Hierarchical Bayesian copula models for joint crash-conflict risk on freeways and arterial roads

This study develops a cross-facility hierarchical Bayesian marginal-copula framework for jointly modeling rear-end crash counts and three connected-vehicle (CV)-derived longitudinal conflict measures: time to collision (TTC) conflicts, deceleration rate to avoid a crash (DRAC) conflicts, and time to collision with disturbance (TTCD)-based conflict risk. The framework is designed for cross-facility generalization between freeways and arterials: hierarchical marginal models with facility-type random effects enable partial pooling and principled information sharing across facility types, while an inference-for-margins (IFM)-estimated multivariate Gaussian copula characterizes crash-conflict associations among the four safety indicators while preserving outcome-specific marginal distributions. The empirical analysis combines police-reported rear-end crashes with CV trajectory data aggregated to freeway and arterial segments in Ann Arbor, Michigan. Results show strong exposure effects: an e-fold increase in annual average daily traffic (AADT) is associated with an approximately threefold increase in expected crash counts, whereas an e-fold increase in CV exposure increases TTC and DRAC conflict counts by about 2.5 to 2.6 times and TTCD-based conflict risk by roughly a factor of 4 to 5. The conflict measures are more strongly concordant with one another (Kendall's τ≈0.47 for TTC-DRAC) than with crashes (all crash-conflict τ<0.20), suggesting that TTC and DRAC capture closely related longitudinal interaction mechanisms whereas crash occurrence is only weakly associated with any single conflict metric. Cross-facility prediction experiments show that naive freeway-to-arterial extrapolation can substantially degrade predictive performance; for example, TTC-conflict root mean square error (RMSE) increases by about 89%. By contrast, the hierarchical pooled specification mitigates this degradation and achieves arterial predictive accuracy comparable to an arterial-only benchmark, with sensitivity results indicating stable performance under moderately reduced arterial training samples.