Full Bayesian Poisson-Hierarchical Models for Crash Data Analysis: Investigating the Impact of Model Choice on Site-Specific Predictions

The Poisson-gamma (PG) and Poisson-lognormal (PLN) regression models are among the most popular means for motor-vehicle crash data analysis. Both models belong to the Poisson-hierarchical family of models, which provides a straightforward framework for interpretation of parameters. Over the last two decades, highway safety researchers have increasingly favored a full Bayesian approach to estimation of Poisson-hierarchical models due to its theoretical and computational advantages. While numerous studies have compared the overall performance of alternative Bayesian Poisson-hierarchical models, little research has addressed the impact of model choice on the expected crash frequency prediction at individual sites. This dissertation takes a microscopic approach to comparing the models’ predictions and strives to identify possible trends e.g., that an alternative model’s prediction for sites with certain conditions tends to be higher (or lower) than that from another model. The practical importance of such trends is reflected most clearly when alternative models are utilized to identify hazardous highway sites (e.g., roadway segments, intersection, etc.) by ranking the sites with respect to their expected crash frequency. \n\nIn addition to the PG and PLN models, this research formulates a new member of the Poisson-hierarchical family of models: the Poisson-inverse gamma (PIGam). The PIGam model was of special interest because of the heavy tail of the inverse gamma distribution and the conjectured potential of the PIGam model in dealing with highly over-dispersed data. Four field datasets (from Toronto, Texas, Michigan and Indiana) covering a wide range of over-dispersion characteristics were selected for analysis. \n\nThis study discovered that the disparities between the alternative models predictions are mainly associated with the sites where the observed crash frequency is significantly larger or smaller than expected for a site with similar traffic and physical characteristics. \n\nFor both scenarios, it was demonstrated that the PIGam model tends to predict a higher expectation for crash frequency than would the PLN and PG models, in order. In consequence, sites with unusually high number of observed crashes are likely to be ranked higher (in terms of expected crash frequency) when the PIGam model is used instead of the PLN model, and similarly when the PLN model is used instead of the PG model. \n\nFurthermore, the disparities between alternative model predictions were found to be even more important when the calibrated models were applied to predict crash frequency at sites with no observed crash count. For all four datasets, the PIGam model tended to predict higher expected crash frequencies than did the PLN and PG models, in order. \n\nFinally, a comparison between the models goodness-of-fit using the deviance information criterion (DIC) refuted the conjecture that models with heavy-tailed distributions will certainly perform better as the data become more over-dispersed. The author believes that the relative goodness-of-fit of alternative models to a given dataset is too complicated to be reliably predicted before actually fitting the models. However, the study demonstrated that models with similar measures of goodness-of-fit may predict considerably different crash frequencies at individual sites. This dissertation identified the relationships between alternative models’ predictions at individual sites and described the resulting practical implications of choosing one model over another.

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