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Bayesian Multivariate Logistic Regression
Author(s) -
O'Brien Sean M.,
Dunson David B.
Publication year - 2004
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2004.00224.x
Subject(s) - logistic regression , categorical variable , multivariate statistics , statistics , multinomial logistic regression , mathematics , prior probability , binary data , econometrics , logistic model tree , logistic distribution , bayesian probability , bayesian multivariate linear regression , computer science , regression analysis , binary number , arithmetic
Summary 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.