Evaluating alternate discrete choice frameworks for modeling ordinal discrete variables

There is considerable debate on the appropriate discrete choice framework for examining injury severity. Researchers in the safety field have employed ordered and unordered frameworks for examining the various factors influencing injury severity. The objective of the current study is to investigate the performance of the ordered and unordered response frameworks at a fundamental level. Towards this end, we undertake a comparison of the alternative frameworks by estimating ordered and unordered response models using data generated through ordered, unordered data and a combination of ordered and unordered data generation processes. We also examine the influence of aggregate sample shares on the appropriateness of the modeling framework. Rather than be limited by the aggregate sample shares in an empirical dataset, simulation allows us to explore the influence of a broad spectrum of sample shares on the performance of ordered and unordered frameworks. We also extend the data generation process based analysis to under reported data and compare the performance of the ordered and unordered response frameworks. Finally, based on these simulation exercises, we provide a discussion of the merits of the different approaches. The results clearly highlight the emergence of the generalized ordered logit model as a true equivalent ordered response model to the multinomial logit model for ordinal discrete variables.     

Analysis of injury severity of large truck crashes in work zones

Work zones are critical parts of the transportation infrastructure renewal process consisting of rehabilitation of roadways, maintenance, and utility work. Given the specific nature of a work zone (complex arrangements of traffic control devices and signs, narrow lanes, duration) a number of crashes occur with varying severities involving different vehicle sizes. In this paper we attempt to investigate the causal factors contributing to injury severity of large truck crashes in work zones. Considering the discrete nature of injury severity categories, a number of comparable econometric models were developed including multinomial logit (MNL), nested logit (NL), ordered logit (ORL), and generalized ordered logit (GORL) models. The MNL and NL models belong to the class of unordered discrete choice models and do not recognize the intrinsic ordinal nature of the injury severity data. The ORL and GORL models, on the other hand, belong to the ordered response framework that was specifically developed for handling ordinal dependent variables. Past literature did not find conclusive evidence in support of either framework. This study compared these alternate modeling frameworks for analyzing injury severity of crashes involving large trucks in work zones. The model estimation was undertaken by compiling a database of crashes that (1) involved large trucks and (2) occurred in work zones in the past 10 years in Minnesota. Empirical findings indicate that the GORL model provided superior data fit as compared to all the other models. Also, elasticity analysis was undertaken to quantify the magnitude of impact of different factors on work zone safety and the results of this analysis suggest the factors that increase the risk propensity of sustaining severe crashes in a work zone include crashes in the daytime, no control of access, higher speed limits, and crashes occurring on rural principal arterials.     

A hybrid finite mixture model for exploring heterogeneous ordering patterns of driver injury severity

Debates on the ordering patterns of crash injury severity are ongoing in the literature. Models without proper econometrical structures for accommodating the complex ordering patterns of injury severity could result in biased estimations and misinterpretations of factors. This study proposes a hybrid finite mixture (HFM) model aiming to capture heterogeneous ordering patterns of driver injury severity while enhancing modeling flexibility. It attempts to probabilistically partition samples into two groups in which one group represents an unordered/nominal data-generating process while the other represents an ordered data-generating process. Conceptually, the newly developed model offers flexible coefficient settings for mining additional information from crash data, and more importantly it allows the coexistence of multiple ordering patterns for the dependent variable. A thorough modeling performance comparison is conducted between the HFM model, and the multinomial logit (MNL), ordered logit (OL), finite mixture multinomial logit (FMMNL) and finite mixture ordered logit (FMOL) models. According to the empirical results, the HFM model presents a strong ability to extract information from the data, and more importantly to uncover heterogeneous ordering relationships between factors and driver injury severity. In addition, the estimated weight parameter associated with the MNL component in the HFM model is greater than the one associated with the OL component, which indicates a larger likelihood of the unordered pattern than the ordered pattern for driver injury severity.     

