A Bayesian spatial bivariate multinomial logit model for joint analysis of crash type and injury severity at signalized intersections

Crash type and injury severity at signalized intersections may be shaped by overlapping risk mechanisms and spatially clustered influences, yet they are often modeled as separate outcomes. This study applies a Bayesian spatial joint bivariate random-parameters logit framework to jointly analyze crash type and binary injury severity at signalized intersections using Texas crash records from 2022 to 2024. Crash type is represented by rear-end, sideswipe, and left-turn/angle crashes, while injury severity is modeled as injury versus no injury. The framework integrates three components: cross-equation dependence through correlated intersection-level latent effects, unobserved heterogeneity through random parameters, and residual spatial dependence through conditional autoregressive effects across neighboring intersections. Model comparison based on WAIC and DIC shows that the spatial joint random-parameters specification consistently outperforms independent and non-spatial alternatives. The results indicate that unobserved intersection-level factors jointly influence crash-type composition and injury outcomes, with injury severity more strongly aligned with latent risk associated with left-turn/angle crashes than with sideswipe crashes. Several covariates, including driver age, adverse roadway or weather conditions, multi-vehicle involvement, and distraction-related factors, show distinct associations across crash types and injury severity. These findings support a more integrated and spatially informed interpretation of signalized-intersection safety and provide evidence for mechanism-oriented diagnosis and targeted intervention prioritization.