Multi-level Bayesian analyses for single- and multi-vehicle freeway crashes



R. J. Yu;M. Abdel-Aty


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Abbreviated Journal Title

Accid. Anal. Prev.


Safety performance functions; Bivariate Poisson-lognormal model; Random; parameter; Bayesian logistic regression; Mountainous freeway; SAFETY PERFORMANCE FUNCTIONS; REAL-TIME WEATHER; MOUNTAINOUS FREEWAY; TRAFFIC DATA; SEVERITY; REGRESSION; FREQUENCY; MODELS; RISK; PREDICTION; Ergonomics; Public, Environmental & Occupational Health; Social; Sciences, Interdisciplinary; Transportation


This study presents multi-level analyses for single- and multi-vehicle crashes on a mountainous freeway. Data from a 15-mile mountainous freeway section on 1-70 were investigated. Both aggregate and disaggregate models for the two crash conditions were developed. Five years of crash data were used in the aggregate investigation, while the disaggregate models utilized one year of crash data along with real-time traffic and weather data. For the aggregate analyses, safety performance functions were developed for the purpose of revealing the contributing factors for each crash type. Two methodologies, a Bayesian bivariate Poisson-lognormal model and a Bayesian hierarchical Poisson model with correlated random effects, were estimated to simultaneously analyze the two crash conditions with consideration of possible correlations. Except for the factors related to geometric characteristics, two exposure parameters (annual average daily traffic and segment length) were included. Two different sets of significant explanatory and exposure variables were identified for the single-vehicle (SV) and multi-vehicle (MV) crashes. It was found that the Bayesian bivariate Poisson-lognormal model is superior to the Bayesian hierarchical Poisson model, the former with a substantially lower DIC and more significant variables. In addition to the aggregate analyses, microscopic real-time crash risk evaluation models were developed for the two crash conditions. Multi-level Bayesian logistic regression models were estimated with the random parameters accounting for seasonal variations, crash-unit-level diversity and segment-level random effects capturing unobserved heterogeneity caused by the geometric characteristics. The model results indicate that the effects of the selected variables on crash occurrence vary across seasons and crash units; and that geometric characteristic variables contribute to the segment variations: the more unobserved heterogeneity have been accounted, the better classification ability. Potential applications of the modeling results from both analysis approaches are discussed. (C) 2013 Elsevier Ltd. All rights reserved.

Journal Title

Accident Analysis and Prevention



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