Analysis of driver injury severity in wrong-way driving crashes on controlled-access highways

For more than five decades, wrong-way driving (WWD) has been notorious as a traffic safety issue for controlled-access highways. Numerous studies and efforts have tried to identify factors that contribute to WWD occurrences at these sites in order to delineate between WWD and non-WWD crashes. However, none of the studies investigate the effect of various confounding variables on the injury severity being sustained by the at-fault drivers in a WWD crash. This study tries to fill this gap in the existing literature by considering possible variables and taking into account the ordinal nature of injury severity using three different ordered-response models: ordered logit or proportional odds (PO), generalized ordered logit (GOL), and partial proportional odds (PPO) model. The findings of this study reveal that a set of variables, including driver’s age, condition (i.e., intoxication), seatbelt use, time of day, airbag deployment, type of setting, surface condition, lighting condition, and type of crash, has a significant effect on the severity of a WWD crash. Additionally, a comparison was made between the three proposed methods. The results corroborate that the PPO model outperforms the other two models in terms of modeling injury severity using our database. Based on the findings, several countermeasures at the engineering, education, and enforcement levels are recommended.     

Examining driver injury severity outcomes in rural non-interstate roadway crashes using a hierarchical ordered logit model

Rural non-interstate crashes induce a significant amount of severe injuries and fatalities. Examination of such injury patterns and the associated contributing factors is of practical importance. Taking into account the ordinal nature of injury severity levels and the hierarchical feature of crash data, this study employs a hierarchical ordered logit model to examine the significant factors in predicting driver injury severities in rural non-interstate crashes based on two-year New Mexico crash records. Bayesian inference is utilized in model estimation procedure and 95% Bayesian Credible Interval (BCI) is applied to testing variable significance. An ordinary ordered logit model omitting the between-crash variance effect is evaluated as well for model performance comparison. Results indicate that the model employed in this study outperforms ordinary ordered logit model in model fit and parameter estimation. Variables regarding crash features, environment conditions, and driver and vehicle characteristics are found to have significant influence on the predictions of driver injury severities in rural non-interstate crashes. Factors such as road segments far from intersection, wet road surface condition, collision with animals, heavy vehicle drivers, male drivers and driver seatbelt used tend to induce less severe driver injury outcomes than the factors such as multiple-vehicle crashes, severe vehicle damage in a crash, motorcyclists, females, senior drivers, driver with alcohol or drug impairment, and other major collision types. Research limitations regarding crash data and model assumptions are also discussed. Overall, this research provides reasonable results and insight in developing effective road safety measures for crash injury severity reduction and prevention.     

Analysis of crash severities using nested logit model—Accounting for the underreporting of crashes

Recent studies in the area of highway safety have demonstrated the usefulness of logit models for modeling crash injury severities. Use of these models enables one to identify and quantify the effects of factors that contribute to certain levels of severity. Most often, these models are estimated assuming equal probability of the occurrence for each injury severity level in the data. However, traffic crash data are generally characterized by underreporting, especially when crashes result in lower injury severity. Thus, the sample used for an analysis is often outcome-based, which can result in a biased estimation of model parameters. This is more of a problem when a nested logit model specification is used instead of a multinomial logit model and when true shares of the outcomes-injury severity levels in the population are not known (which is almost always the case). This study demonstrates an application of a recently proposed weighted conditional maximum likelihood estimator in tackling the problem of underreporting of crashes when using a nested logit model for crash severity analyses.     

Analysis of driver injury severity in single-vehicle crashes on rural and urban roadways

This study analyzes driver injury severities for single-vehicle crashes occurring in rural and urban areas using data collected in New Mexico from 2010 to 2011. Nested logit models and mixed logit models are developed in order to account for the correlation between severity categories (No injury, Possible injury, Visible injury, Incapacitating injury and fatality) and individual heterogeneity among drivers. Various factors, such as crash and environment characteristics, geometric features, and driver behavior are examined in this study. Nested logit model and mixed logit model reveal similar results in terms of identifying contributing factors for driver injury severities. In the analysis of urban crashes, only the nested logit model is presented since no random parameter is found in the mixed logit model. The results indicate that significant differences exist between factors contributing to driver injury severity in single-vehicle crashes in rural and urban areas. There are 5 variables found only significant in the rural model and six significant variables identified only in the urban crash model. These findings can help transportation agencies develop effective policies or appropriate strategies to reduce injury severity resulting from single-vehicle crashes.     

