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Keywords: data augmentation, parameter-expanded data augmentation, correlated binary data, multivariate probit model.
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 are motivated to develop efficient parameter-expanded data augmentations to analyze correlated binary data using multivariate probit models. We investigate both the identifiable and non-identifiable multivariate probit models and develop the corresponding parameter-expanded data augmentation algorithms. 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 data set from the Six Cities study.