Yue Quansheng, Guo Yanyong, Sayed Tarek, Liu Pan, Lyu Hao, Fan Wentao
School of Transportation, Southeast University, Nanjing 211189, China; Jiangsu Key Laboratory of Urban ITS, Jiangsu Collaborative Innovation Center of Modern, Urban Traffic Technologies, China.
Department of Civil Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada.
Accid Anal Prev. 2025 Sep;220:108164. doi: 10.1016/j.aap.2025.108164. Epub 2025 Jul 10.
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.
极值理论（EVT）模型被广泛用于通过交通冲突来估计碰撞风险，以进行主动式交通安全管理。然而，现有的EVT模型假定碰撞风险在整个研究区域内均匀分布，忽略了该区域内不同区域之间的空间效应。本研究提出了一种基于最大稳定过程（MSP）方法的空间EVT建模框架，用于交通冲突分析，同时考虑空间依赖性。利用来自美国101号公路车辆轨迹的交通冲突数据（源自NGSIM数据集），将碰撞时间（TTC）作为冲突指标。使用三种类型的MSP模型来捕捉空间依赖性：施拉特模型、布朗 - 雷斯尼克模型和史密斯模型，每个模型都有相应的相关函数。针对每个MSP模型提出了各种相关函数和链接函数。采用成对复合似然估计方法来估计MSP模型的参数，并使用极值系数指标来描述不同区域之间的空间依赖性。对研究区域内的每个区域估计碰撞风险。模型结果表明，极端交通冲突中存在显著的空间相关性。此外，这些极端冲突中的空间依赖性随距离减小，在较短距离处显示出更强的相关性。在MSP模型中，M1具有最佳的拟合优度，这表明在阈值和尺度参数中纳入空间协变量有效地解释了观测数据中的大量变异。特别是，具有幂指数相关函数的施拉特模型比史密斯模型和布朗 - 雷斯尼克模型表现更好。碰撞风险分析结果表明，内侧（快车道）车道的碰撞风险低于外侧车道；入口匝道处的碰撞风险高于出口匝道。从空间EVT模型估计的碰撞风险与TTC热图一致，特别是在高冲突区域，这证明了空间EVT建模方法用于交通安全分析的可靠性和有效性。
