Comparison of Sichel and Negative Binomial Models in Estimating Empirical Bayes Estimates

Traditionally, transportation safety analysts have used the empirical Bayes (EB) method to improve the estimate of the long-term mean of individual sites and to identify hotspot locations. The EB method combines two sources of information: (a) the expected number of crashes estimated by crash prediction models and (b) the observed number of crashes at individual sites. Because of the overdispersion commonly found in crash data, a negative binomial (NB) modeling framework has been used extensively in crash prediction estimation models. Recent studies have shown that the Sichel (SI) distribution provides a promising avenue for developing crash prediction models. The objective of this study was to examine the application of the SI model in calculating EB estimates. The study used crash data collected at four-lane undivided rural highways in Texas to develop SI models with fixed and varying dispersion terms. The results led to the following main conclusions: (a) the selection of the crash prediction model (i.e., the SI or the NB model) affected the value of the weight factor used for estimating the EB output and (b) the identification of hazardous sites, based on the EB method, could be different when the SI model was used. Finally, a simulation study that is designed to examine which crash prediction model can identify hotspots better is recommended for future research.