The Bayes factor for inequality and about equality constrained models
Computational Statistics & Data Analysis
Statistics and Computing
MCMC algorithms for constrained variance matrices
Computational Statistics & Data Analysis
Short communication: An encompassing prior generalization of the Savage-Dickey density ratio
Computational Statistics & Data Analysis
Prior adjusted default Bayes factors for testing (in)equality constrained hypotheses
Computational Statistics & Data Analysis
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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.