Abstract
We consider Bayesian approaches for the hypothesis testing problem in the analysis-of-variance (ANOVA) models. With the aid of the singular value decomposition of the centered designed matrix, we reparameterize the ANOVA models with linear constraints for uniqueness into a standard linear regression model without any constraint. We derive the Bayes factors based on mixtures of -priors and study their consistency properties with a growing number of parameters. It is shown that two commonly used hyper-priors on (the Zellner-Siow prior and the beta-prime prior) yield inconsistent Bayes factors due to the presence of an inconsistency region around the null model. We propose a new class of hyper-priors to avoid this inconsistency problem. Simulation studies on the two-way ANOVA models are conducted to compare the performance of the proposed procedures with that of some existing ones in the literature.
Citation
Min Wang. "Mixtures of -Priors for Analysis of Variance Models with a Diverging Number of Parameters." Bayesian Anal. 12 (2) 511 - 532, June 2017. https://doi.org/10.1214/16-BA1011
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