Copula-Based Joint Model of Injury Severity and Vehicle Damage in Two-Vehicle Crashes

In the transportation safety field, in an effort to improve safety, statistical models are developed to identify factors that contribute to crashes as well as those that affect injury severity. This study contributes to the literature on severity analysis. Injury severity and vehicle damage are two important indicators of severity in crashes and are typically modeled independently. However, there are common observed and unobserved factors affecting the two crash indicators that lead to potential interrelationships. Failure to account for the interrelationships between the indicators may lead to biased coefficient estimates in crash severity prediction models. The focus of this study was to explore interrelationships between injury severity and vehicle damage and to also identify the nature of these correlations across different types of crashes. A copula-based methodology that could simultaneously model injury severity and vehicle damage while also accounting for the interrelationships between the two indicators was employed. Furthermore, parameterization of the copula structure was used to represent the interrelationships between the crash indicators as a function of crash characteristics. In this study, six specifications of the copula model—Gaussian, Farlie–Gumbel–Morgenstern, Frank, Clayton, Joe, and Gumbel—were developed. On the basis of goodness-of-fit statistics, the Gaussian copula model was found to outperform the other copula-based model specifications. Results indicated that interrelationships between injury severity and vehicle damage varied with different crash characteristics including manner of collision and collision type.