A copula-based approach for jointly modeling crash severity and number of vehicles involved in express bus crashes on expressways considering temporal stability of data

The consequences of crashes, including injury, loss of lives, and damage to properties, are further worsened when buses plying expressways are involved in the crash. Previous studies have separately analyzed crash severity in terms of monetary cost, injuries and loss of lives, and the size of crashes in terms of the number of vehicles involved. However, as both outcome variables are correlated, it is imperative to perform a combined analysis using an appropriate econometric model to achieve a better model fit. This study contributes to the literature by jointly exploring the factors influencing the severity and size of express bus-involved crashes that occur on expressways and characterizes the dependence between both outcome variables by employing a more plausible copula regression framework. Likelihood ratio tests were also conducted to investigate the temporal stability of the factors that affect both crash severity and size. Based on the goodness-of-fit statistics, the Frank copula model proved superior to the independent ordered probit model. The estimate of the underlying dependence between the outcome variables provided a better comprehension of the correlation between them. Temporal instability was detected for the individual parameters in the models and is attributed to the changing driving behavior due to the heightened road safety campaigns. The results suggest that traffic exposure measures are significantly associated with a higher propensity of observing increased bus crash severity and size. Insights into the factors influencing the size and severity of express bus crashes are discussed, and appropriate engineering, enforcement, and education-related countermeasures are proposed.