Determination of Optimal Spatial Sample Sizes for Fitting Negative Binomial-Based Crash Prediction Models with Consideration of Statistical Modeling Assumptions

Abstract

Transportation authorities aim to boost road safety by identifying risky locations and applying suitable safety measures. The Highway Safety Manual (HSM) is a vital resource for US transportation professionals, aiding in the creation of Safety Performance Functions (SPFs), which are predictive models for crashes. These models rely on Negative Binomial distribution-based regression and misinterpreting them due to unmet statistical assumptions can lead to erroneous conclusions, including inaccurately assessing crash rates or missing high-risk sites. The Florida Department of Transportation (FDOT) has introduced context classifications to HSM SPFs, complicating assumption violation identification. This study, part of an FDOT-sponsored project, investigates established statistical diagnostic tests to identify model violations and proposes a novel approach to determine optimal spatial regions for Empirical Bayes adjustment. This adjustment aligns HSM-SPFs with regression assumptions. The study employs a case study involving Florida roads. Results indicate that a 20-mile radius offers an optimal spatial sample size for modeling crashes of all injury levels, ensuring accurate assumptions. For severe injury crashes, which are less frequent and harder to predict, a 60-mile radius is suggested to fulfill statistical modeling assumptions. This methodology guides FDOT practitioners in assessing the conformity of HSM-SPFs with intended assumptions and determining appropriate region sizes.