Bayesian Inference for the Negative Binomial-Sushila Linear Model

Abstract

The aim of this article is to develop a new linear model for count data. The main idea is in an application of a new generalized linear model framework, which we call the Negative Binomial-Sushila linear model. The Negative Binomial-Sushila distribution has been proposed recently and applied to count data. This distribution is constructed as a mixture of the Negative Binomial and Sushila distributions. The mixed distribution is a flexible alternative to the Poisson distribution when over-dispersed count data is analyzed. The parameters of this distribution are estimated using a Bayesian approach with R2jags package of the R language. The Negative Binomial-Sushila linear model is applied to fit two real data sets with an over-dispersion and its performance is compared with the performance of some traditional models. The results show that the Negative Binomial-Sushila generalized linear model fits the data sets better than the traditional generalized models for these data sets.