Department of Civil and Environmental Engineering, The Pennsylvania State University, 231 Sackett Building, University Park, PA, 16802, United States.
Accid Anal Prev. 2021 Jul;157:106173. doi: 10.1016/j.aap.2021.106173. Epub 2021 May 8.
Statistical models of expected crash frequency are referred to as Safety Performance Functions (SPFs) in the first edition of the American Association of State Highway and Transportation Officials' Highway Safety Manual (HSM). The SPFs in the HSM specify expected annual crash frequencies as a function of various roadway and roadside features, with the most important predictor variable being traffic volume, which serves as a measure of vehicle exposure to crashes. Traffic volumes are typically measured using the average annual daily traffic and are incorporated into the SPFs using a natural logarithm transformation. This specification suggests that the relationship between expected crash frequency and traffic volume increases non-linearly with a constant elasticity over the range of observed values. While researchers concur that the relationship between expected crash frequencies and traffic volume is non-linear, further exploration of the functional form of this relationship may offer additional insights concerning the association between safety performance and vehicle exposure. This paper proposes an alternative functional form for the traffic volume variable in SPFs that allows for different elasticities between traffic volume and expected crash frequency within different traffic volume ranges, while preserving the same general non-linear relationship in existing HSM SPFs. Although other forms-like the Hoerl function-have been proposed in the literature, the proposed model allows for natural breakpoints in the traffic volume for which roadway or geometric features might have varying effects on low- or high-volume roads. The proposed functional form was applied to SPFs developed for two-lane rural roadways in Pennsylvania. Comparisons with SPFs developed using the traditional and Hoerl functional forms suggest that this proposed functional form offers an improved fit and predictive performance, and thus might be considered for the development of future SPFs.
期望碰撞频率的统计模型在第一版美国州际公路和运输官员协会（AASHTO）公路安全手册（HSM）中被称为安全性能函数（SPF）。HSM 中的 SPF 将预期的年碰撞频率指定为各种道路和路边特征的函数，最重要的预测变量是交通量，它是衡量车辆与碰撞接触的指标。交通量通常使用年平均日交通量来测量，并通过自然对数变换纳入 SPF 中。这种规格表明，预期碰撞频率与交通量之间的关系随着观察值范围内的弹性常数呈非线性增加。虽然研究人员一致认为预期碰撞频率与交通量之间的关系是非线性的，但进一步探讨这种关系的函数形式可能会提供有关安全性能与车辆暴露之间关联的更多见解。本文提出了一种替代 SPF 中交通量变量的函数形式，允许在不同的交通量范围内，交通量和预期碰撞频率之间具有不同的弹性，同时保持现有 HSM SPF 中相同的一般非线性关系。虽然文献中已经提出了其他形式，如 Hoerl 函数，但所提出的模型允许交通量存在自然断点，道路或几何特征可能对低流量或高流量道路产生不同的影响。所提出的函数形式应用于宾夕法尼亚州双车道农村道路的 SPF 中。与使用传统和 Hoerl 函数形式开发的 SPF 进行比较表明，该提议的函数形式提供了更好的拟合和预测性能，因此可能会考虑用于开发未来的 SPF。
