Safety performance functions (SPFs) are the main building blocks in understanding the relationships between crash risk factors and crash frequencies. Many research efforts have focused on high-volume roadways that typically experience more crashes. A few studies have documented SPFs for non-federal aid system (NFAS) roads including rural minor collectors, rural local roads, and urban local roads. NFAS roads are characterized by unique features such as lower speeds, and shorter segment lengths, and they usually experience fewer crashes given the low exposure of these roads. As a result, there is a clear need to investigate the associated safety issues of NFAS roadways and generate distinct SPFs for them. The main objective of this study is to bridge the gap in the literature and develop SPFs for NFAS roads. This study examined the application of traditional negative binomial and zero-favored negative binomial models (i.e., negative binomial-Lindley). Both groups of models were formulated by different variance and dispersion structures. Using crash, roadway inventory, and traffic volume data from 2014 to 2018 in Virginia, the results showed that the NB-L models perform better than the traditional NB models. Furthermore, an appropriate variance structure along with a reasonably chosen dispersion function can further improve the model performance.

安全绩效功能（SPF）是了解撞车危险因素与撞车频率之间关系的主要组成部分。许多研究工作都集中在通常经历更多车祸的大流量道路上。少数研究记录了非联邦援助系统（NFAS）道路的SPF，包括农村未成年人收集器，农村当地道路和城市当地道路。NFAS道路具有独特的特征，例如较低的速度和较短的路段长度，并且由于这些道路的暴露程度较低，它们通常遭受较少的撞车事故。因此，显然有必要调查NFAS道路的相关安全问题并为其生成独特的SPF。这项研究的主要目的是弥合文献中的空白，并开发用于NFAS道路的SPF。这项研究检查了传统的负二项式和零偏好的负二项式模型（即负二项式-Lindley）的应用。两组模型均由不同的方差和分散结构制定。使用2014年至2018年弗吉尼亚州的碰撞，道路库存和交通量数据，结果显示NB-L模型的性能优于传统NB模型。此外，适当的方差结构以及合理选择的色散函数可以进一步改善模型性能。结果表明，NB-L模型的性能优于传统的NB模型。此外，适当的方差结构以及合理选择的色散函数可以进一步改善模型性能。结果表明，NB-L模型的性能优于传统的NB模型。此外，适当的方差结构以及合理选择的色散函数可以进一步改善模型性能。