Analyzing Different Functional Forms of the Varying Weight Parameter for Finite Mixture of Negative Binomial Regression Models

Previously, the weight parameter of the finite mixture of regression models has been assumed to be invariant of the characteristics of the observations under study. Recently, it has been shown that the weight parameter of the finite mixture of negative binomial (NB) models can be dependent upon the attributes of the sites. Since the selection of the functional form for weight parameter has a significant impact on the classification results, there is a need to investigate how different functional forms affect the estimation of the varying weight parameter and whether there is a common functional form that can be properly used to model the weight parameter for different crash datasets. The primary objective of this research is to investigate the effect of different functional forms on estimation of the weight parameter as well as the group classification. To accomplish the study objectives, ten different functional forms for the varying weight parameter were estimated using three different multilane rural highway segment datasets: Texas undivided data, Texas divided data and Washington divided data. The results of this study confirm that the selection of the functional form for weight parameter will affect the classification results significantly. Among ten different functional forms, one functional form stands out for the three datasets. Therefore, when using the finite mixture of NB models with varying weight parameters to analyze the crash data, it is suggested that transportation safety analysts should include Model 5 (which models the classification as a function of the segment length raised to a power) along with other alternative functional forms for describing the weight parameter and select the most appropriate functional form based on not only the goodness-of-fit statistics, but also the classification results.