Modeling correlation and heterogeneity in crash rates by collision types using full bayesian random parameters multivariate Tobit model

Crashes present different collision types. There usually exist unobserved risk factors which could jointly affect crash rates of different types, resulting in correlation and heterogeneity issues across observations. The primary objective of the study is to propose a novel random parameters multivariate Tobit (RPMV-Tobit) model for evaluating risk factors on crash rates of different collision types. Crash data from 367 freeway diverge areas in a three-year period were obtained for modeling. Three major types of collisions including rear-end, sideswipe, and angle collisions were considered. The RPMV-Tobit model was structured to simultaneously accommodate correlations between crash rates across collision types and unobserved heterogeneity across observations. The RPMV-Tobit model was compared with a multivariate Tobit (MV-Tobit) model, a random effect multivariate Tobit (REMV-Tobit) model, and independent univariate Tobit (IU-Tobit) models under the Bayesian framework. The results showed that MV-Tobit model outperforms the IU-Tobit models on fitting crash rates, indicating that accounting for the correlation between crash types can improve model fit. The RPMV-Tobit model and REMV-Tobit model perform better than the MV-Tobit model, suggesting that accounting for the unobserved heterogeneous can further improve model fit. The improvement of model performance with the RPMV-Tobit model is higher than that with the REMV-Tobit model. The impacts of each risk factor on crash rates were estimated and some differences were found across different collision types. The lane-balanced design, number of lanes on mainline, speed limit, and speed difference present significant heterogeneous effects on crash rates. Findings suggest that the RPMV-Tobit model is a superior approach for comprehensive crash rates modeling and traffic safety evaluation purposes.