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 mixed logit analysis of two-vehicle crash severities involving a motorcycle

Using motorcycle crash data for Iowa from 2001 to 2008, this paper estimates a mixed logit model to investigate the factors that affect crash severity outcomes in a collision between a motorcycle and another vehicle. These include crash-specific factors (such as manner of collision, motorcycle rider and non-motorcycle driver and vehicle actions), roadway and environmental conditions, location and time, motorcycle rider and non-motorcycle driver and vehicle attributes. The methodological approach allows the parameters to vary across observations as opposed to a single parameter representing all observations. Our results showed non-uniform effects of rear-end collisions on minor injury crashes, as well as of the roadway speed limit greater or equal to 55 mph, the type of area (urban), the riding season (summer) and motorcyclist's gender on low severity crashes. We also found significant effects of the roadway surface condition, clear vision (not obscured by moving vehicles, trees, buildings, or other), light conditions, speed limit, and helmet use on severe injury outcomes.     

An empirical analysis of farm vehicle crash injury severities on Iowa's public road system

Farm vehicle crashes are a major safety concern for farmers as well as all other users of the public road system in agricultural states. Using data on farm vehicle crashes that occurred on Iowa's public roads between 2004 and 2006, we estimate a multinomial logit model to identify crash-, farm vehicle-, and driver-specific factors that determine farm vehicle crash injury severity outcomes. Estimation findings indicate that there are crash patterns (rear-end manner of collision; single-vehicle crash; farm vehicle crossed the centerline or median) and conditions (obstructed vision and crash in rural area; dry road, dark lighting, speed limit 55 mph or higher, and harvesting season), as well as farm vehicle and driver-contributing characteristics (old farm vehicle, young farm vehicle driver), where targeted intervention can help reduce the severity of crash outcomes. Determining these contributing factors and their effect is the first step to identifying countermeasures and safety strategies in a bid to improve transportation safety for all users on the public road system in Iowa as well as other agricultural states.     

Modeling rear-end collisions including the role of driver's visibility and light truck vehicles using a nested logit structure

This paper presents an analysis of the effect of the geometric incompatibility of light truck vehicles (LTV)--light-duty trucks, vans, and sport utility vehicles--on drivers' visibility of other passenger cars involved in rear-end collisions. The geometric incompatibility arises from the fact that most LTVs ride higher and are wider than regular passenger cars. The objective of this paper is to explore the effect of the lead vehicle's size on the rear-end crash configuration. Four rear-end crash configurations are defined based on the type of the two involved vehicles (lead and following vehicles). Nested logit models were calibrated to estimate the probabilities of the four rear-end crash configurations as a function of driver's age, gender, vehicle type, vehicle maneuver, light conditions, driver's visibility and speed. Results showed that driver's visibility and inattention in the following (striker) vehicle have the largest effect on being involved in a rear-end collision of configuration CarTrk (a regular passenger car striking an LTV). Possibly, indicating a sight distance problem. A driver of a smaller car following an LTV, have a problem seeing the roadway beyond the LTV, and therefore would not be able to adjust his/her speed accordingly, increasing the probability of a rear-end collision. Also, the probability of a CarTrk rear-end crash increases in the case that the lead vehicle stops suddenly.     

Highway accident severities and the mixed logit model: an exploratory empirical analysis

Many transportation agencies use accident frequencies, and statistical models of accidents frequencies, as a basis for prioritizing highway safety improvements. However, the use of accident severities in safety programming has been often been limited to the locational assessment of accident fatalities, with little or no emphasis being placed on the full severity distribution of accidents (property damage only, possible injury, injury)-which is needed to fully assess the benefits of competing safety-improvement projects. In this paper we demonstrate a modeling approach that can be used to better understand the injury-severity distributions of accidents on highway segments, and the effect that traffic, highway and weather characteristics have on these distributions. The approach we use allows for the possibility that estimated model parameters can vary randomly across roadway segments to account for unobserved effects potentially relating to roadway characteristics, environmental factors, and driver behavior. Using highway-injury data from Washington State, a mixed (random parameters) logit model is estimated. Estimation findings indicate that volume-related variables such as average daily traffic per lane, average daily truck traffic, truck percentage, interchanges per mile and weather effects such as snowfall are best modeled as random-parameters-while roadway characteristics such as the number of horizontal curves, number of grade breaks per mile and pavement friction are best modeled as fixed parameters. Our results show that the mixed logit model has considerable promise as a methodological tool in highway safety programming.     

