Multivariate copula temporal modeling of intersection crash consequence metrics: A joint estimation of injury severity, crash type, vehicle damage and driver error

This study employs a copula-based multivariate temporal ordered probit model to simultaneously estimate the four common intersection crash consequence metrics – driver error, crash type, vehicle damage and injury severity – by accounting for potential correlations due to common observed and unobserved factors, while also accommodating the temporal instability of model estimates over time. To this end, a comprehensive literature review of relevant studies was conducted; four different copula model specifications including Frank, Clayton, Joe and Gumbel were estimated to identify the dominant factors contributing to each crash consequence indicator; the temporal effects on model estimates were investigated; the elasticity effects of the independent variables with regard to all four crash consequence indicators were measured to express the magnitude of the effects of an independent variable on the probability change for each level of four indicators; and specific countermeasures were recommended for each of the contributing factors to improve the intersection safety. The model goodness-of-fit illustrates that the Joe copula model with the parameterized copula parameters outperforms the other models, which verifies that the injury severity, crash type, vehicle damage and driver error are significantly correlated due to common observed and unobserved factors and, accounting for their correlations, can lead to more accurate model estimation results. The parameterization of the copula function indicates that their correlation varies among different crashes, including crashes that occurred at stop-controlled intersections, four-leg intersections and crashes which involved drivers younger than 25. The model coefficient estimates indicate that the driver's age, driving under the influence of drugs and alcohol, intersection geometry and control types, and adverse weather and light conditions are the most critical factors contributing to severe crash consequences. The coefficient estimates of four-leg intersections, yield and stop-controlled intersections and adverse weather conditions varied over time, which indicates that the model estimation of crash data may not be stable over time and should be accommodated in crash prediction analysis. In the end, relevant countermeasures corresponding to law enforcement and intersection infrastructure design are recommended to all of the contributing factors identified by the model. It is anticipated that this study can shed light on selecting valid statistical models for crash data analysis, identifying intersection safety issues, and helping develop effective countermeasures to improve intersection safety.