Highlights • Hierarchical modeling can account for unobserved heterogeneity. • Considering one random factor at level-2 of data structure hinders exploring the crossed effects of other random factors on the response variable. • Utilizing the concept of Cross-Classified Random Effects Modeling (CCREM) can account for the crossed effects of different random factors. • The maximum probability of critical crashes arises on dry pavements and steep downgrades. • Real-time interventions should be applied based on both traffic-related predictors and various combinations of environmental conditions.

Abstract Traditional hierarchical modeling has been proposed to account for unobserved heterogeneity in the crash analysis. Previous studies investigated the grouping of individual observations between different clusters by considering a single random factor at level-2 of data structure. This approach, however, hinders exploring the possible crossed effects of additional random factors at the level-2 of data hierarchy on the response variable. The current study aims to expand the previous attempts by introducing the concept of Cross-Classified Random Effects Modeling (CCREM) and utilizing crossed random intercepts to account for the crossed effects of two random factors. Aligned with the Connected Vehicle Pilot Deployment Program on Interstate-80 (I-80), this paper intends to cluster critical crashes, involving fatal or incapacitating injuries, versus non-critical crashes through a 402-mile I-80 in Wyoming during the first five months of 2017. Aggregated environmental conditions were conflated with disaggregated real-time traffic observations. Concerning road surface conditions and longitudinal grade categories, four Logistic Regression models were calibrated under Bayesian Inference. Model-1 considered these two factors as fixed parameters; however, in each of Model-2 and Model-3, one of these factors was treated as a random intercept. Model-4 considered both factors as random intercepts and investigated their crossed effect on the critical crash probability. Model-4 outperformed the others and showed that the maximum probability of critical crashes arises on dry pavements and steep downgrades. In contrast, the combined effect of wet pavements and less steep downgrades is associated with the minimum risk of critical crashes. It was revealed that the probability of critical crashes varies at any given value of real-time traffic-related predictors according to different combinations of longitudinal grade and road surface conditions. This finding indicates an essential need for Active Traffic Management to timely apply interventions not only based on real-time traffic-related predictors but also according to various combinations of environmental conditions.