A spatial generalized extreme value framework for traffic conflict using max-stable process approach

Abstract

Extreme value theory (EVT) models are widely used to estimate crash risk from traffic conflicts for proactive traffic safety management. However, existing EVT models assume that the crash risks are evenly distributed across the entire study area, ignoring the spatial effect across different zones within the area. This study proposes a spatial EVT modeling framework using max-stable process (MSP) approach for traffic conflicts while accounting for spatial dependence. Traffic conflict data from vehicle trajectories on U.S.101, sourced from the NGSIM dataset, were utilized with time to collision (TTC) as the conflict indicator. Three types of MSP models are used to capture spatial dependence: Schlather, Brown-Resnick, and Smith, each with corresponding correlation functions. Various correlation functions and link functions for each MSP model were proposed. The pairwise composite likelihood estimation approach is utilized to estimate the MSP models’ parameters, and the extremal coefficient indicator is employed to describe the spatial dependence across different zones. Crash risk is estimated for each zone within the study area. Model results show significant spatial correlation in extreme traffic conflicts. Moreover, spatial dependence in these extreme conflicts diminishes with distance, showing stronger correlations at shorter distances. M1 achieved the best goodness-of-fit among the MSP models, indicates that the integration of spatial covariates in the threshold and scale parameters effectively explains a significant amount of variation in the observed data. In particular, the Schlather model with a powered exponential correlation function performs better than the Smith and Brown-Resnick models. The crash risk analysis result shows that inner (fast) lanes have lower crash risk than outer lanes, and crash risk is higher on the entrance ramp than the exit ramp. The crash risk estimated from the spatial EVT model is consistent with the TTC heatmap, particularly in high conflict zones, demonstrating the reliability and validity of the spatial EVT modeling approach for traffic safety analysis.