A study of factors affecting highway accident rates using the random-parameters tobit model

A large body of previous literature has used a variety of count-data modeling techniques to study factors that affect the frequency of highway accidents over some time period on roadway segments of a specified length. An alternative approach to this problem views vehicle accident rates (accidents per mile driven) directly instead of their frequencies. Viewing the problem as continuous data instead of count data creates a problem in that roadway segments that do not have any observed accidents over the identified time period create continuous data that are left-censored at zero. Past research has appropriately applied a tobit regression model to address this censoring problem, but this research has been limited in accounting for unobserved heterogeneity because it has been assumed that the parameter estimates are fixed over roadway-segment observations. Using 9-year data from urban interstates in Indiana, this paper employs a random-parameters tobit regression to account for unobserved heterogeneity in the study of motor-vehicle accident rates. The empirical results show that the random-parameters tobit model outperforms its fixed-parameters counterpart and has the potential to provide a fuller understanding of the factors determining accident rates on specific roadway segments.     

A multivariate tobit analysis of highway accident-injury-severity rates

Relatively recent research has illustrated the potential that tobit regression has in studying factors that affect vehicle accident rates (accidents per distance traveled) on specific roadway segments. Tobit regression has been used because accident rates on specific roadway segments are continuous data that are left-censored at zero (they are censored because accidents may not be observed on all roadway segments during the period over which data are collected). This censoring may arise from a number of sources, one of which being the possibility that less severe crashes may be under-reported and thus may be less likely to appear in crash databases. Traditional tobit-regression analyses have dealt with the overall accident rate (all crashes regardless of injury severity), so the issue of censoring by the severity of crashes has not been addressed. However, a tobit-regression approach that considers accident rates by injury-severity level, such as the rate of no-injury, possible injury and injury accidents per distance traveled (as opposed to all accidents regardless of injury-severity), can potentially provide new insights, and address the possibility that censoring may vary by crash-injury severity. Using five-year data from highways in Washington State, this paper estimates a multivariate tobit model of accident-injury-severity rates that addresses the possibility of differential censoring across injury-severity levels, while also accounting for the possible contemporaneous error correlation resulting from commonly shared unobserved characteristics across roadway segments. The empirical results show that the multivariate tobit model outperforms its univariate counterpart, is practically equivalent to the multivariate negative binomial model, and has the potential to provide a fuller understanding of the factors determining accident-injury-severity rates on specific roadway segments.     

Modeling accident frequencies as zero-altered probability processes: An empirical inquiry

This paper presents an empirical inquiry into the applicability of zero-altered counting processes to roadway section accident frequencies. The intent of such a counting process is to distinguish sections of roadway that are truly safe (near zero-accident likelihood) from those that are unsafe but happen to have zero accidents observed during the period of observation (e.g. one year). Traditional applications of Poisson and negative binomial accident frequency models do not account for this distinction and thus can produce biased coefficient estimates because of the preponderance of zero-accident observations. Zero-altered probability processes such as the zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) distributions are examined and proposed for accident frequencies by roadway functional class and geographic location. The findings show that the ZIP structure models are promising and have great flexibility in uncovering processes affecting accident frequencies on roadway sections observed with zero accidents and those with observed accident occurrences. This flexibility allows highway engineers to better isolate design factors that contribute to accident occurrence and also provides additional insight into variables that determine the relative accident likelihoods of safe versus unsafe roadways. The generic nature of the models and the relatively good power of the Vuong specification test used in the non-nested hypotheses of model specifications offers roadway designers the potential to develop a global family of models for accident frequency prediction that can be embedded in a larger safety management system.     

A note on modeling vehicle accident frequencies with random-parameters count models

In recent years there have been numerous studies that have sought to understand the factors that determine the frequency of accidents on roadway segments over some period of time, using count data models and their variants (negative binomial and zero-inflated models). This study seeks to explore the use of random-parameters count models as another methodological alternative in analyzing accident frequencies. The empirical results show that random-parameters count models have the potential to provide a fuller understanding of the factors determining accident frequencies.     

Markov switching negative binomial models: An application to vehicle accident frequencies

In this paper, two-state Markov switching models are proposed to study accident frequencies. These models assume that there are two unobserved states of roadway safety, and that roadway entities (roadway segments) can switch between these states over time. The states are distinct, in the sense that in the different states accident frequencies are generated by separate counting processes (by separate Poisson or negative binomial processes). To demonstrate the applicability of the approach presented herein, two-state Markov switching negative binomial models are estimated using five-year accident frequencies on Indiana interstate highway segments. Bayesian inference methods and Markov Chain Monte Carlo (MCMC) simulations are used for model estimation. The estimated Markov switching models result in a superior statistical fit relative to the standard (single-state) negative binomial model. It is found that the more frequent state is safer and it is correlated with better weather conditions. The less frequent state is found to be less safe and to be correlated with adverse weather conditions.     

