Analyzing Different Parameterizations of the Varying Dispersion Parameter as a Function of Segment Length

Until a few years ago, the dispersion parameter of Poisson–gamma models had been assumed to be invariant of the characteristics of the observations under study, but recent research in highway safety has shown that the dispersion parameter can depend on the covariates of the model. To account for this dependence, some researchers have reported that the dispersion parameter should be modeled solely as a function of segment length. The primary objective of this research was to examine empirically whether the dispersion parameter should be characterized using only the length of the segment. If not, the secondary objective consisted of determining alternative parameterizations using other covariates that would offer a better approach for characterizing the variance function of Poisson–gamma models. To accomplish the study objectives, 10 parameterizations describing the varying dispersion parameter were estimated with three different data sets collected in Texas, California, and Washington State. Flow-only models were used for comparing the parameterizations. The Akaike information criterion and other related goodness-of-fit (GOF) measures were used for evaluating and comparing the different models. The results of this study show that no single functional form or parameterization is suitable for all the data sets. Traffic flow was more significantly associated with the structured variation observed in the data than segment length. It is therefore recommended that transportation safety analysts evaluate different parameterizations and select the most appropriate one using a combination of GOF criteria, including the significance of the model's coefficients.