Examining the role of random parameters and unobserved heterogeneity in the frequency-severity of rural freeway run-off-road and fixed-object crashes: A Bayesian hierarchical-geospatial approach.

Fixed-object collisions and run-off-road (FOC-ROR) crashes are more severe and frequent in rural freeways compared to other crash types, particularly involving light vehicles. The relationship between influential factors and crash frequency-severity is complex due to unobserved heterogeneities. This study developed a comprehensive method integrating spatial autocorrelation cluster analysis and the Bayesian Hierarchical Random Parameter (BHRP) model to quantitatively examine unobserved effects and parameter uncertainties in FOC-ROR, FOC, and ROR crashes separately. The study also emphasizes segmentation length's impact on the proposed model performance. Based on the variables of crash type, crash severity, and segment length, the proposed approach was examined in 24 scenarios, and as a result, the FOC-ROR model for 292-meter segments demonstrated the best performance. Following this, the influential variables were identified, and Kernel Density thematic maps was employed to evaluate the spatial autocorrelation of crash frequency-severity on road segments, focusing on causes of occurrence. Results confirmed unobserved factors and influential variables like young drivers (-0.047), narrow shoulder width (-0.231), and rainfall depth (0.034) affecting fatal-injury FOC-ROR crashes, while low visibility (-0.490), low air temperature (-0.433), and driver haste (0.270) influenced PDO FOC-ROR crashes. Compared to traditional methods, the proposed spatial autocorrelation approach allows transportation authorities to prioritize geometric corrections and optimize traffic safety planning, offering a cost-effective strategy for reducing crash risks on rural freeways.