Differences in passenger car and large truck involved crash frequencies at urban signalized intersections: An exploratory analysis

The influence of intersection features on safety has been examined extensively because intersections experience a relatively large proportion of motor vehicle conflicts and crashes. Although there are distinct differences between passenger cars and large trucks-size, operating characteristics, dimensions, and weight-modeling crash counts across vehicle types is rarely addressed. This paper develops and presents a multivariate regression model of crash frequencies by collision vehicle type using crash data for urban signalized intersections in Tennessee. In addition, the performance of univariate Poisson-lognormal (UVPLN), multivariate Poisson (MVP), and multivariate Poisson-lognormal (MVPLN) regression models in establishing the relationship between crashes, traffic factors, and geometric design of roadway intersections is investigated. Bayesian methods are used to estimate the unknown parameters of these models. The evaluation results suggest that the MVPLN model possesses most of the desirable statistical properties in developing the relationships. Compared to the UVPLN and MVP models, the MVPLN model better identifies significant factors and predicts crash frequencies. The findings suggest that traffic volume, truck percentage, lighting condition, and intersection angle significantly affect intersection safety. Important differences in car, car–truck, and truck crash frequencies with respect to various risk factors were found to exist between models. The paper provides some new or more comprehensive observations that have not been covered in previous studies.     

Differences in male and female injury severities in sport-utility vehicle, minivan, pickup and passenger car accidents

This research explores differences in injury severity between male and female drivers in single and two-vehicle accidents involving passenger cars, pickups, sport-utility vehicles (SUVs), and minivans. Separate multivariate multinomial logit models of injury severity are estimated for male and female drivers. The models predict the probability of four injury severity outcomes: no injury (property damage only), possible injury, evident injury, and fatal/disabling injury. The models are conditioned on driver gender and the number and type of vehicles involved in the accident. The conditional structure avoids bias caused by men and women's different reporting rates, choices of vehicle type, and their different rates of participation as drivers, which would affect a joint model of all crashes. We found variables that have opposite effects for the genders, such as striking a barrier or a guardrail, and crashing while starting a vehicle. The results suggest there are important behavioral and physiological differences between male and female drivers that must be explored further and addressed in vehicle and roadway design.     

Identifying significant predictors of injury severity in traffic accidents using a series of artificial neural networks

Understanding the circumstances under which drivers and passengers are more likely to be killed or more severely injured in an automobile accident can help improve the overall driving safety situation. Factors that affect the risk of increased injury of occupants in the event of an automotive accident include demographic or behavioral characteristics of the person, environmental factors and roadway conditions at the time of the accident occurrence, technical characteristics of the vehicle itself, among others. This study uses a series of artificial neural networks to model the potentially non-linear relationships between the injury severity levels and crash-related factors. It then conducts sensitivity analysis on the trained neural network models to identify the prioritized importance of crash-related factors as they apply to different injury severity levels. In the process, the problem of five-class prediction is decomposed into a set of binary prediction models (using a nationally representative sample of 30358 police-recorded crash reports) in order to obtain the granularity of information needed to identify the "true" cause and effect relationships between the crash-related factors and different levels of injury severity. The results, mostly validated by the findings of previous studies, provide insight into the changing importance of crash factors with the changing injury severity levels.     

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.     

Refined-scale panel data crash rate analysis using random-effects tobit model

Random effects tobit models are developed in predicting hourly crash rates with refined-scale panel data structure in both temporal and spatial domains. The proposed models address left-censoring effects of crash rates data while accounting for unobserved heterogeneity across groups and serial correlations within group in the meantime. The utilization of panel data in both refined temporal and spatial scales (hourly record and 1-mile roadway segments on average) exhibits strong potential on capturing the nature of time-varying and spatially varying contributing variables that is usually ignored in traditional aggregated traffic accident modeling. 1-year accident data and detailed traffic, environment, road geometry and surface condition data from a segment of I-25 in Colorado are adopted to demonstrate the proposed methodology. To better understand significantly different characteristics of crashes, two separate models, one for daytime and another for nighttime, have been developed. The results show major difference in contributing factors towards crash rate between daytime and nighttime models, implying considerable needs to investigate daytime and nighttime crashes separately using refined-scale data. After the models are developed, a comprehensive review of various contributing factors is made, followed by discussions on some interesting findings.     

