Bivariate Bayesian hierarchical extreme value modeling using multi-type traffic conflict for crash estimation on freeway horizontal curves

Freeway horizontal curves pose great challenges to vehicle driving safety due to suboptimal road alignment, poor visual conditions, and higher demands for driving maneuvers. The interaction between multiple conflicting vehicles may generate multi-type crash risks with correlations. Modeling individual types of crash risks separately will result in biased crash estimation. In this study, a bivariate Bayesian hierarchical extreme value modeling approach, which consists of a bivariate extreme value model and a Bayesian hierarchical structure, is developed. The former integrates two different conflict indicators while also accounting for their correlation. The latter combines traffic conflicts across different sites, incorporating block-level and site-level covariates and unobserved heterogeneity. Using rear-end and lane-changing conflicts collected from 14 directional curved segments of the Yinkun freeway, several univariate Bayesian hierarchical extreme value models (UBHMS) and bivariate Bayesian hierarchical extreme value models (BBHMS) were constructed to estimate expected rear-end crashes and side crashes. The crash estimation results show that the bivariate model considering correlation between multi-type conflicts has smaller standard deviations of the model parameters and outperforms the univariate models in both accuracy and precision of crash estimation. The covariate analysis suggests that a larger proportion of large vehicles and standard deviation of speed will lead to an increase in both rear-end and side crash risks; the number of car-following vehicles and the number of lane-changing vehicles have positive influences on rear-end and side crash risks, respectively, whereas the higher the overspeed and the lane space occupancy instead reduce rear-end crash risk. Finally, when vertical curves overlap with horizontal curves, the rear-end and side crash risks on sag vertical curves exceed those on crest vertical curves.