Analysis of driver injury severity in rural single-vehicle crashes

Rural roads carry less than fifty percent of the traffic in the United States. However, more than half of the traffic accident fatalities occurred on rural roads. This research focuses on analyzing injury severities involving single-vehicle crashes on rural roads, utilizing a latent class logit (LCL) model. Similar to multinomial logit (MNL) models, the LCL model has the advantage of not restricting the coefficients of each explanatory variable in different severity functions to be the same, making it possible to identify the impacts of the same explanatory variable on different injury outcomes. In addition, its unique model structure allows the LCL model to better address issues pertinent to the independence from irrelevant alternatives (IIA) property. A MNL model is also included as the benchmark simply because of its popularity in injury severity modeling. The model fitting results of the MNL and LCL models are presented and discussed. Key injury severity impact factors are identified for rural single-vehicle crashes. Also, a comparison of the model fitting, analysis marginal effects, and prediction performance of the MNL and LCL models are conducted, suggesting that the LCL model may be another viable modeling alternative for crash-severity analysis.     

Analysis of factors associated with injury severity in crashes involving young New Zealand drivers

Young people are a risk to themselves and other road users, as motor vehicle crashes are the leading cause of their death. A thorough understanding of the most important factors associated with injury severity in crashes involving young drivers is important for designing well-targeted restrictive measures within youth-oriented road safety programs. The current study estimates discrete choice models of injury severity of crashes involving young drivers conditional on these crashes having occurred. The analysis examined a comprehensive set of single-vehicle and two-vehicle crashes involving at least one 15–24 year-old driver in New Zealand between 2002 and 2011 that resulted in minor, serious or fatal injuries. A mixed logit model accounting for heterogeneity and heteroscedasticity in the propensity to injury severity outcomes and for correlation between serious and fatal injuries proved a better fit than a binary and a generalized ordered logit. Results show that the young drivers’ behavior, the presence of passengers and the involvement of vulnerable road users were the most relevant factors associated with higher injury severity in both single-vehicle and two-vehicle crashes. Seatbelt non-use, inexperience and alcohol use were the deadliest behavioral factors in single-vehicle crashes, while fatigue, reckless driving and seatbelt non-use were the deadliest factors in two-vehicle crashes. The presence of passengers in the young drivers’ vehicle, and in particular a combination of males and females, dramatically increased the probability of serious and fatal injuries. The involvement of vulnerable road users, in particular on rural highways and open roads, considerably amplified the probability of higher crash injury severity.     

Built environment effects on cyclist injury severity in automobile-involved bicycle crashes

This analysis uses a generalized ordered logit model and a generalized additive model to estimate the effects of built environment factors on cyclist injury severity in automobile-involved bicycle crashes, as well as to accommodate possible spatial dependence among crash locations. The sample is drawn from the Seattle Department of Transportation bicycle collision profiles. This study classifies the cyclist injury types as property damage only, possible injury, evident injury, and severe injury or fatality. Our modeling outcomes show that: (1) injury severity is negatively associated with employment density; (2) severe injury or fatality is negatively associated with land use mixture; (3) lower likelihood of injuries is observed for bicyclists wearing reflective clothing; (4) improving street lighting can decrease the likelihood of cyclist injuries; (5) posted speed limit is positively associated with the probability of evident injury and severe injury or fatality; (6) older cyclists appear to be more vulnerable to severe injury or fatality; and (7) cyclists are more likely to be severely injured when large vehicles are involved in crashes. One implication drawn from this study is that cities should increase land use mixture and development density, optimally lower posted speed limits on streets with both bikes and motor vehicles, and improve street lighting to promote bicycle safety. In addition, cyclists should be encouraged to wear reflective clothing.     

