Bivariate Severity Analysis of Train Derailments using Copula-Based Regression Models

Abstract

The far-reaching consequences of train derailments have been a major concern to industry and government despite their relatively low occurrence. These consequences include injury, loss of life and property, interruption of services, and destruction of the environment. Thus, it is imperative to carefully examine train derailment severity. The majority of extant literature has failed to consider the multivariate nature of derailment severity and has instead focused mainly on only one severity outcome, namely, the number of derailed cars. However, it is also important to analyze the monetary damage incurred by railroads during derailments. In this paper, a joint mixed copula-based model for derailed cars and monetary damage is presented for the combined analysis of their relationship with a set of covariates that might affect both outcomes. Marginal generalized regression linear models are combined with a bivariate copula, which characterizes the dependence between the two variables. Copulas also address endogeneity due to similar unobserved or omitted variables that may affect both response variables. The copula-based regression model was found to be more appropriate than the independent multivariate regression model. The incorporation of the copula to characterize the dependence resulted in a greater effect on the dispersion estimate than the point estimates. Derailment speed was found to have the most pronounced effect on both response variables. However, it was found to have a greater impact on monetary damage than the number of derailed cars.