Abstract:
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Data augmentation has been commonly utilized to analyze correlated binary data using multivariate probit models in Bayesian analysis. However, the identification issue in the multivariate probit models necessitates a rigorous Metropolis-Hastings algorithm for sampling a correlation matrix, which may cause slow convergence and inefficiency of Markov chains. It is well-known that the parameter-expanded data augmentation, by introducing a working/artificial parameter or parameter vector, makes an identifiable model be non-identifiable and improves the mixing and convergence of data augmentation components. Therefore, we develop efficient parameter-expanded data augmentations to analyze correlated binary data using multivariate probit models. We point out that the approaches, based on the non-identifiable models, circumvent a Metropolis-Hastings algorithm for sampling a correlation matrix and outperform those that entail sampling a correlation matrix. We illustrate our proposed approaches using simulation studies and through the application to a longitudinal dataset from the Six Cities study.
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