Partial proportional odds model—An alternate choice for analyzing pedestrian crash injury severities

The conventional methods for crash injury severity analyses include either treating the severity data as ordered (e.g. ordered logit/probit models) or non-ordered (e.g. multinomial models). The ordered models require the data to meet proportional odds assumption, according to which the predictors can only have the same effect on different levels of the dependent variable, which is often not the case with crash injury severities. On the other hand, non-ordered analyses completely ignore the inherent hierarchical nature of crash injury severities. Therefore, treating the crash severity data as either ordered or non-ordered results in violating some of the key principles. To address these concerns, this paper explores the application of a partial proportional odds (PPO) model to bridge the gap between ordered and non-ordered severity modeling frameworks. The PPO model allows the covariates that meet the proportional odds assumption to affect different crash severity levels with the same magnitude; whereas the covariates that do not meet the proportional odds assumption can have different effects on different severity levels. This study is based on a five-year (2008–2012) national pedestrian safety dataset for Switzerland. A comparison between the application of PPO models, ordered logit models, and multinomial logit models for pedestrian injury severity evaluation is also included here. The study shows that PPO models outperform the other models considered based on different evaluation criteria. Hence, it is a viable method for analyzing pedestrian crash injury severities.     

A multinomial logit model-Bayesian network hybrid approach for driver injury severity analyses in rear-end crashes

Rear-end crash is one of the most common types of traffic crashes in the U.S. A good understanding of its characteristics and contributing factors is of practical importance. Previously, both multinomial Logit models and Bayesian network methods have been used in crash modeling and analysis, respectively, although each of them has its own application restrictions and limitations. In this study, a hybrid approach is developed to combine multinomial logit models and Bayesian network methods for comprehensively analyzing driver injury severities in rear-end crashes based on state-wide crash data collected in New Mexico from 2010 to 2011. A multinomial logit model is developed to investigate and identify significant contributing factors for rear-end crash driver injury severities classified into three categories: no injury, injury, and fatality. Then, the identified significant factors are utilized to establish a Bayesian network to explicitly formulate statistical associations between injury severity outcomes and explanatory attributes, including driver behavior, demographic features, vehicle factors, geometric and environmental characteristics, etc. The test results demonstrate that the proposed hybrid approach performs reasonably well. The Bayesian network reference analyses indicate that the factors including truck-involvement, inferior lighting conditions, windy weather conditions, the number of vehicles involved, etc. could significantly increase driver injury severities in rear-end crashes. The developed methodology and estimation results provide insights for developing effective countermeasures to reduce rear-end crash injury severities and improve traffic system safety performance.     

Examining driver injury severity in two vehicle crashes – A copula based approach

A most commonly identified exogenous factor that significantly affects traffic crash injury severity sustained is the collision type variable. Most studies consider collision type only as an explanatory variable in modeling injury. However, it is possible that each collision type has a fundamentally distinct effect on injury severity sustained in the crash. In this paper, we examine the hypothesis that collision type fundamentally alters the injury severity pattern under consideration. Toward this end, we propose a joint modeling framework to study collision type and injury severity sustained as two dimensions of the severity process. We employ a copula based joint framework that ties the collision type (represented as a multinomial logit model) and injury severity (represented as an ordered logit model) through a closed form flexible dependency structure to study the injury severity process. The proposed approach also accommodates the potential heterogeneity (across drivers) in the dependency structure. Further, the study incorporates collision type as a vehicle-level, as opposed to a crash-level variable as hitherto assumed in earlier research, while also examining the impact of a comprehensive set of exogenous factors on driver injury severity. The proposed modeling system is estimated using collision data from the province of Victoria, Australia for the years 2006 through 2010.     

