Copula-based regression modeling of bivariate severity of temporary disability and permanent motor injuries. (April 2016) - Ayuso, Mercedes; Bermúdez, Lluís; Santolino, Miguel
Highlights: Positive dependence is detected between temporary and permanent injuries. Error estimates are particularly low when independence is wrongly assumed. A victim disabled for one day will have permanent injuries with a 60% of probability. This probability is more than 96% when the victim is disabled for hundred days. Abstract: The analysis of factors influencing the severity of the personal injuries suffered by victims of motor accidents is an issue of major interest. Yet, most of the extant literature has tended to address this question by focusing on either the severity of temporary disability or the severity of permanent injury. In this paper, a bivariate copula-based regression model for temporary disability and permanent injury severities is introduced for the joint analysis of the relationship with the set of factors that might influence both categories of injury. Using a motor insurance database with 21, 361 observations, the copula-based regression model is shown to give a better performance than that of a model based on the assumption of independence. The inclusion of the dependence structure in the analysis has a higher impact on the variance estimates of the injury severities than it does on the point estimates. By taking into account the dependence between temporary and permanent severities a more extensive factor analysis can be conducted. We illustrate that the conditional distribution functions of injury severities may be estimated, thus, providing decision makers with valuable information.