### Abstract

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

Original language | English |
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Pages (from-to) | 109-122 |

Journal | Statistics and Computing |

Volume | 23 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2013 |

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### Cite this

*Statistics and Computing*,

*23*(1), 109-122. https://doi.org/10.1007/s11222-011-9295-3

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*Statistics and Computing*, vol. 23, no. 1, pp. 109-122. https://doi.org/10.1007/s11222-011-9295-3

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

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Bayesian tests on components of the compound symmetry covariance matrix

AU - Mulder, J.

AU - Fox, J.P.

N1 - >2000 woorden

PY - 2013

Y1 - 2013

N2 - 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

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

U2 - 10.1007/s11222-011-9295-3

DO - 10.1007/s11222-011-9295-3

M3 - Article

VL - 23

SP - 109

EP - 122

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

IS - 1

ER -