A comprehensive analysis of contributing factors in bus crashes: integrating passenger injury severity and vehicle damage severity using the Frank copula model.

Bus crashes remain a significant public safety concern due to their potential to cause both passenger injuries and substantial vehicle damage. These two severity outcomes are interrelated, as the physical forces in high-impact crashes contribute simultaneously to occupant harm and structural damage. However, most existing studies model these outcomes independently, overlooking their statistical dependence and shared risk factors. To address this gap, this study employs a copula-based modeling framework to jointly analyze passenger injury and vehicle damage severity using bus crash data from Maryland (2015-2022). The joint estimation results reveal distinct sets of significant predictors for passenger injury severity and vehicle damage severity. For injury outcomes, the most influential variables include driver fault, airbag deployment, and safety equipment usage, underscoring the critical role of both human error and protective systems in shaping injury levels. In contrast, vehicle damage severity is more strongly associated with vehicle type, movement status at the time of impact, and mechanical condition. The inclusion of the vehicle type variable shows that school buses, despite being structurally safer, are frequently involved in crashes due to high exposure, contributing to notable damage risks. Additionally, adverse vehicle conditions and airbag deployment exhibit a strong association with disabling or destroyed damage, highlighting the role of structural integrity and energy dissipation mechanisms in post-impact outcomes. These patterns, revealed through the Copula-MNL model, reflect not only the different underlying risk structures of the two severity measures but also their shared dependence on critical safety-related factors.