Bayesian Tests on Components of the Compound Symmetry Covariance Matrix

• Activity Number: 298
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Joris Mulder*+ and Jean-Paul Fox
• Companies: Tilburg University and University of Twente
• Keywords: Bayes factor ; compound symmetry ; covariance matrices ; Gibbs Sampler ; intra-class correlation

Abstract

Complex dependency structures are often conditionally modeled, where random effects parameters are used to specify the natural heterogeneity in the population. When interest is focused on the dependency structure, inferences can be made from a complex covariance matrix using a marginal modeling approach. In this marginal modeling framework, assumptions about conditional independence and random effects distributions are not required. Furthermore, testing covariance parameters is not a boundary problem in the marginal framework. In this paper, Bayesian tests on covariance parameter(s) of the compound symmetry structure are proposed assuming multivariate normally distributed observations. Innovative proper prior distributions are introduced for the covariance components such that the positive definiteness of the (compound symmetry) covariance matrix is ensured. The proposed priors on the covariance parameters lead to balanced Bayes factors for testing inequality constrained hypotheses. As an illustration, the proposed Bayes factors are used for testing (non-)invariant intra-class correlations across public and Catholic schools using the 1982 High School and Beyond survey data.