Bayes factor consistency for unbalanced ANOVA models

Abstract

In practical situations, most experimental designs often yield unbalanced data which have different numbers of observations per unit because of cost constraints, missing data, etc. In this paper, we consider the Bayesian approach to hypothesis testing or model selection under the one-way unbalanced fixed-effects analysis-of-variance (ANOVA) model. We adopt Zellner's g-prior with the beta-prime distribution for g, which results in an explicit closed-form expression of the Bayes factor without integral representation. Furthermore, we investigate the model selection consistency of the Bayes factor under three different asymptotic scenarios: either the number of units goes to infinity, the number of observations per unit goes to infinity, or both go to infinity. The results presented extend some existing ones of the Bayes factor for the balanced ANOVA models in the literature.

Keywords:

• hypothesis testing
• Zellner's g-prior
• Bayes factor
• unbalanced ANOVA model
• model selection consistency

2000 MSC: :

• 62F15
• 62J10
• 62F03

Acknowledgements

The authors are very grateful to the Editor, an Associate Editor and two anonymous referees for their constructive suggestions that led to several improvements of this paper.