Contributory fault and level of personal injury to drivers involved in head-on collisions: Application of copula-based bivariate ordinal models.

The main objective of this study is to simultaneously investigate the degree of injury severity sustained by drivers involved in head-on collisions with respect to fault status designation. This is complicated to answer due to many issues, one of which is the potential presence of correlation between injury outcomes of drivers involved in the same head-on collision. To address this concern, we present seemingly unrelated bivariate ordered response models by analyzing the joint injury severity probability distribution of at-fault and not-at-fault drivers. Moreover, the assumption of bivariate normality of residuals and the linear form of stochastic dependence implied by such models may be unduly restrictive. To test this, Archimedean copula structures and normal mixture marginals are integrated into the joint estimation framework, which can characterize complex forms of stochastic dependencies and non-normality in residual terms. The models are estimated using 2013 Virginia police reported two-vehicle head-on collision data, where exactly one driver is at-fault. The results suggest that both at-fault and not-at-fault drivers sustained serious/fatal injuries in 8% of crashes, whereas, in 4% of the cases, the not-at-fault driver sustained a serious/fatal injury with no injury to the at-fault driver at all. Furthermore, if the at-fault driver is fatigued, apparently asleep, or has been drinking the not-at-fault driver is more likely to sustain a severe/fatal injury, controlling for other factors and potential correlations between the injury outcomes. While not-at-fault vehicle speed affects injury severity of at-fault driver, the effect is smaller than the effect of at-fault vehicle speed on at-fault injury outcome. Contrarily, and importantly, the effect of at-fault vehicle speed on injury severity of not-at-fault driver is almost equal to the effect of not-at-fault vehicle speed on injury outcome of not-at-fault driver. Compared to traditional ordered probability models, the study provides evidence that copula based bivariate models can provide more reliable estimates and richer insights. Practical implications of the results are discussed.