Random-Parameter Bayesian Hierarchical Extreme Value Modeling Approach with Heterogeneity in Means and Variances for Traffic Conflict–Based Crash Estimation

Abstract

Using random parameters in combination with extreme value theory (EVT) models has been shown to capture unobserved heterogeneity and improve crash estimation based on traffic conflicts. However, in existing random-parameter EVT models, the predefined distribution means and variances for random parameters are usually constant, which may not capture unobserved heterogeneity well. Therefore, the present study develops a random-parameter Bayesian hierarchical extreme value model with heterogeneity in means and variances (RPBHEV-HMV) to better capture unobserved heterogeneity. The developed model offers two main advantages: (1) it allows random parameters to be normally distributed with varying means and variances; and (2) it incorporates several factors contributing to a heterogeneous distribution of means and variances of random parameters. Application of the developed model to conflict-based rear-end crash prediction was conducted at four signalized intersections in the city of Surrey, British Columbia, Canada. The modified time to collision was employed to fit the generalized extreme value distribution. Three conflict indicators and three traffic parameters were considered as covariates to capture nonstationarity in conflict extremes as well as heterogeneity in means and variances. The results indicated that the RPBHEV-HMV model outperforms existing RPBHEV models in terms of goodness of fit, explanatory power, and crash estimation accuracy and precision.