Flexible Bayesian Dirichlet mixtures of generalized linear mixed models for count data

Abstract

The need to model count data correctly calls for introducting a flexible yet robust model that can sufficiently handle various types of count data. Models such as Ordinary Least Squares (OLS) used in the past were considered unsuitable. The introduction of the Generalized Linear Model (GLM) and its various extensions was the first breakthrough recorded in modeling count data. Thishis article, propose the Bayesian Dirichlet process mixture prior of generalized linear mixed models (DPMglmm). Metropolis Hasting Monte Carlo Markov Chain (M-H MCMC) was used to draw parameters from target posterior distribution. The Iterated Weighted Least Square (IWLS) proposal was used to determine the acceptance probability in the M-H MCMC phase. Under and over-dispersed count data were simulated, 500 Burn-in was scanned to allow for stability in the chain. 100 thinning interval was allowed so as to nullify the possible effect of autocorrelation in the data due to the Monte Carlo procedure. The DPMglmm and other competing models were fitted to the simulated data, and real-life health insurance claims data sets. The results obtained showed that DPMglmm outperformed MCMCglmm, Bayesian Discrete Weibull, and four other frequentist models. This indicates that DPMglmm is flexible and can fit count data best, either under-dispersed or over-dispersed data.