Venky Shankar

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.

Random parameter models of interstate crash frequencies by severity, number of vehicles involved, collision and location type

A nine-year (1999-2007) continuous panel of crash histories on interstates in Washington State, USA, was used to estimate random parameter negative binomial (RPNB) models for various aggregations of crashes. A total of 21 different models were assessed in terms of four ways to aggregate crashes, by: (a) severity, (b) number of vehicles involved, (c) crash type, and by (d) location characteristics. The models within these aggregations include specifications for all severities (property damage only, possible injury, evident injury, disabling injury, and fatality), number of vehicles involved (one-vehicle to five-or-more-vehicle), crash type (sideswipe, same direction, overturn, head-on, fixed object, rear-end, and other), and location types (urban interchange, rural interchange, urban non-interchange, rural non-interchange). A total of 1153 directional road segments comprising of the seven Washington State interstates were analyzed, yielding statistical models of crash frequency based on 10,377 observations. These results suggest that in general there was a significant improvement in log-likelihood when using RPNB compared to a fixed parameter negative binomial baseline model. Heterogeneity effects are most noticeable for lighting type, road curvature, and traffic volume (ADT). Median lighting or right-side lighting are linked to increased crash frequencies in many models for more than half of the road segments compared to both-sides lighting. Both-sides lighting thereby appears to generally lead to a safety improvement. Traffic volume has a random parameter but the effect is always toward increasing crash frequencies as expected. However that the effect is random shows that the effect of traffic volume on crash frequency is complex and varies by road segment. The number of lanes has a random parameter effect only in the interchange type models. The results show that road segment-specific insights into crash frequency occurrence can lead to improved design policy and project prioritization.

Model of Relationship Between Interstate Crash Occurrence and Geometrics: Exploratory Insights from Random Parameter Negative Binomial Approach

This paper proposes the use of a random parameter negative binomial (NB) model for the analysis of crash counts. With the use of a 9-year, continuous panel of histories of total crash frequencies on Interstate highways in Washington State for 1999 to 2007, a random parameter NB model was estimated to account for parameter correlations, panel effects that contributed to intrasegment temporal variations, and between-site effects. Interstate geometric variables, such as lighting type proportions by length, shoulder width proportions, lane cross-section proportions, and curvature variables, were used in the model specification. Curvature variables included the number of horizontal curves in a segment, the number of vertical curves in a segment, the shortest horizontal curve in a segment length, the largest degree of curvature in a segment, the smallest vertical curve gradient, and the largest vertical curve gradient in a segment. Segments were analyzed at the interchange and the noninterchange levels. A total of 1,153 directional segments of the seven Washington State Inter-states were analyzed. The analysis yielded a statistical model of crash frequency on the basis of 10,377 observations. Several curvature effects were found to be random, which meant that they varied from segment to segment. Although, for example, the numbers of horizontal and vertical curves in a segment were fixed-parameter effects, the largest degree of curvature, as well as the smallest and largest vertical curve gradient variables, were random parameters. The logarithm of average daily travel and the median and point lighting proportions were also found to be random parameters. These results suggested that segment-specific insights into crash frequency occurrence could be improved for appropriate design policy and prioritization.

Freight Travel Demand Modeling: Synthesis of Approaches and Development of a Framework

It is increasingly being recognized at all levels of decision making that freight transportation and economic development are inextricably linked. As a result, many urban entities and states are embarking upon comprehensive freight transportation planning efforts aimed at ensuring safe, efficient, and smooth movement of freight along multimodal and intermodal networks. Over the past few decades there has been considerable published research on (1) freight transportation factors, (2) freight travel demand modeling methods, (3) freight transportation planning issues, and (4) freight data needs, deficiencies, and collection methods. A synthesis of the body of knowledge in these four areas is provided with a view to developing a comprehensive statewide freight transportation planning framework. The proposed framework consists of two interrelated components that facilitate demand estimation and decision making in the freight transportation sector.

A simultaneous equations model of crash frequency by severity level for freeway sections

This paper presents a simultaneous equations model of crash frequencies by severity level for freeway sections using five-year crash severity frequency data for 275 multilane freeway segments in the State of Washington. Crash severity is a subject of much interest in the context of freeway safety due to higher speeds of travel on freeways and the desire of transportation professionals to implement measures that could potentially reduce crash severity on such facilities. This paper applies a joint Poisson regression model with multivariate normal heterogeneities using the method of Maximum Simulated Likelihood Estimation (MSLE). MSLE serves as a computationally viable alternative to the Bayesian approach that has been adopted in the literature for estimating multivariate simultaneous equations models of crash frequencies. The empirical results presented in this paper suggest the presence of statistically significant error correlations across crash frequencies by severity level. The significant error correlations point to the presence of common unobserved factors related to driver behavior and roadway, traffic and environmental characteristics that influence crash frequencies of different severity levels. It is found that the joint Poisson regression model can improve the efficiency of most model coefficient estimators by reducing their standard deviations. In addition, the empirical results show that observed factors generally do not have the same impact on crash frequencies at different levels of severity.

