Bayesian Regression Model for Counts in Scholarship

Abstract

Discrete Weibul (DW) is considered to have the ability to capture under and over-dispersion simultaneously and also have a closed-form analytical expression of the quantiles of the conditional distribution. There is a need to further investigate how effective the model is, as compared to other competing models in the context of classical and Bayesian technique. In this study, the strength of DW is investigated, for both on frequentist and Bayesian technique. The Bayesian DW adopts parameterization, which makes both parameters of the discrete Weibull distribution to be dependent on the predictors. Bayesian Generalized linear mixed model is also implemented and is compared with the BDW, since Bayesian generalized linear mixed model is known to be robust in handling over-dispersion in count data. A simulation study and real life data was carried out for over and under-dispersed count data. The empirical analysis shows the superiority of Bayesian Generalized linear mixed model over Bayesian DW in the case of over-dispersed data as identified in the simulated data and real life data, but not for under-dispersed data as in the case of simulated study.

Keywords: Discrete Weibull, Bayesian Statistics, MCMCGlmm, over-dispersion, under-dispersion