Effects of the Varying Dispersion Parameter of Poisson-gamma models on the estimation of Confidence Intervals of Crash Prediction models

The most common probabilistic structure of the models used by transportation safety analysts for modeling motor vehicle crashes are the traditional Poisson and Poissongamma (or Negative Binomial) distributions. Since crash data have been shown to exhibit over-dispersion, Poisson-gamma models are usually preferred over Poisson regression models. Up until recently, the dispersion parameter of Poisson-gamma models has been assumed to be fixed, but recent research in highway safety has shown that the parameter can potentially be dependent upon the covariates, especially for flow-only models. Given the fact that the dispersion parameter is a key variable for computing confidence intervals, there is a reason to believe that a varying dispersion parameter could affect the computation of confidence intervals. The primary objective of this paper is to evaluate whether the varying dispersion parameter affects the computation of the confidence intervals for the gamma mean ( m ) and predicted response ( y ) on sites that have not been used for estimating the predictive model. To accomplish the objective of the study, predictive models with fixed and varying dispersion parameters were estimated using data collected in California at 537 3-legged rural unsignalized intersections. The study shows that models developed using a varying dispersion parameter usually produce smaller confidence intervals, hence more precise estimates, than models with a fixed dispersion parameter both for the gamma mean and the predicted response. Therefore, it is recommended to develop models with a varying dispersion whenever possible, especially if they are used for screening purposes.