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Bayesian tests on components of the compound symmetry covariance matrix

Statistics and Computing volume 23, pages109–122(2013)Cite this article

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.

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Author information

Affiliations

  1. Department of Methodology and Statistics, Tilburg University, Tilburg, The Netherlands

    Joris Mulder

  2. Department of Research Methodology, Measurement and Data Analysis, University of Twente, Enschede, The Netherlands

    Jean-Paul Fox

Authors
  1. Joris Mulder
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  2. Jean-Paul Fox
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Correspondence to Joris Mulder.

Additional information

This research was supported by grant NWO-VICI-453-05-002 of the Netherlands Organization for Scientific Research.

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Mulder, J., Fox, J. Bayesian tests on components of the compound symmetry covariance matrix. Stat Comput 23, 109–122 (2013). https://doi.org/10.1007/s11222-011-9295-3

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Keywords

  • Bayes factor
  • Covariance matrices
  • Gibbs Sampler
  • Intra-class correlation
  • Compound symmetry
  • Savage-Dickey density ratio