Texas A&M University, 3136 TAMU, College Station, TX 77843-3136, United States.
Texas A&M Transportation Institute, 3500 NW Loop 410, Suite 315 San Antonio, TX 78229, United States.
Accid Anal Prev. 2022 Jun;170:106638. doi: 10.1016/j.aap.2022.106638. Epub 2022 Mar 24.
The expected crash frequency is the long-term average crash count for a specific site. It is extensively used to systematically evaluate the crash risk associated with roadway elements. To estimate the expected crashes, the Empirical Bayesian (EB) approach is typically employed. The EB method is a computationally convenient approximation to the Full Bayesian (FB) method, which gained popularity due to its simple interpretation, computational efficiency, and the ability to account for the regression to the mean bias. However, the common EB method used in traffic safety analysis is only applicable when the traditional Negative Binomial (NB) model is used. The NB model, however, is not a suitable choice when data is highly dispersed, skewed, or has a large number of zero observations. The Negative Binomial-Lindley (NB-L) model is a mixture of the NB and Lindley distributions and has shown superior fit compared to the NB model, especially when the dataset is characterized by excess zero observations. Even though several studies have used the NB-L in developing crash prediction models, the application of the NB-L in other safety-related tasks (e.g., hot spot identification) is largely neglected. This study proposed a framework to develop the EB method for the NB-L model and subsequently estimate the expected crash values. A comparison between the EB and FB estimates was performed to validate the approximation framework in general. The results indicated that the proposed EB framework is able to estimate expected crashes with comparable precision to the FB estimate, but with much less computational cost. In addition, a site ranking analysis using the EB estimates was conducted to validate the proposed approximation method in safety studies. However, it should be noted that any other type of safety analysis that requires access to the expected crashes can benefit from the proposed EB method. This study concluded that the proposed EB framework can properly approximate the underlying FB approach and can reasonably be considered as an alternative to the traditional EB formula derived from the NB model. The results of this study can help to extend the application of the advanced predictive models beyond predicting crashes to other safety-related tasks, with no additional computational efforts.
期望碰撞频率是特定地点的长期平均碰撞次数。它被广泛用于系统地评估与道路元素相关的碰撞风险。为了估计期望碰撞次数，通常采用经验贝叶斯（EB）方法。EB 方法是全贝叶斯（FB）方法的一种计算方便的近似方法，由于其简单的解释、计算效率以及能够考虑到均值回归偏差，因此广受欢迎。然而，在交通安全分析中常用的通用 EB 方法仅适用于传统负二项式（NB）模型。然而，当数据高度分散、偏斜或有大量零观测值时，NB 模型并不是一个合适的选择。负二项式-林德利（NB-L）模型是 NB 和林德利分布的混合体，与 NB 模型相比，它具有更好的拟合度，尤其是当数据集具有过多的零观测值时。尽管有几项研究已经在开发碰撞预测模型中使用了 NB-L，但 NB-L 在其他安全相关任务（例如热点识别）中的应用在很大程度上被忽视了。本研究提出了一个用于 NB-L 模型的 EB 方法的框架，并随后估计了期望碰撞值。通过比较 EB 和 FB 估计值来验证该近似框架的一般适用性。结果表明，所提出的 EB 框架能够以与 FB 估计值相当的精度估计期望碰撞次数，但计算成本要低得多。此外，还使用 EB 估计值进行了站点排名分析，以验证该近似方法在安全研究中的有效性。然而，需要注意的是，任何需要获取期望碰撞次数的其他类型的安全分析都可以从所提出的 EB 方法中受益。本研究得出的结论是，所提出的 EB 框架可以正确地近似基础 FB 方法，可以合理地考虑作为源自 NB 模型的传统 EB 公式的替代方法。本研究的结果可以帮助将先进的预测模型的应用扩展到预测碰撞以外的其他安全相关任务，而无需额外的计算工作。
