Incorporating temporal correlation into a multivariate random parameters Tobit model for modeling crash rate by injury severity

This study develops three temporal multivariate random parameters Tobit models to analyze crash rate by injury severity; these models simultaneously accommodate temporal correlation and unobserved heterogeneity across observations and correlations across injury severity. The three models are estimated and compared in the Bayesian context with a crash dataset collected from Hong Kong's Traffic Information System, which contains crash, road geometry, traffic, and environmental information on 194 directional road segments over a five-year period (2002-2006). Significant temporal effects are found in all of the temporal models, and the inclusion of temporal correlation considerably improves the goodness of fit of the multivariate random parameters Tobit regression, according to the results of deviance information criteria (DIC) and Bayesian R-2, indicating the strength of considering cross-period temporal correlation. Moreover, after accounting for temporal effects, the magnitude of the correlation between the crash rates at various injury degrees decreases, probably because a portion of the correlation may be attributed to unobserved or unobservable factors with timedependent or autoregressive safety effects. Among the three candidate temporal models, the one with independent temporal effects has lower DIC and R-2 values, which suggests better model-fit performance than the two with constant or correlated temporal effects. This finding supports the model with independent temporal effects as a good alternative for traffic safety analysis.