Influencing Factor Analysis Based on Jointly Modeling for Freeway Rear-End and Sideswipe Crashes Considering Spatial and Site Correlations

As the primary collision patterns on China’s freeways, in-depth exploration of the influencing factors of rear-end and sideswipe crashes has long been crucial for implementing targeted countermeasures. However, the structural and traffic flow continuity of freeways endows crash data with complex spatial and site correlations, which—if neglected in safety modeling—can lead to biased estimates of safety effects. To address this issue, this study develops a bivariate conditional autoregressive (CAR) model based on the Poisson lognormal (PLN) distribution: the copula joint distribution captures the site correlation between the two crash types, while the CAR model addresses spatial correlations across adjacent segments. Compared with univariate models and bivariate models with jointly distributed residuals, the proposed model achieves optimal performance and reveals the distinct determinants of the two crash types. For instance, factors such as spiral curve length and mean speed affect both crash types but to varying degrees, while continuous horizontal curve length only influences rear-end crashes. The proposed model and the identified influencing factors provide significant support for engineers to improve road safety.