Age and pedestrian injury severity in motor-vehicle crashes: a heteroskedastic logit analysis

This research explores the injury severity of pedestrians in motor-vehicle crashes. It is hypothesized that the variance of unobserved pedestrian characteristics increases with age. In response, a heteroskedastic generalized extreme value model is used. The analysis links explanatory factors with four injury outcomes: fatal, incapacitating, non-incapacitating, and possible or no injury. Police-reported crash data between 1997 and 2000 from North Carolina, USA, are used. The results show that pedestrian age induces heteroskedasticity which affects the probability of fatal injury. The effect grows more pronounced with increasing age past 65. The heteroskedastic model provides a better fit than the multinomial logit model. Notable factors increasing the probability of fatal pedestrian injury: increasing pedestrian age, male driver, intoxicated driver (2.7 times greater probability of fatality), traffic sign, commercial area, darkness with or without streetlights (2-4 times greater probability of fatality), sport-utility vehicle, truck, freeway, two-way divided roadway, speeding-involved, off roadway, motorist turning or backing, both driver and pedestrian at fault, and pedestrian only at fault. Conversely, the probability of a fatal injury decreased: with increasing driver age, during the PM traffic peak, with traffic signal control, in inclement weather, on a curved roadway, at a crosswalk, and when walking along roadway.     

Severity of motorcycle crashes in Calgary

Motorcycle riders would be more vulnerable in the event of a crash because of their lack of protection which would often result in them suffering more severe injuries than car drivers. This paper estimated three crash severity models to identify factors that contributed to increasing the severity of motorcycle involved crashes in the Canadian City of Calgary. We found that results from the ordered logit model, heterogeneous choice model and partially constrained generalized ordered logit model produced estimates that were very similar which attested to their robustness. Injury severity tended to increase in neighborhoods with loops and lollipops types of streets or involved right-angle and left-turn-across-path crashes, a truck, unsafe speed or alcohol use but tended to decrease if the crash occurred in parking lots or during winter, involved a van or male rider, or a rider following-too-closely to the vehicle in front.     

Analysis of injury severity of drivers involved in single- and two-vehicle crashes on highways in Ontario

This study analyzes driver's injury severity in single- and two-vehicle crashes and compares the effects of explanatory variables among various types of crashes. The study identified factors affecting injury severity and their effects on severity levels using 5-year crash records for provincial highways in Ontario, Canada. Considering heteroscedasticity in the effects of explanatory variables on injury severity, the heteroscedastic ordered logit (HOL) models were developed for single- and two-vehicle crashes separately. The results of the models show that there exists heteroscedasticity for young drivers (≤30), safety equipment and ejection in the single-vehicle crash model, and female drivers, safety equipment and head-on collision in the two-vehicle crash models. The results also show that young car drivers have opposite effects between single-car and car–car crashes, and sideswipe crashes have opposite effects between car–car and truck–truck crashes. The study demonstrates that separate HOL models for single-vehicle and different types of two-vehicle crashes can identify differential effects of factors on driver's injury severity.     

A latent class modeling approach for identifying vehicle driver injury severity factors at highway-railway crossings

In this paper, we aim to identify the different factors that influence injury severity of highway vehicle occupants, in particular drivers, involved in a vehicle-train collision at highway-railway grade crossings. The commonly used approach to modeling vehicle occupant injury severity is the traditional ordered response model that assumes the effect of various exogenous factors on injury severity to be constant across all accidents. The current research effort attempts to address this issue by applying an innovative latent segmentation based ordered logit model to evaluate the effects of various factors on the injury severity of vehicle drivers. In this model, the highway-railway crossings are assigned probabilistically to different segments based on their attributes with a separate injury severity component for each segment. The validity and strength of the formulated collision consequence model is tested using the US Federal Railroad Administration database which includes inventory data of all the railroad crossings in the US and collision data at these highway railway crossings from 1997 to 2006. The model estimation results clearly highlight the existence of risk segmentation within the affected grade crossing population by the presence of active warning devices, presence of permanent structure near the crossing and roadway type. The key factors influencing injury severity include driver age, time of the accident, presence of snow and/or rain, vehicle role in the crash and motorist action prior to the crash.     

