A Copula Model of Ramp Crash Frequency by Severity Outcomes

The approach presented in the study aims to advance the freeway interchange safety analysis by introducing the copula bivariate count model to analyze crash frequency at off-ramps by severity outcomes. Previous research uses univariate count models for crash data categorized by severity levels, overlooking the potential dependence, which can reduce the model's efficiency. Two years of crash data for Washington State's interstate system was analyzed. Three bivariate count models with three copula functions outperformed all other bivariate (without copula) and univariate count models in the study, while Frank copula was the best fit for the data. The statistical power of the copula model motivated a plausible joint modeling architecture for crash occurrence on the different interchange components. Findings indicate significant dependence parameters between fetal, severe, and evident injury (KAB) and possible, and property damage-only injury (CO), which was also confirmed by the likelihood ratio (LR) dependence test. This study investigates the influence of ramp terminal geometry and traffic control on crash occurrence on the off-ramp segment. Traffic signal on the ramp terminal, sharpest horizontal curve radius, average daily traffic at the off-ramp, illumination on the off-ramp, and number of horizontal and vertical curves had significant estimated effects in the model results.