Improving functional form in cross-sectional regression studies to capture the non-linear safety effects of roadway attributes - Freeway median width case study

Crash modification factors (CMFs) for several roadway attributes are based on cross-sectional regression models, in the main because of the lack of data for the preferred observational before-after study. In developing these models, little attention has been paid to those functional forms that reflect the reality that CMFs should not be single-valued, as most available ones are, but should vary with application circumstance. Using a full Bayesian Markov Chain Monte Carlo (MCMC) approach, this study aimed to improve the functional forms used to derive CMFs in cross-sectional regression models, with a focus on capturing the variability inherent in crash modification functions (CMFunctions). The estimated CMFunction for target crashes for freeway median width, used for a case study, indicates that the approach is capable of developing a function that can capture the logical reality that the CMF for a given change in a feature’s value depends not only on the amount of the change but also on the original value. The results highlight the importance of using the functional forms that can capture non-linear effects of road attributes for CMF estimation in cross-sectional models. The case study provides credible CMFs for assessing the safety implications of decisions on freeway median width that could be used in improving current design practice.