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

Up until a few years ago, the dispersion parameter of Poisson-gamma models has 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 potentially be dependent upon the covariates of the model. To account for this dependence, some researchers have reported that the dispersion parameter should solely be modeled as a function of segment length. The primary objective of this research was to empirically examine whether the dispersion parameter should only be characterized using the length of the segment. If not, the secondary objective consisted of determining alternative parametrizations using other covariates that would offer a better approach for characterizing the variance function of Poisson-gamma models. To accomplish the study objectives, ten different parametrizations describing the varying dispersion parameter were estimated using three different datasets collected in Texas, California and Washington. Flow-only models were used for comparing the parametrizations. The Akaike Information Criterion (AIC) and other related goodness-of-fit (GOF) measures were used for evaluating and comparing the different models. The results of this study show that there is no single functional form or parametrization that is suitable for all the datasets. 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 parametrizations and select the most appropriate one using a combination of GOF criteria, including the significance of the model’s coefficients.