Zero-state Markov switching count-data models: An empirical assessment

In this study, a two-state Markov switching count-data model is proposed as an alternative to zero-inflated models to account for the preponderance of zeros sometimes observed in transportation count data, such as the number of accidents occurring on a roadway segment over some period of time. For this accident-frequency case, zero-inflated models assume the existence of two states: one of the states is a zero-accident count state, which has accident probabilities that are so low that they cannot be statistically distinguished from zero, and the other state is a normal-count state, in which counts can be non-negative integers that are generated by some counting process, for example, a Poisson or negative binomial. While zero-inflated models have come under some criticism with regard to accident-frequency applications - one fact is undeniable - in many applications they provide a statistically superior fit to the data. The Markov switching approach we propose seeks to overcome some of the criticism associated with the zero-accident state of the zero-inflated model by allowing individual roadway segments to switch between zero and normal-count states over time. An important advantage of this Markov switching approach is that it allows for the direct statistical estimation of the specific roadway-segment state (i.e., zero-accident or normal-count state) whereas traditional zero-inflated models do not. To demonstrate the applicability of this approach, a two-state Markov switching negative binomial model (estimated with Bayesian inference) and standard zero-inflated negative binomial models are estimated using five-year accident frequencies on Indiana interstate highway segments. It is shown that the Markov switching model is a viable alternative and results in a superior statistical fit relative to the zero-inflated models.     

Analysis of injury severity and vehicle occupancy in truck- and non-truck-involved accidents.

The impact that large trucks have on accident severity has long been a concern in the accident analysis literature. One important measure of accident severity is the most severely injured occupant in the vehicle. Such data are routinely collected in state accident data files in the U.S. Among the many risk factors that determine the most severe level of injury sustained by vehicle occupants, the number of occupants in the vehicle is an important factor. These effects can be significant because vehicles with higher occupancies have an increased likelihood of having someone seriously injured. This paper studies the occupancy/injury severity relationship using Washington State accident data. The effects of large trucks, which are shown to have a significant impact on the most severely injured vehicle occupant, are accounted for by separately estimating nested logit models for truck-involved accidents and for non-truck-involved accidents. The estimation results uncover important relationships between various risk factors and occupant injury. In addition, by comparing the accident characteristics between truck-involved accidents and non-truck-involved accidents, the risk factors unique to large trucks are identified along with the relative importance of such factors. The findings of this study demonstrate that nested logit modeling, which is able to take into account vehicle occupancy effects and identify a broad range of factors that influence occupant injury, is a promising methodological approach.     

Factors affecting the probability of bus drivers being at-fault in bus-involved accidents

Previous research has provided little insight into factors that influence the probability of bus drivers being at-fault in bus-involved accidents. In this study, an analysis was conducted on accident data compiled by a bus company that include an assessment on whether the bus driver was deemed by the company to hold primary responsibility for accident occurrence. Using a mixed logit modelling approach, roadway/environmental, vehicle and driver related variables that were identified to be influential were road type, speed limit, traffic/lighting conditions, bus priority, bus age/length and driver's age/gender/experience/historic at-fault accident record. Results were indicative of possible confined road-space issues that bus drivers face along routes with roadside traffic friction and point to the provision of exclusive right of way for buses as a possible way to address this. Results also suggest benefits in assigning routes comprising mainly divided roads as well as newer and shorter buses to less experienced drivers.     

Risk factors affecting the severity of single vehicle traffic accidents in Hong Kong

A population-based case-control study was conducted to examine factors affecting the severity of single vehicle traffic accidents in Hong Kong. In particular, single vehicle accident data of three major vehicle types, namely private vehicles, goods vehicles and motorcycles, which contributed to over 80% of all single vehicle accidents during the 2-year-period 1999-2000, were considered. Data were obtained from the newly implemented traffic accident data system (TRADS), which was developed jointly by the Transport Department, Police Force and Information Technology Services Department, Hong Kong. The effect of district, human, vehicle, safety, environmental and site factors on injury severity of an accident was examined. Unique risk factors associated with each of the vehicle types were identified by means of stepwise logistic regression models. For private vehicles, district board, gender of driver, age of vehicle, time of the accident and street light conditions are significant factors determining injury severity. For goods vehicles, seat-belt usage and weekday occurrence are the only two significant factors associated with injury severity. For motorcycles, age of vehicle, weekday and time of the accident were determined to be important factors affecting the injury severity. Identification of potential risk factors pertinent to the particular vehicle type has important implications to relevant official organisations in modifying safety measures in order to reduce the occurrence of severe traffic accidents, which would help to promote a safe road environment.     

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.     

