Bivariate extreme value modeling for road safety estimation

Surrogate safety measures have been advocated as a complementary approach to study safety from a broader perspective than relying on crash data alone. This study proposes an approach to incorporate different surrogate safety measures in a unified framework for road safety estimation within the bivariate extreme value theory framework. The model structure, model specification, threshold selection method, and parameter estimation method of the bivariate threshold excess model are introduced. Two surrogate safety measures, post encroachment time (PET) and length proportion of merging (LPM), are chosen to characterize the severity of merging events on freeway entrance merging areas. Based on the field data collected along Highway 417 in the City of Ottawa, Ontario, Canada, the bivariate modelling methods with seven distribution functions are applied and compared, and the model with logistic distribution function is selected as the best model. The best bivariate models' estimation results are then evaluated by comparing them to their two marginal (univariate Generalized Pareto distribution) models. The results show that the bivariate models tend to generate crash estimates that are much closer to observed crashes than univariate models. A more important finding is that incorporating two surrogate safety measures into the bivariate models can significantly reduce the uncertainty of crash estimates. The efficiency of a bivariate model is not evidently better than either of its marginal models, but it is expected to be improved with data of a prolonged observation period. This study is also a step forward in the direction of developing multivariate safety hierarchy models, since models of the safety hierarchy have been predominantly univariate.