Generalized Laplace regression for cylindrical responses with an application to road traffic accidents

We propose a regression model for cylindrical response variables that arise in the analysis of events occurring randomly over time. Each response consists of two components, one related to the timing of the event (circular), and one related to the intensity or the consequences of the event (linear). We use the multivariate generalized Laplace distribution whose parameters make this model more flexible than—as well as a generalization of—the ordinary multivariate Gaussian model. For inference, we propose standard maximum likelihood procedures. We investigate about 134,000 road traffic accidents from the Fatality Analysis Reporting System of the US National Highway Traffic Safety Administration. We define the circular component as the time of the day at which the accident occurs, and the linear component as the gravity of the event. The latter comprises an overall score for the severity of the injuries experienced by the people involved in the accidents, along with the median age of the victims. Our analysis shows that the timing and severity of the accidents are influenced by temporal and geographical factors.