Bayesian Analysis for Some Regression Models Applicable to Traffic Accident Data

Abstract

Drawing inference from current data could be more reliable if similar data based on previous studies are used. We propose a full Bayesian approach with the power prior to utilize these data. Ibrahim and Chen (2000) proposed the power prior to incorporate certain information from the historical data available from previous studies. The power prior is constructed by raising the likelihood function of the historical data to the power a_0, where 0<=a_0<=1. The power prior is a useful informative prior in Bayesian inference. We consider zero-inflated Poisson (ZIP) and zero-inflated negative binomial regression (ZINB) models to analyze discrete count data containing a considerable amount of zero observations. We use the power prior to estimate regression coefficients. We use Markov chain and Monte Carlo techniques to execute some computations. Finally, we propose a mixture model of the ZIP and the Poisson regression models (PRM) to analyze zero-inflated data sets drawn from traffic accident studies. The Bayesian information criterion is used to compare the proposed model with the ZIP and the PRM. Based on the membership probabilities, observations are well separated into two clusters. One is the ZIP cluster; the other is the standard Poisson cluster. A real data set is analyzed to demonstrate model fitting performances of the proposed model to determine if it can detect accident-prone spots.