On the Bayesian Mixture of Generalized Linear Models with Gamma-Distributed Responses

Abstract

This paper proposes enhanced studies on a model consisting of a finite mixture framework of generalized linear models (GLMs) with gamma-distributed responses estimated using the Bayesian approach coupled with the Markov Chain Monte Carlo (MCMC) method. The log-link function, which relates the mean and linear predictors of the model, is implemented to ensure non-negative values of the predicted gamma-distributed responses. The simulation-based inferential processes related to the Bayesian-MCMC method is carried out using the Gibbs sampler algorithm. The performance of proposed model is conducted through two real data applications on the gross domestic product per capita at purchasing power parity and the annual household income per capita. Graphical posterior predictive checks are carried out to verify the adequacy of the fitted model for the observed data. The predictive accuracy of this model is compared with other Bayesian models using the widely applicable information criterion (WAIC). We find that the Bayesian mixture of GLMs with gamma-distributed responses performs properly when the appropriate prior distri­butions are applied and has better predictive accuracy than the Bayesian mixture of linear regression model and the Bayesian gamma regression model.