Extension of a Negative Binomial GARCH Model: Analyzing the Effects of Gasoline Price and VMT on DUI Fatal Crashes in Texas

Traditional crash count models, such as the Poisson and Negative Binomial models, do not account for the temporal correlation of crash data. In reality, crashes that occur in close proximity in time are likely to share unobserved effects which may have been excluded from the model. If the temporal correlation of crash data is ignored, the estimated parameters could be less precise and biased. Therefore, there is a need to extend the standard crash count data models by incorporating temporal dependence. Whereas the literature for modeling time series count data is well developed, its applications for traffic crash data are limited. A particularly flexible model for time series of counts is the Negative Binomial Integer-valued Generalized Autoregressive Conditional Heteroscedastic (NBINGARCH) model which properly accounts for the overdispersion, non-negativity, and integer-valued features of count data. In this paper, the NBINGARCH model is extended to incorporate covariates, so that the relationship between a time series of counts and correlated external factors may be properly modeled. Improved performance of the NBINGARCH model is demonstrated through a simulation study and an application to monthly DUI (driving under the influence) fatal crashes in Texas between 2003 and 2009. In addition, the relationship between monthly vehicle miles travelled (VMT) and gasoline prices in Texas was also examined. Ultimately, it is concluded that gasoline prices had no significant effect on DUI fatal crashes in Texas, while VMT had a positive effect. Ye, Garcia, Pourahmadi, and Lord