Albeit with the notable benefits associated with Dirichlet crash frequency models and spatial ones, there is little research dedicated to exploring their combined advantages. Such ensemble approach could be a viable alternative to existing models as it accounts for the unobserved heterogeneity by relaxing the constraints of specific distribution placed on the intercept while addressing the spatial correlations among roadway entities. To fill this gap, the authors aimed to develop Dirichlet semi-parametric models over the over-dispersed generalized linear model framework while also incorporating spatially structured random effects using a distance-based weight matrix.
Five models were developed which include four semi-parametric with flexible intercept and one parametric base model for comparison purposes. The four semi-parametric models entailed two models with a popular specification of stick-breaking Dirichlet process (DP) and two models with an alternative approach of Dirichlet distribution (DD), which are first applied in the field of traffic safety. All four models were estimated for mixture of points (discrete) and mixture of normals (continuous). The posterior density plots for the precision parameter justified the employment of the flexible Dirichlet approach to fit the crash data and supported the assumed prior for the precision parameter. All four Dirichlet models demonstrated the presence of distinct subpopulations suggesting that the intercepts of the models were not generated from a common distribution. The DP model based on mixture of normals illustrated better performance indicating its potential superiority to fit both in-sample and out-of-sample crash data. This finding indicated that the approach of continuous densities, unlike discrete points, may lend more flexibility to fit the data.
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