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Bayesian multivariate logistic regression
Authors:O'Brien Sean M  Dunson David B
Institution:Biostatistics Branch, National Institute of Environmental Health Sciences, Research Triangle Park, North Carolina 27709, USA. obrien4@niehs.nih.gov
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.
Keywords:Block updating  Categorical data  Data augmentation  Latent variables  MCMC algorithm  Multiple binary outcomes  Proportional odds
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