Estimation with the nested logit model: specifications and software particularities

The paper discusses the nested logit model for choices between a set of mutually exclusive alternatives (e.g. brand choice, strategy decisions, modes of transportation, etc.). Due to the ability of the nested logit model to allow and account for similarities between pairs of alternatives, the model has become very popular for the empirical analysis of choice decisions. However the fact that there are two different specifications of the nested logit model (with different outcomes) has not received adequate attention. The utility maximization nested logit (UMNL) model and the non-normalized nested logit (NNNL) model have different properties, influencing the estimation results in a different manner. This paper introduces distinct specifications of the nested logit model and indicates particularities arising from model estimation. The effects of using various software packages on the estimation results of a nested logit model are shown using simulated data sets for an artificial decision situation. Financial support by the German Research Foundation (DFG) through the research project #BO1952/1 and the SFB 649 “Economic Risk” is gratefully acknowledged. The authors would like to thank two anonymous reviewers for their helpful and constructive comments.     

Rainfall effect on single-vehicle crash severities using polychotomous response models

As part of the Wisconsin road weather safety initiative, the objective of this study is to assess the effects of rainfall on the severity of single-vehicle crashes on Wisconsin interstate highways utilizing polychotomous response models.Weather-related factors considered in this study include estimated rainfall intensity for 15 min prior to a crash occurrence, water film depth, temperature, wind speed/direction, stopping sight distance and deficiency of car-following distance at the crash moment. For locations with unknown weather information, data were interpolated using the inverse squared distance method. Non-weather factors such as road geometrics, traffic conditions, collision types, vehicle types, and driver and temporal attributes were also considered. Two types of polychotomous response models were compared: ordinal logistic and sequential logistic regressions. The sequential logistic regression was tested with forward and backward formats. Comparative models were also developed for single vehicle crash severity during clear weather.In conclusion, the backward sequential logistic regression model produced the best results for predicting crash severities in rainy weather where rainfall intensity, wind speed, roadway terrain, driver's gender, and safety belt were found to be statistically significant. Our study also found that the seasonal factor was significant in clear weather. The seasonal factor is a predictor suggesting that inclement weather may affect crash severity. These findings can be used to determine the probabilities of single vehicle crash severity in rainy weather and provide quantitative support on improving road weather safety via weather warning systems, highway facility improvements, and speed limit management.     

Detecting unforgiving roadside contributors through the severity analysis of ran-off-road crashes

The objective of this paper is to study the contributors influencing ran-off-road (ROR) crash severities in a setting that has not been analysed in the literature, namely on freeways not designed according to the “forgiving roadside” concept. To accomplish the analysis, ROR crash data were collected on freeway road sections in Portugal and multinomial and mixed logit models were estimated using the driver injury and the most severely injured occupant as outcome variables. Our results are in line with previous findings reported in the literature on ROR crash severity in a number of distinct settings. Most importantly, this study shows the contribution of critical slopes and vehicle rollover towards fatal injuries and highlights the importance of introducing the “forgiving roadside” concept to mitigate ROR crash severity in Portuguese freeways. The study also indicates the importance of protecting errant vehicles particularly in horizontal curves, as these are linked with fatalities. Finally, the empirical findings from the developed models revealed problems in current Portuguese roadside design, especially with regards to criteria for forgiving slopes provision and warrants for safety barrier installation.     

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.     

