Analyzing different functional forms of the varying weight parameter for finite mixture of negative binomial regression models
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Factors that cause heterogeneity found in motor vehicle crash data are often unknown to transportation safety researchers and failure to capture this heterogeneity in statistical models can weaken the validity of modeling results. A finite mixture of regression models has been proposed to address the unobserved heterogeneity in crash data, and a fixed weight parameter for these models (i.e.; the weight parameter is invariant of the characteristics of the observations under study) is commonly assumed. Recent studies have found that the weight parameter of the finite mixture of negative binomial (NB) models can be dependent upon the functional form of the attributes of the sites, and the selection of the functional form for weight parameter has a significant impact on the classification results. This study investigates the effect of different functional forms on the estimation of the weight parameter as well as the group classification of the finite mixture of NB regression models, using crash data collected on rural roadway sections in Indiana. A total of 11 different functional forms for the varying weight parameter were estimated; these functional forms include various combinations of traffic flow and segment length as covariates. The results suggest that the modeling of the weight parameter (which essentially helps in improving the group classification) is generally necessary when using the finite mixture of NB regression models to analyze the crash data, even in the presence of a well-defined mean function. This study also confirms that the selection of the functional form for weight parameter will affect the classification results significantly. Among 11 different functional forms, one functional form, which uses the linear combination of different explanatory variables to model the classification, stands out based on both the goodness-of-fit statistics and the classification results, and is recommended for describing the weight parameter when using the finite mixture of NB regression models with varying weight parameters to analyze crash data. 2013 Elsevier Ltd.
