Multi-type Bayesian hierarchical modeling of traffic conflict extremes for crash estimation

Most existing Extreme Value Theory (EVT) models were developed based on the total number of conflicts or a single type of traffic conflict to estimate the corresponding frequency of crashes. Using the total number of conflicts to estimate the total number of crashes may make it difficult to diagnose safety problems as countermeasures are usually related to specific conflict/crash types. Single-type EVT models may help to better explain the mechanism of crash occurrence of a certain type, but they only reflect the partial safety of a road entity. Therefore, developing EVT models for multiple types of traffic conflicts would be more representative. However, one important issue in modeling various types of traffic conflicts is that there will be considerable correlation among various conflict types. The modeled crash prediction results would be biased if the conflict type correlation is not accounted for. This study proposes a multi-type Bayesian hierarchical extreme value modeling approach, which has four advantages: 1) integrates multiple types of traffic conflicts; 2) incorporates the influence of several covariates; 3) combines traffic conflicts from different sites; 4) accounts for the unobserved heterogeneity in conflict extremes. The proposed multi-type approach was applied to estimate rear-end crashes and side-impact crashes of left-turning vehicles based on their corresponding traffic conflicts observed from two signalized intersections in the city of Surrey, British Columbia. Both conflict types of left-turning vehicles were characterized by the same indicator time-to-collision (TTC). Overall, the results show that the standard errors of the multi-type model parameters are smaller than those of single-type models. Moreover, the multi-type model produces more accurate crash estimates than its corresponding single-type models. The more accurate crash estimates are probably attributed to the two-type model accounting for the conflict type correlation.