Mixed logit analysis of bicyclist injury severity resulting from motor vehicle crashes at intersection and non-intersection locations

Standard multinomial logit (MNL) and mixed logit (MXL) models are developed to estimate the degree of influence that bicyclist, driver, motor vehicle, geometric, environmental, and crash type characteristics have on bicyclist injury severity, classified as property damage only, possible, nonincapacitating or severe (i.e., incapacitating or fatal) injury. This study is based on 10,029 bicycleinvolved crashes that occurred in the State of Ohio from 2002 to 2008. Results of likelihood ratio tests reveal that some of the factors affecting bicyclist injury severity at intersection and non-intersection locations are substantively different and using a common model to jointly estimate impacts on severity at both types of locations may result in biased or inconsistent estimates. Consequently, separate models are developed to independently assess the impacts of various factors on the degree of bicyclist injury severity resulting from crashes at intersection and non-intersection locations.Several covariates are found to have similar impacts on injury severity at both intersection and non-intersection locations. Conversely, six variables were found to significantly influence injury severity at intersection locations but not non-intersection locations while four variables influenced bicyclist injury severity only at non-intersection locations. In crashes occurring at intersection locations, the likelihood of severe bicyclist injury increases by 14.8 percent if the bicyclist is not wearing a helmet, 82.2 percent if the motorist is under the influence of alcohol, 141.3 percent if the crash-involved motor vehicle is a van, 40.6 percent if the motor vehicle strikes the side of the bicycle, and 182.6 percent if the crash occurs on a horizontal curve with a grade. Results from non-intersection locations show the likelihood of severe injuries increases by 374.5 percent if the bicyclist is under the influence of drugs, 150.1 percent if the motorist is under the influence of alcohol, 53.5 percent if the motor vehicle strikes the side of the bicycle and 99.9 percent if the crash-involved motor vehicle is a heavy-duty truck.     

A multinomial logit analysis of risk factors influencing road traffic injury severities in the Erzurum and Kars Provinces of Turkey

A retrospective cross-sectional study is conducted analysing 11,771 traffic accidents reported by the police between January 2008 and December 2013 which are classified into three injury severity categories: fatal, injury, and no injury. Based on this classification, a multinomial logit analysis is performed to determine the risk factors affecting the severity of traffic injuries. The estimation results reveal that the following factors increase the probability of fatal injuries: drivers over the age of 65; primary-educated drivers; single-vehicle accidents; accidents occurring on state routes, highways or provincial roads; and the presence of pedestrian crosswalks. The results also indicate that accidents involving cars or private vehicles or those occurring during the evening peak, under clear weather conditions, on local city streets or in the presence of traffic lights decrease the probability of fatal injuries. This study comprises the most comprehensive database ever created for a Turkish sample. This study is also the first attempt to use an unordered response model to determine risk factors influencing the severity of traffic injuries in Turkey.     

Analysis of large truck crash severity using heteroskedastic ordered probit models

Long-combination vehicles (LCVs) have significant potential to increase economic productivity for shippers and carriers by decreasing the number of truck trips, thus reducing costs. However, size and weight regulations, triggered by safety concerns and, in some cases, infrastructure investment concerns, have prevented large-scale adoption of such vehicles. Information on actual crash performance is needed. To this end, this work uses standard and heteroskedastic ordered probit models, along with the United States’ Large Truck Crash Causation Study, General Estimates System, and Vehicle Inventory and Use Survey data sets, to study the impact of vehicle, occupant, driver, and environmental characteristics on injury outcomes for those involved in crashes with heavy-duty trucks. Results suggest that the likelihood of fatalities and severe injury is estimated to rise with the number of trailers, but fall with the truck length and gross vehicle weight rating (GVWR). While findings suggest that fatality likelihood for two-trailer LCVs is higher than that of single-trailer non-LCVs and other trucks, controlling for exposure risk suggest that total crash costs of LCVs are lower (per vehicle-mile traveled) than those of other trucks.     

