework was developed to examine the significant factors influencing the fatal, incapacitating injury (or suspected serious injury), and non-incapacitating injury pedestrian crashes at 409 signalized intersections in the Austin area. Various explanatory variables were used to examine the pedestrian crashes, including traffic characteristics, road geometry, built environment features, and pedestrian exposure volume at intersections, which was estimated through a direct demand model as part of the study. Model results revealed valuable insights. The superior performance of the multivariate model over the univariate model emphasized the need to jointly model multiple pedestrian crash severities. The results showed the significant positive influence of speed limit on fatal pedestrian crashes and revealed that both incapacitating and non-incapacitating injury crashes increase with increasing motorized traffic volume. Bus stop presence was found to have a negative influence on incapacitating injury crashes and a positive influence on non-incapacitating injury crashes. Moreover, the pedestrian volume at intersections positively influences non-incapacitating injury crashes. The difference in influence across crash types warrants careful and focused policy design of intersections to reduce pedestrian crashes of all severity types.

Endogenous commercial driver's traffic violations and freight truck-involved crashes on mainlines of expressway

Freight truck-involved crashes result in a high mortality rate and significantly impact logistic costs; therefore, many researchers have analyzed the causes of truck-involved traffic crashes. In the existing literature, it was found that truck-involved crashes are affected by factors such as road geometry, weather, driver and vehicle characteristics, and traffic volume based on a variety of statistical methodologies; however, the endogenous impact resulting from driver traffic violation has not been considered. The goal of the study is to discover the factors influencing freight vehicle crashes and develop more accurate crash probability estimation by explaining the endogenous driver traffic violations. To achieve the purpose of this study, we applied the two-stage residual inclusion (2SRI) approach, a methodology used in the nonlinear regression analysis model for capturing the endogeneity issue. This method improves the accuracy of the model by capturing the unobserved effects of driver traffic violations. From the results, traffic violations were identified to be influenced by the driver's physical condition, as well as driver and vehicle characteristics. Furthermore, variables of driver traffic violations such as improper passing, speeding, and safe distance violation were found to be endogenous in the probability model of freight truck crashes on expressway mainlines.