This current study proposes to model crash count and conflict risk measures jointly by developing a multivariate copula-based modeling framework. As conflict risk measures can either be event counts or continuous random variables, the proposed framework is devised to accommodate mixed count-continuous margins. Specifically, three longitudinal conflict risk measures extracted from real-world connected vehicle data collected in Ann Arbor, Michigan as well as rear-end crash count are modeled via the multivariate Gaussian copula. The presence of stronger dependences among conflict risk measures than those between conflict risk measures and crash count are revealed and the dependency structure is relatively stable across different conflict risk measure threshold values and sample sizes. Comparing to the existing crash count and conflict risk measures modeling approaches, the proposed modeling framework also contributes to the transportation safety literature by (a) better reflecting safety by treating conflict risk measures and crashes equally; (b) better accounting for the impact of potential unobserved factors on crash count and conflict risk measures simultaneously; and (c) better accounting for the exposure and traffic risk factors and their heterogenous impact on crash count and conflict risk measures. For practical applications, the proposed copula-based approach not only achieves better in-sample crash count prediction accuracies across different sample sizes of conflict risk measure comparing to several classical crash frequency models in literature, but also connects with the commonly used high-risk location ranking measure, namely potential for safety improvement, for high-risk location identification as there is great similarity between the marginal cumulative distribution functions that constitute the copula and the potential for safety improvement. Based on the total rank differences test, the copula-based high-risk location ranking measure shows the potential to identify high-risk locations that are risky by both crash count and conflict risk measures simultaneously.

这项当前的研究建议通过开发基于多变量copula的建模框架共同对事故计数和冲突风险度量进行建模。由于冲突风险度量既可以是事件计数，也可以是连续的随机变量，因此设计了建议的框架以适应混合的计数-连续边距。具体来说，通过多变量高斯copula对从密歇根州安阿伯市收集的现实世界中连接的车辆数据中提取的三个纵向冲突风险度量以及追尾事故计数进行建模。结果表明，冲突风险度量之间的依赖性比冲突风险度量和崩溃计数之间的依赖性强，并且在不同的冲突风险度量阈值和样本量之间，依赖性结构相对稳定。与现有的事故计数和冲突风险度量建模方法相比，拟议的建模框架还通过以下方面为运输安全文献做出了贡献：（a）通过平等对待冲突风险度量和碰撞来更好地反映安全性；（b）更好地同时考虑潜在的不可观察因素对崩溃数量和冲突风险措施的影响；（c）更好地说明暴露和交通风险因素，以及它们对撞车次数和冲突风险措施的不同影响。在实际应用中，与文献中的几种经典碰撞频率模型相比，所提出的基于copula的方法不仅在冲突风险度量的不同样本大小上实现了更好的样本内碰撞计数预测准确性，而且还与用于高风险位置识别的常用高风险位置排名度量方法（即安全性改善的潜力）相关联，因为构成copula的边际累积分布函数与安全性改善的潜力之间存在极大的相似性。基于总排名差异测试，基于copula的高风险位置排名度量显示了通过崩溃计数和冲突风险度量同时识别高风险位置的潜力。