Analysis of Naturalistic Driving Data: Prospective View on Methodological Paradigms

Recently completed naturalistic (i.e., unobtrusive) driving studies provide safety researchers with an unprecedented opportunity to study and analyze the occurrence of crashes and a range of near-crash events. Rather than focus on the details of the events immediately before the crash, this study seeks to identify methodological paradigms that can be used to answer questions long of interest to safety researchers. In particular, an attempt is made to shed some light on the four important components of methodological paradigms for naturalistic driving analysis: surrogates, evaluative aspects related to model structures, interpretation of driving context, and assessment of risk and associated sampling issues. The methodological paradigms are founded on a formal definition of the attributes of a valid crash surrogate that can be used in model formulation and testing. After a brief summary of the type of data collected in the studies, an overall framework for the analysis and a range of specific models to test hypotheses of interest are presented. A summary is given of how the systematic analyses with statistical models can extend safety knowledge beyond an assessment of “causes” of individual crashes.

Analysis of Naturalistic Driving Event Data

Naturalistic driving studies have been conducted over the past 5 years or more and have commonly reviewed video and kinematic data to identify and analyze crash, near-crash, and critical-incident events. But statistical methods that are applicable to these event data are needed. This paper addresses two issues in model development for naturalistic driving event data: the test for omitted-variable bias and the exploration of the advantages of hierarchical model structures in data analysis. With roadway departure event data from the 100-Car Naturalistic Driving Study conducted at Virginia Tech Transportation Institute, Blacksburg, Virginia, logit models were used to estimate the probability that a crash or a near crash would occur, rather than a critical incident. The models indicated a substantial omitted-variable bias for estimation of the effect of context variables but little difference for driver variables. These tests indicated that modeling of naturalistic event data should have included variables that described the attributes of the event, the driver, and the context to reduce the likelihood of bias. Hierarchical model structures offer the advantage of driver-level predictors to parameterize the effects of event attributes and contexts. The models thus reflect how driver decisions are executed: drivers with particular characteristics (one level) find themselves in contexts in which they execute specific driving maneuvers (second level), which lead to certain outcomes. Suggestions for further research include testing with additional data sets and potential applications to analysis of crash surrogates.

Pavement Marking Retroreflectivity Inspection Data: A Weibull Analysis

Quantifiable life-cycle models of the service life of pavement markings are essential for a cost-efficient pavement marking management system. A study was conducted to develop an analysis procedure for typical pavement marking retroreflectivity inspection data. Retroreflectivity data collected by the National Transportation Product Evaluation Program on water-based paints in 2002 on a Pennsylvania test deck were used. Those data were considered interval-level duration data, and a Weibull analysis was performed. A Weibull analysis is a typical method in reliability engineering in which Weibull scale and shape parameters are estimated from failure data for making objective maintenance decisions. Results of the Weibull analysis indicated that the water-based paints had shape and scale parameters of 1.42 (±0.05), and 601.67 (±17.73) days, respectively, for skip line areas and 2.38 (±0.08) and 227.41 (±4.48) days, respectively, for left wheelpath areas. It was also determined that the probability of 2-year water-based paints lasting above 100 mcd/m2/lx varied from 0% to 27%. The lower limit corresponds to the left wheelpath, and the upper limit corresponds to the skip line area. The left wheelpath markings failed to stay above 100 mcd/m2/lx after approximately a year, while skip line markings could maintain 100 mcd/m2/lx ratings or higher for more than 1,000 days. White markings were found to last longer than yellow markings for the same exposure. This study used data from a single site in Pennsylvania. A multisite analysis accounting for time and space variations is recommended before adopting this method for minimum pavement marking retroreflectivity standard assessment.

Analysis of Existing Data: Prospective Views on Methodological Paradigms

A large component of the safety research undertaken in the second Strategic Highway Research Program (SHRP 2) is aimed at reducing the injuries and fatalities that result from highway crashes. Through a naturalistic driving study (NDS) involving more than 3,000 volunteer drivers, SHRP 2 expects to learn more about how individual driver behavior interacts with vehicle and roadway characteristics. In anticipation of the large volume of data to be collected during the NDS, several projects were conducted to demonstrate that it is possible to use existing data from previous naturalistic driving studies and data from other sources to further the understanding of the risk factors associated with road crashes. More specifically, the four S01 projects, entitled Development of Analysis Methods Using Recent Data, examined the statistical relationship between surrogate measures of collisions (conflicts, critical incidents, near collisions, and roadside encroachment) and actual collisions. This report presents the results of one of these projects, undertaken by Pennsylvania State University. It documents the second phase of a two-phase project under SHRP 2 Safety Project S01B.