Revisiting the variability of the dispersion parameter of safety performance for two-lane rural roads

Safety performance functions (SPFs) are commonly calibrated using negative binomial regression in which a dispersion parameter that represents extra-Poisson variation is estimated. The primary use of this parameter is in empirical Bayes (EB) estimation for safety management applications such as treatment evaluation and network screening. It stands to reason, therefore, that the importance of precise estimation of the dispersion parameter should be established. Recent research has suggested that the dispersion parameter is not constant but actually varies from site to site, depending on site characteristics such as segment length. In revisiting the dispersion parameter issue in this empirical investigation, we reinforce previous research on this issue by contributing to a filling number of knowledge gaps. First, we cast light on the dispersion parameter variation for SPFs for two-lane rural roads, an important entity type for which there is little or no knowledge in this regard. In so doing, we investigate more precise model forms to represent the variation with respect to the key variable, segment length. This investigation confirmed that the dispersion parameter is inversely related to segment length but revealed that it is not inversely proportional to segment length as has been suggested in other research. Second, we found that the dispersion parameter is smaller, and the variation less pronounced, with better specified models. Finally, we provide additional evidence to suggest that the dispersion parameter variation matters more for shorter segment lengths.