Bayes Factor Approaches for Hypothesis Testing in ANOVA Models

• Activity Number: 450
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 3:05 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Min Wang*
• Companies: Michigan Techonlogical University
• Keywords: ANOVA designs ; g-prior ; Bayes factor ; hypothesis testing ; model selection consistency

Abstract

In this paper, we consider Bayes factor approaches for the hypothesis testing problem in analysis-of-variance (ANOVA) designs. We first reparameterize the ANOVA model with constraints for uniqueness into a classical linear regression model without constraints. Thereafter, we adopt Zellner's g-prior for the regression coefficients and place a hyper-g prior for g, which results in a closed-form expression for Bayes factor without integral representation. In addition, we investigate the consistency of Bayes factors with various g-priors under different asymptotic scenarios. The proposed results generalize some existing ones for the one-way/two-way ANOVA models and can directly be applied to the three or more factorial models. Applications to two real-data sets are presented to compare the performances between the proposed and previous Bayesian methods in the literature.