Random parameters Bayesian hierarchical modeling of traffic conflict extremes for crash estimation

The use of Extreme Value Theory (EVT) models for traffic conflict-based crash estimation is becoming increasingly popular with considerable recent advances achieved. The latest advances include developing EVT models that combine several conflict indicators and the use of data from several sites to increase the sample size of conflict extremes. Nevertheless, one important issue while developing EVT models is accounting for the unobserved heterogeneity across different conflict observation sites and road user behaviours which can lead to biased and inefficient parameter estimates and erroneous inferences. This study proposes a random parameters (RP) Bayesian hierarchical extreme value modeling approach to account for the unobserved heterogeneity. The proposed approach is applied to estimate rear-end crashes from traffic conflicts collected from four signalized intersections in the city of Surrey, British Columbia. Traffic conflicts were characterized by four indicators: time to collision (TTC), modified TTC (MTTC), post-encroachment time (PET), and deceleration rate to avoid a crash (DRAC). MTTC was used to fit the generalized extreme value distribution, while the other three conflict indicators were treated as covariates. Six covariates including TTC, PET, DRAC, traffic volume, shock wave area, and platoon ratio were considered to account for non-stationarity in conflict extremes. Several RP, random intercepts (RI), and fixed parameters (FP) Bayesian hierarchical univariate extreme value models were developed. The results indicate that the RP model outperforms both the RI model and the FP model in terms of crash estimation accuracy and precision. Such superiority may be due to the ability of the RP model to better account for the unobserved heterogeneity.