Bayes Factors for Testing Equality-Constrained and Order-Constrained Hypotheses on Correlation Matrices

• Activity Number: 604
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
• Sponsor: International Society for Bayesian Analysis (ISBA)
• Author(s): Joris Mulder*+
• Companies: Tilburg University
• Keywords: Bayes factor ; correlation matrix ; balanced prior ; order constraint

Abstract

Bayes factors are developed for testing hypotheses with equality constraints and order constraints on the zero-level correlations in an unstructured correlation matrix. Such hypotheses are often formulated in practice because expectations on correlations are often formulated using order constraints. Therefore, the developed methods can be seen as a useful expansion of testing a correlational "pattern hypothesis" which specifies that certain elements in the correlation matrix are equal to a constant or equal to each other. Another useful aspect of the proposed method is that it can be used for testing multiple non-nested constrained hypotheses which is not possible using classical p-values. Particular attention is paid to proper prior specification of correlation matrices which is crucial when computing Bayes factors. Priors will be considered that (i) result in positive definite correlation matrices, (ii) are `balanced' in the sense that every possible ordering is equally likely a priori, and (iii) result in Bayes factors that are consistent for testing equality-constrained and order-constrained hypotheses on correlation matrices.