Multiple Comparison in ANOVA Models using Bayes Factor

Keywords

ANOVA full and reduced models, Zellner’s g prior, Jeffrey-Zellner-Siow prior, Hyper-g prior, Bayes Factor, Shrinkage Factor and data simulation

Abstract

The traditional ANOVA method is used to compare multiple means followed by the multiple comparison methods to identify the significantly differing pairs on the rejection of null hypotheses. Accordingly, we identify the non-significant treatment pairs in the ANOVA model to formulate suitable reduced models. The present study is to ascertain the strength of the treatments in the model through the Bayesian approach by comparing the full and reduced models with null model based on the Bayes and shrinkage factors. Moreover, we also demonstrate the behaviour of different priors such as Zellner's g-prior, Jeffreys-Zellner- Siow prior and Hyper-g priors based on the Bayes factor. Finally, we validate using the simulated data the nature of variability in Bayes factor among the five priors considered in this study.

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