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

摘要

Statistical models have been very popular for estimating the performance of highwaysafety improvement programs which are intended to reduce motor vehicle crashes. Thetraditional Poisson and Poisson-gamma (negative binomial) models are the most popularprobabilistic models used by transportation safety analysts for analyzing traffic crashdata. The Poisson-gamma model is usually preferred over traditional Poisson modelsince crash data usually exhibit over-dispersion. Although the Poisson-gamma model ispopular in traffic safety analysis, this model has limitations particularly when crash dataare characterized by small sample size and low sample mean values. Also, researchershave found that the Poisson-gamma model has difficulties in handling under-dispersedcrash data. The primary objective of this research is to evaluate the performance of theConway-Maxwell-Poisson (COM-Poisson) model for various situations and to examineits application for analyzing traffic crash datasets exhibiting over- and under-dispersion.This study makes use of various simulated and observed crash datasets for accomplishingthe 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 credibleintervals are found to be wider for low sample mean values. The computational burden ofits implementation is also not prohibitive. Using intersection crash data collected inToronto and segment crash data collected in Texas, the results show that COM-Poissonmodels 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-highwaycrossings in South Korea, several COM-Poisson models were estimated and it was foundthat the COM-Poisson model can handle crash data when the modeling output showssigns of under-dispersion. The results also show that the COM-Poisson model providesbetter statistical performance than the gamma probability and traditional Poisson models.Furthermore, it was found that the COM-Poisson model has limitations similar to that ofthe Poisson-gamma model when handling data with low sample mean and small samplesize. Despite its limitations for low sample mean values for over-dispersed datasets, theCOM-Poisson is still a flexible method for analyzing crash data.