Examining the application of conway-maxwell-poisson models for analyzing traffic crash data

Statistical models have been very popular for estimating the performance of highway safety improvement programs which are intended to reduce motor vehicle crashes. The traditional Poisson and Poisson-gamma (negative binomial) models are the most popular probabilistic models used by transportation safety analysts for analyzing traffic crash data. The Poisson-gamma model is usually preferred over traditional Poisson model since crash data usually exhibit over-dispersion. Although the Poisson-gamma model is popular in traffic safety analysis, this model has limitations particularly when crash data are characterized by small sample size and low sample mean values. Also, researchers have found that the Poisson-gamma model has difficulties in handling under-dispersed crash data. The primary objective of this research is to evaluate the performance of the Conway-Maxwell-Poisson (COM-Poisson) model for various situations and to examine its application for analyzing traffic crash datasets exhibiting over- and under-dispersion. This study makes use of various simulated and observed crash datasets for accomplishing the objectives of this research. Using a simulation study, it was found that the COM-Poisson model can handle under-, equi- and over-dispersed datasets with different mean values, although the credible intervals are found to be wider for low sample mean values. The computational burden of its implementation is also not prohibitive. Using intersection crash data collected in Toronto and segment crash data collected in Texas, the results show that COM-Poisson models perform as well as Poisson-gamma models in terms of goodness-of-fit statistics and predictive performance. With the use of crash data collected at railway-highway crossings in South Korea, several COM-Poisson models were estimated and it was found that the COM-Poisson model can handle crash data when the modeling output shows signs of under-dispersion. The results also show that the COM-Poisson model provides better statistical performance than the gamma probability and traditional Poisson models. Furthermore, it was found that the COM-Poisson model has limitations similar to that of the Poisson-gamma model when handling data with low sample mean and small sample size. Despite its limitations for low sample mean values for over-dispersed datasets, the COM-Poisson is still a flexible method for analyzing crash data.