Copula-based joint modeling of crash count and conflict risk measures with accommodation of mixed count-continuous margins

Di Yang, Kun Xie, Kaan Ozbay, Zifeng Zhao, Hong Yang

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number100162
JournalAnalytic Methods in Accident Research
StatePublished - Sep 2021


  • Archimedean Copula
  • Crash Count
  • Gaussian Copula
  • Mixed Margins
  • Multivariate Modeling
  • Traffic Conflict

ASJC Scopus subject areas

  • Transportation
  • Safety Research


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