Objective Bayesian variable selection in linear regression model

Abstract

Variable selection in a regression model with k potential explanatory variables requires the choosing of a model among the possible $2^k$ submodels, which is a difficult task when the number of explanatory variables is moderately large. In this study, we propose the objective Bayesian variable selection procedures where the encompassing of the underlying nonnested linear models is crucial. Based on the encompassed models, objective priors for the multiple testing problem involved in the variable selection problem can be defined. The proposed approach provides a considerable reduction in the size of the compared models by restricting the posterior search for the right models, from $2^k$ to only k + 1, given k explanatory variables. Furthermore, the consistency of the proposed variable selection procedures was checked and their performance was examined using real examples and simulation analyzes by comparing the classical and Bayesian procedures of search in all possible submodels.

Keywords:

• Bayes factor
• consistency
• encompassing
• intrinsic prior
• variable selection
• linear regression model

2010 Mathematics Subject Classification:

• 62F15

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2018R1D1A1B07043352).