Analysis of left-turn crash injury severity by conflicting pattern using partial proportional odds models

The purpose of this study is to examine left-turn crash injury severity. Left-turning traffic colliding with opposing through traffic and with near-side through traffic are the two most frequently occurring conflicting patterns among left-turn crashes (Patterns 5 and 8 in the paper, respectively), and they are prone to be severe. Ordered probability models with either logit or probit function is commonly applied in crash injury severity analyses; however, its critical assumption that the slope coefficients do not vary over different alternatives except the cut-off points is usually too restrictive. Partial proportional odds models are generalizations of ordered probability models, for which some of the beta coefficients can differ across alternatives, were applied to investigate Patterns 5 and 8, and the total left-turn crash injuries. The results show that partial proportional odds models consistently perform better than ordered probability models. By focusing on specific conflicting patterns, locating crashes to the exact crash sites and relating approach variables to crash injury in the analysis, researchers are able to investigate how these variables affect left-turn crash injuries. For example, opposing through traffic and near-side crossing through traffic in the hour of collision were identified significant for Patterns 5 and 8 crash injuries, respectively. Protected left-turn phasing is significantly correlated with Pattern 5 crash injury. Many other variables in driver attributes, vehicular characteristics, roadway geometry design, environmental factors, and crash characteristics were identified. Specifically, the use of the partial proportional formulation allows a much better identification of the increasing effect of alcohol and/or drug use on crash injury severity, which previously was masked using the conventional ordered probability models.     

A stable and optimized neural network model for crash injury severity prediction

The study proposes a convex combination (CC) algorithm to fast and stably train a neural network (NN) model for crash injury severity prediction, and a modified NN pruning for function approximation (N2PFA) algorithm to optimize the network structure. To demonstrate the proposed approaches and to compare them with the NN trained by traditional back-propagation (BP) algorithm and an ordered logit (OL) model, a two-vehicle crash dataset in 2006 provided by the Florida Department of Highway Safety and Motor Vehicles (DHSMV) was employed. According to the results, the CC algorithm outperforms the BP algorithm both in convergence ability and training speed. Compared with a fully connected NN, the optimized NN contains much less network nodes and achieves comparable classification accuracy. Both of them have better fitting and predicting performance than the OL model, which again demonstrates the NN’s superiority over statistical models for predicting crash injury severity. The pruned input nodes also justify the ability of the structure optimization method for identifying the factors irrelevant to crash-injury outcomes. A sensitivity analysis of the optimized NN is further conducted to determine the explanatory variables’ impact on each injury severity outcome. While most of the results conform to the coefficient estimation in the OL model and previous studies, some variables are found to have non-linear relationships with injury severity, which further verifies the strength of the proposed method.     

Statistical implications of using moving violations to determine crash responsibility in young driver crashes

Traditional methods for determining crash responsibility – most commonly moving violation citations – may not accurately characterize at-fault status among crash-involved drivers given that: (1) issuance may vary by factors that are independent of fault (e.g., driver age, gender), and (2) these methods do not capture driver behaviors that are not illegal but still indicative of fault. We examined the statistical implications of using moving violations to determine crash responsibility in young driver crashes by comparing it with a method based on crash-contributing driver actions. We selected all drivers in police-reported passenger-vehicle crashes (2010–2011) that involved a New Jersey driver <21 years old (79,485 drivers < age 21, 61,355 drivers ≥ age 21). For each driver, crash responsibility was determined from the crash report using two alternative methods: (1) issuance of a moving violation citation; and (2) presence of a driver action (e.g., failure to yield, inattention). Overall, 18% of crash-involved drivers were issued a moving violation while 50% had a driver action. Only 32.2% of drivers with a driver action were cited for a moving violation. Further, the likelihood of being cited given the presence of a driver action was higher among certain driver subgroups—younger drivers, male drivers, and drivers in single-vehicle and more severe crashes. Specifically among young drivers, those driving at night, carrying peer passengers, and having a suspended or no license were more often cited. Conversely, fatally-injured drivers were almost never cited. We also demonstrated that using citation data may lead to statistical bias in the characterization of at-fault drivers and of quasi-induced exposure measures. Studies seeking to accurately determine crash responsibility should thoughtfully consider the potential sources of bias that may result from using legal culpability methods. For many studies, determining driver responsibility via the identification of driver actions may yield more accurate characterizations of at-fault drivers.     

