Model selection in finite mixture of regression models: a Bayesian approach with innovative weighted g priors and reversible jump Markov chain Monte Carlo implementation

Abstract

Finite mixture of regression (FMR) models are aimed at characterizing subpopulation heterogeneity stemming from different sets of covariates that impact different groups in a population. We address the contemporary problem of simultaneously conducting covariate selection and determining the number of mixture components from a Bayesian perspective that can incorporate prior information. We propose a Gibbs sampling algorithm with reversible jump Markov chain Monte Carlo implementation to accomplish concurrent covariate selection and mixture component determination in FMR models. Our Bayesian approach contains innovative features compared to previously developed reversible jump algorithms. In addition, we introduce component-adaptive weighted g priors for regression coefficients, and illustrate their improved performance in covariate selection. Numerical studies show that the Gibbs sampler with reversible jump implementation performs well, and that the proposed weighted priors can be superior to non-adaptive unweighted priors.

Keywords:

• Bayesian variable selection
• finite normal mixtures
• weighted prior
• reversible jump algorithm
• Metropolis–Hastings algorithm

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Acknowledgements

We sincerely thank the anonymous reviewer, Associate Editor, and Editor for their valuable comments, which had substantially improved the manuscript. The views expressed in this article do not represent the official position of the U.S. Food and Drug Administration.

Additional information

Funding

Dr Wei Liu's research was partially supported by the ‘Fundamental Research Funds for the Central Universities’ through Grant [HIT.NSRIF.2012063]. Dr Jian Tao's research was supported by the National Natural Science Foundation of China (Grant No. 11171059).