Bayesian tests on components of the compound symmetry covariance matrix

J. Mulder, J.P. Fox

Research output: Contribution to journalArticleScientificpeer-review

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, testing covariance parameters is not a boundary problem. 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. Furthermore, it is shown that the proposed priors on the covariance parameters lead to a balanced Bayes factor, in case of testing an inequality constrained hypothesis. As an illustration, the proposed Bayes factor is used for testing (non-)invariant intra-class correlations across different group types (public and Catholic schools), using the 1982 High School and Beyond survey data.
Keywords: Bayes factor, Covariance matrices, Gibbs Sampler, Intra-class correlation, Compound symmetry, Savage-Dickey density ratio
Original languageEnglish
Pages (from-to)109-122
JournalStatistics and Computing
Volume23
Issue number1
DOIs
Publication statusPublished - 2013

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Compound Symmetry
Covariance matrix
Bayes Factor
Intraclass Correlation
Testing
Positive Definiteness
Gibbs Sampler
Survey Data
Boundary Problem
Prior distribution
Random Effects
Modeling
Invariant
Symmetry
Bayes factor

Cite this

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Bayesian tests on components of the compound symmetry covariance matrix. / Mulder, J.; Fox, J.P.

In: Statistics and Computing, Vol. 23, No. 1, 2013, p. 109-122.

Research output: Contribution to journalArticleScientificpeer-review

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AB - 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, testing covariance parameters is not a boundary problem. 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. Furthermore, it is shown that the proposed priors on the covariance parameters lead to a balanced Bayes factor, in case of testing an inequality constrained hypothesis. As an illustration, the proposed Bayes factor is used for testing (non-)invariant intra-class correlations across different group types (public and Catholic schools), using the 1982 High School and Beyond survey data.Keywords: Bayes factor, Covariance matrices, Gibbs Sampler, Intra-class correlation, Compound symmetry, Savage-Dickey density ratio

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