Asymptotic Properties of Bayes Factor in One- Way Repeated Measurements Model

Abstract

In this paper, we consider the linear one- way repeated measurements model which has only one within units factor and one between units factor incorporating univariate random effects as well as the experimental error term. In this model, we investigate the consistency property of Bayes factor for testing the fixed effects linear one- way repeated measurements model against the mixed one- way repeated measurements alternative model. Under some conditions on the prior and design matrix, we identify the analytic form of the Bayes factor and show that the Bayes factor is consistent.

Keywords:  One- Way Repeated Measurements Model, ANOVA, Mixed model, Prior Distribution, Posterior Distribution, covariance matrix, Bayes Factor, Consistent.