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.     

Relating crash frequency and severity: Evaluating the effectiveness of shoulder rumble strips on reducing fatal and major injury crashes

To approach the goal of “Toward Zero Deaths,” there is a need to develop an analysis paradigm to better understand the effects of a countermeasure on reducing the number of severe crashes. One of the goals in traffic safety research is to search for an effective treatment to reduce fatal and major injury crashes, referred to as severe crashes. To achieve this goal, the selection of promising countermeasures is of utmost importance, and relies on the effectiveness of candidate countermeasures in reducing severe crashes. Although it is important to precisely evaluate the effectiveness of candidate countermeasures in reducing the number of severe crashes at a site, the current state-of-the-practice often leads to biased estimates. While there have been a few advanced statistical models developed to mitigate the problem in practice, these models are computationally difficult to estimate because severe crashes are dispersed spatially and temporally, and cannot be integrated into the Highway Safety Manual framework, which develops a series of safety performance functions and crash modification factors to predict the number of crashes. Crash severity outcomes are generally integrated into the Highway Safety Manual using deterministic distributions rather than statistical models. Accounting for the variability in crash severity as a function geometric design, traffic flow, and other roadway and roadside features is afforded by estimating statistical models. Therefore, there is a need to develop a new analysis paradigm to resolve the limitations in the current Highway Safety Manual methods. We propose an approach which decomposes the severe crash frequency into a function of the change in the total number of crashes and the probability of a crash becoming a severe crash before and after a countermeasure is implemented. We tested this approach by evaluating the effectiveness of shoulder rumble strips on reducing the number of severe crashes. A total of 310 segments that have had shoulder rumble strips installed during 2002–2009 are included in the analysis. It was found that shoulder rumble strips reduce the total number of crashes, but have no statistically significant effect on reducing the probability of a severe crash outcome.     

Effects of excessive speeding and falling asleep while driving on crash injury severity in Ethiopia: A generalized ordered logit model analysis

The severity of injury from vehicle crash is a result of a complex interaction of factors related to drivers’ behavior, vehicle characteristics, road geometric and environmental conditions. Knowing to what extent each factor contributes to the severity of an injury is very important. The objective of the study was to assess factors that contribute to crash injury severity in Ethiopia. Data was collected from June 2012 to July 2013 on one of the main and busiest highway of Ethiopia, which extends from the capital Addis Ababa to Hawassa. During the study period a total of 819 road crashes was recorded and investigated by trained crash detectors. A generalized ordered logit/partial proportional odds model was used to examine factors that might influence the severity of crash injury. Model estimation result suggested that, alcohol use (Coef. = 0.5565; p-value = 0.017), falling asleep while driving (Coef. = 1.3102; p-value = 0.000), driving at night time in the absence of street light (Coef. = 0.3920; p-value = 0.033), rainfall (Coef. = 0.9164; p-value = 0.000) and being a minibus or vans (Coef. = 0.5065; p-value = 0.013) were found to be increased crash injury severity. On the other hand, speeding was identified to have varying coefficients for different injury levels, its highest effects on sever and fatal crashes. In this study risky driving behaviors (speeding, alcohol use and sleep/fatigue) were a powerful predictor of crash injury severity. Therefore, better driver licensing and road safety awareness campaign complimented with strict police enforcement can play a pivotal role to improve road safety. Further effort needed as well to monitor speed control strategies like; using the radar control and physical speed restraint measures (i.e., rumble strips).     

Analysis of powered two-wheeler crashes in Italy by classification trees and rules discovery

Aim of the study was the analysis of powered two-wheeler (PTW) crashes in Italy in order to detect interdependence as well as dissimilarities among crash characteristics and provide insights for the development of safety improvement strategies focused on PTWs. At this aim, data mining techniques were used to analyze the data relative to the 254,575 crashes involving PTWs occurred in Italy in the period 2006–2008.