The existence of preponderant zero crash sites and/or sites with large crash counts can present challenges during the statistical analysis of crash count data. Additionally, unobserved heterogeneity in crash data due to the absence of important variables could negatively impact the estimated model parameters. The traditional negative binomial (NB) model with fixed parameters might not adequately handle highly over-dispersed data or unobserved heterogeneity. Many research efforts that have involved the negative binomial–Lindley (NB-L) model or the random parameters negative binomial (RPNB) model, for example, have attempted to improve the inference of estimated coefficients by explicitly accounting for extra variation in crash data. The NB-L is a mixed modeling approach which provides flexibility to account for additional dispersion in data. The RP modeling approach accommodates the effect of unobserved variables by allowing the model parameters to vary from one observation to another. The following study proposes a combination of these models – the random parameters NB-L (RPNB-L) generalized linear model (GLM) – to account for underlying heterogeneity and address excess over-dispersion. The results show that the RPNB-L model not only provides a superior goodness-of-fit (GOF) with the sample data, but also offers a better understanding about the effects of potential contributing factors. The paper uses the Bayesian framework to provide a strategy for eliminating the potential for poor mixing in the Markov Chain Monte Carlo (MCMC) chains during the estimation of the RPNB-L model.

优势零崩溃站点和/或具有大崩溃计数的站点的存在会在对崩溃计数数据进行统计分析期间提出挑战。此外，由于缺少重要变量而导致的崩溃数据中未观察到的异质性可能会对估计的模型参数产生负面影响。具有固定参数的传统负二项式（NB）模型可能无法充分处理高度过度分散的数据或未观察到的异质性。例如，许多涉及负二项式-Lindley（NB-L）模型或随机参数负二项式（RPNB）模型的研究尝试通过明确考虑碰撞数据的额外变化来改善估计系数的推论。NB-L是一种混合建模方法，可提供灵活性以解决数据中的其他分散问题。RP建模方法通过允许模型参数从一个观察值到另一个观察值变化来适应未观察到的变量的影响。以下研究提出了这些模型的组合-随机参数NB-L（RPNB-L）广义线性模型（GLM）-以说明潜在的异质性并解决过度的过度分散问题。结果表明，RPNB-L模型不仅为样本数据提供了出色的拟合优度（GOF），而且还提供了对潜在影响因素影响的更好理解。本文使用贝叶斯框架提供了一种在RPNB-L模型估计期间消除马尔可夫链蒙特卡洛（MCMC）链中混合不良的可能性的策略。