Accident prediction models for urban roads

This paper describes some of the main findings from two separate studies on accident prediction models for urban junctions and urban road links described in [Uheldsmodel for bygader-Del1: Modeller for 3-og 4-benede kryds. Notat 22, The Danish Road Directorate, 1995; Uheldsmodel for bygader- Del2: Modeller for straekninger. Notat 59, The Danish Road Directorate, 1998] (Greibe and Hemdorff, 1995, 1988).The main objective for the studies was to establish simple, practicable accident models that can predict the expected number of accidents at urban junctions and road links as accurately as possible. The models can be used to identify factors affecting road safety and in relation to 'black spot' identification and network safety analysis undertaken by local road authorities.The accident prediction models are based on data from 1036 junctions and 142 km road links in urban areas. Generalised linear modelling techniques were used to relate accident frequencies to explanatory variables.The estimated accident prediction models for road links were capable of describing more than 60% of the systematic variation ('percentage-explained' value) while the models for junctions had lower values. This indicates that modelling accidents for road links is less complicated than for junctions, probably due to a more uniform accident pattern and a simpler traffic flow exposure or due to lack of adequate explanatory variables for junctions.Explanatory variables describing road design and road geometry proved to be significant for road link models but less important in junction models. The most powerful variable for all models was motor vehicle traffic flow.     

Disaggregate analysis of road accident severities

A comprehensive understanding of the relationship between road accident occurrence and severity of consequences permits the formulation of safety measures that are most cost-effective. A disaggregate model of road accident severity based on sequential logit models is presented. The sequential binary approach is able to account for the dependency between different levels of severity. Factors that affect the level of damage experienced by individuals involved in road accidents include: accident dynamics, seating position, vehicle condition, vehicle size, driver condition and driver action. Separate models are calibrated for three accident situations: single-vehicle accidents, two-vehicle accidents and multi-vehicle accidents. Ontario road accident police reports are used to calibrate and validate the models. The results of a simple application of the models to a safety protocol involving the effectiveness of passenger restraint devices is presented.     

An assessment of the effect of driver age on traffic accident involvement using log-linear models

Statistical models were developed to help understand the relationship between the driver age and several important accident-related factors and circumstances such as injury severity, collision types, average daily traffic (ADT), roadway character, speed ratio, alcohol involvement, and accident location. By using techniques of categorical analysis on the 1994 and 1995 Florida accident database, four log-linear models with three variables in each model with all possible two-way interactions were developed. In order to compare the differences in response between the age groups and a particular accident-related variable, odds multipliers were computed. The effects of age and accident-related factors were examined, and interactions among them were considered. The results indicated significant relationships between the driver age and ADT, injury severity, manner of collision, speed, alcohol involvement, and roadway character. The findings' contribution to the understanding of the effect of age on accident involvement is addressed. A discussion of how log-linear and logit modeling with estimation of `odds multipliers' may contribute to traffic safety studies is also provided.     

Modeling crash outcome probabilities at rural intersections: application of hierarchical binomial logistic models

It is important to examine the nature of the relationships between roadway, environmental, and traffic factors and motor vehicle crashes, with the aim to improve the collective understanding of causal mechanisms involved in crashes and to better predict their occurrence. Statistical models of motor vehicle crashes are one path of inquiry often used to gain these initial insights. Recent efforts have focused on the estimation of negative binomial and Poisson regression models (and related deviants) due to their relatively good fit to crash data. Of course analysts constantly seek methods that offer greater consistency with the data generating mechanism (motor vehicle crashes in this case), provide better statistical fit, and provide insight into data structure that was previously unavailable. One such opportunity exists with some types of crash data, in particular crash-level data that are collected across roadway segments, intersections, etc. It is argued in this paper that some crash data possess hierarchical structure that has not routinely been exploited. This paper describes the application of binomial multilevel models of crash types using 548 motor vehicle crashes collected from 91 two-lane rural intersections in the state of Georgia. Crash prediction models are estimated for angle, rear-end, and sideswipe (both same direction and opposite direction) crashes. The contributions of the paper are the realization of hierarchical data structure and the application of a theoretically appealing and suitable analysis approach for multilevel data, yielding insights into intersection-related crashes by crash type.     

Driving performance assessment: effects of traffic accident location and alarm content

According to accident statistics for Taiwan, the two most common traffic accident locations in urban areas are roadway segments and intersections. On roadway segments, most collisions are due to drivers not noticing the status of leading vehicle. At intersections, most collisions are due to the other driver failing to obey traffic signs. Using a driving simulator equipped with a collision warning system, this study investigated driving performance at different accident locations and between different alarm contents, and identified the relationship between crash occurrences and driving performance. Thirty participants, aged 20-29 years, were recruited in this study. Driving performance measures were perception-reaction time, movement-reaction time, speed and a crash. Experimental results indicated that due to different demands for processing information under different traffic conditions, driving performance differed at the two traffic accident locations. On a roadway segment, perception-reaction time for a beep was shorter than the time for a speech message. Nevertheless, at an intersection, a speech message was a great help to drivers and, thus, perception-reaction time was effectively reduced. In addition, logistic regression analysis indicates that perception-movement time had the greatest influence on crash occurrence.