Heterogeneous impacts of gender-interpreted contributing factors on driver injury severities in single-vehicle rollover crashes

In this study, a mixed logit model is developed to identify the heterogeneous impacts of gender-interpreted contributing factors on driver injury severities in single-vehicle rollover crashes. The random parameter of the variables in the mixed logit model, the heterogeneous mean, is elaborated by driver gender-based linear regression models. The model is estimated using crash data in New Mexico from 2010 to 2012. The percentage changes of factors’ predicted probabilities are calculated in order to better understand the model specifications. Female drivers are found more likely to experience severe or fatal injuries in rollover crashes than male drivers. However, the probability of male drivers being severely injured is higher than female drivers when the road surface is unpaved. Two other factors with fixed parameters are also found to significantly increase driver injury severities, including Wet and Alcohol Influenced. This study provides a better understanding of contributing factors influencing driver injury severities in rollover crashes as well as their heterogeneous impacts in terms of driver gender. Those results are also helpful to develop appropriate countermeasures and policies to reduce driver injury severities in single-vehicle rollover crashes.     

Investigating driver injury severity patterns in rollover crashes using support vector machine models

Rollover crash is one of the major types of traffic crashes that induce fatal injuries. It is important to investigate the factors that affect rollover crashes and their influence on driver injury severity outcomes. This study employs support vector machine (SVM) models to investigate driver injury severity patterns in rollover crashes based on two-year crash data gathered in New Mexico. The impacts of various explanatory variables are examined in terms of crash and environmental information, vehicle features, and driver demographics and behavior characteristics. A classification and regression tree (CART) model is utilized to identify significant variables and SVM models with polynomial and Gaussian radius basis function (RBF) kernels are used for model performance evaluation. It is shown that the SVM models produce reasonable prediction performance and the polynomial kernel outperforms the Gaussian RBF kernel. Variable impact analysis reveals that factors including comfortable driving environment conditions, driver alcohol or drug involvement, seatbelt use, number of travel lanes, driver demographic features, maximum vehicle damages in crashes, crash time, and crash location are significantly associated with driver incapacitating injuries and fatalities. These findings provide insights for better understanding rollover crash causes and the impacts of various explanatory factors on driver injury severity patterns.     

Mixed logit model-based driver injury severity investigations in single- and multi-vehicle crashes on rural two-lane highways

Crashes occurring on rural two-lane highways are more likely to result in severe driver incapacitating injuries and fatalities. In this study, mixed logit models are developed to analyze driver injury severities in single-vehicle (SV) and multi-vehicle (MV) crashes on rural two-lane highways in New Mexico from 2010 to 2011. A series of significant contributing factors in terms of driver behavior, weather conditions, environmental characteristics, roadway geometric features and traffic compositions, are identified and their impacts on injury severities are quantified for these two types of crashes, respectively. Elasticity analyses and transferability tests were conducted to better understand the models’ specification and generality. The research findings indicate that there are significant differences in causal attributes determining driver injury severities between SV and MV crashes. For example, more severe driver injuries and fatalities can be observed in MV crashes when motorcycles or trucks are involved. Dark lighting conditions and dusty weather conditions are found to significantly increase MV crash injury severities. However, SV crashes demonstrate different characteristics influencing driver injury severities. For example, the probability of having severe injury outcomes is higher when vans are identified in SV crashes. Drivers’ overtaking actions will significantly increase SV crash injury severities. Although some common attributes, such as alcohol impaired driving, are significant in both SV and MV crash severity models, their effects on different injury outcomes vary substantially. This study provides a better understanding of similarities and differences in significant contributing factors and their impacts on driver injury severities between SV and MV crashes on rural two-lane highways. It is also helpful to develop cost-effective solutions or appropriate injury prevention strategies for rural SV and MV crashes.