A multivariate method for evaluating safety from conflict extremes in real time

Several studies have advocated the use of extreme value theory (EVT) traffic conflict models for real-time crash risk prediction using real-time safety indices such as the risk of crash (RC) and return level of a cycle (RLC). This approach provides a logical framework to estimate crash risk by extrapolating from the observed level (i.e., traffic conflict) to the unobserved level (i.e., crash). In these studies, only univariate EVT models that consider only one conflict indicator (e.g. modified time to collision, MTTC) were used which affects the models’ accuracy and precision in estimating crash risk. The use of univariate models is likely due to that existing safety analysis multivariate EVT models have limited capability of delineating the complex dependence structure between multiple conflict indicators for application to real-time safety evaluation. This study proposes a multivariate method for evaluating real-time safety from conflict extremes which consists of novel multivariate EVT models that flexibly integrate multiple conflict indicators and several joint safety indices that comprehensively characterize the safety level of a road facility from multiple dimensions. The proposed approach has several advantages including: 1) it uses four parametric models (tilted Dirichlet, pairwise beta, Husler-Reiss, and extremal-$t$) for the angular density function for fully describing the dependence level between multiple conflict extremes; and 2) it innovatively develops several important real-time safety indices (e.g., crash risk, joint return levels, and return level concomitant) from the multivariate joint distribution for multidimensionally assessing safety. A seven-step approximate likelihood-based Bayesian inference method for model development is proposed. The proposed model estimation method is applied for cycle-level real-time safety evaluation by combining several conflict indicators at four signalized intersections in the city of Surrey, British Columbia. Three conflict indicators are used: MTTC, post encroachment time (PET), and deceleration rate to avoid a crash (DRAC). Four types of multivariate EVT models were developed. Among these models, for both bivariate and trivariate framework, the Husler-Reiss model has the best goodness-of-fit as it better captures the dependence level among the three conflict indicators. The results indicate that multivariate models identify higher numbers of crash-risk cycles than their corresponding univariate models. Further, most of crash-risk cycles have at least one of joint return levels higher than the threshold (0 for both MTTC and PET, 8.5 m/s² for DRAC) between a conflict and a collision. For joint return levels from most cycles, one return level exceeds the threshold, while others are lower than the threshold. Under the bivariate framework, all the concomitants of positive return levels are below their own thresholds.