In recent years, there is growing recognition that common unobserved factors that influence crash frequency by one attribute level are also likely to influence crash frequency by other attribute levels. The most common approach employed to address the potential unobserved heterogeneity in safety literature is the development of multivariate crash frequency models. The current study proposes an alternative joint econometric framework to accommodate for the presence of unobserved heterogeneity – referred to as joint negative binomial-multinomial logit fractional split (NB-MNLFS) model. Furthermore, the study undertakes a first of its kind comparison exercise between the most commonly used multivariate model (multivariate random parameter negative binomial model) and the proposed joint approach by generating an equivalent log-likelihood measure. The empirical analysis is based on the zonal level crash count data for different collision types from the state of Florida for the year 2015. The model results highlight the presence of common unobserved effects affecting the two components of the joint model as well as the presence of parameter heterogeneity. The equivalent log-likelihood and goodness of fit measures clearly highlight the comparable performance offered by the proposed joint model relative to the commonly used multivariate approach. Overall, the model interpretations and fit measures clearly highlight the potential complementary role of the proposed approach for crash frequency analyses.

近年来，人们越来越认识到，通过一个属性级别影响碰撞频率的常见不可观察因素也可能通过其他属性级别影响碰撞频率。解决安全文献中潜在的未观察到的异质性最常用的方法是开发多元碰撞频率模型。当前的研究提出了一种替代的联合计量经济学框架，以适应未观察到的异质性的存在-称为联合负二项式多项式对数分数分裂（NB-MNLFS）模型。此外，该研究通过生成等效的对数似然度量，在最常用的多元模型（多元随机参数负二项式模型）与建议的联合方法之间进行了首次同类比较。实证分析基于佛罗里达州2015年不同碰撞类型的区域级碰撞计数数据。模型结果突出显示了影响关节模型两个部分的常见未观察到的影响以及参数异质性。等效对数似然度和拟合优度清楚地凸显了所提出的联合模型相对于常用的多变量方法所提供的可比性能。总体而言，模型的解释和拟合度量清楚地突出了所提出的碰撞频率分析方法的潜在补充作用。模型结果突出显示了影响关节模型两个组件的常见不可观察效应的存在以及参数异质性的存在。等效对数似然性和拟合优度清楚地凸显了所提出的联合模型相对于常用的多变量方法所提供的可比性能。总体而言，模型的解释和拟合度量清楚地突出了所提出的碰撞频率分析方法的潜在补充作用。模型结果突出显示了影响关节模型两个组件的常见不可观察效应以及参数异质性的存在。等效对数似然度和拟合优度清楚地凸显了所提出的联合模型相对于常用的多变量方法所提供的可比性能。总体而言，模型的解释和拟合度量清楚地突出了所提出的碰撞频率分析方法的潜在补充作用。