Bayesian multivariate logistic regression |
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Authors: | O'Brien Sean M Dunson David B |
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Institution: | Biostatistics Branch, National Institute of Environmental Health Sciences, Research Triangle Park, North Carolina 27709, USA. obrien4@niehs.nih.gov |
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Abstract: | Bayesian analyses of multivariate binary or categorical outcomes typically rely on probit or mixed effects logistic regression models that do not have a marginal logistic structure for the individual outcomes. In addition, difficulties arise when simple noninformative priors are chosen for the covariance parameters. Motivated by these problems, we propose a new type of multivariate logistic distribution that can be used to construct a likelihood for multivariate logistic regression analysis of binary and categorical data. The model for individual outcomes has a marginal logistic structure, simplifying interpretation. We follow a Bayesian approach to estimation and inference, developing an efficient data augmentation algorithm for posterior computation. The method is illustrated with application to a neurotoxicology study. |
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Keywords: | Block updating Categorical data Data augmentation Latent variables MCMC algorithm Multiple binary outcomes Proportional odds |
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