Prior elicitation, variable selection and Bayesian computation for logistic regression models

M.-H. Chen, J. G. Ibrahim, C. Yiannoutsos

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1999 · Volume 61 · Issue 1

Abstract

Bayesian selection of variables is often difficult to carry out because of the challenge in specifying prior distributions for the regression parameters for all possible models, specifying a prior distribution on the model space and computations. We address these three issues for the logistic regression model. For the first, we propose an informative prior distribution for variable selection. Several theoretical and computational properties of the prior are derived and illustrated with several examples. For the second, we propose a method for specifying an informative prior on the model space, and for the third we propose novel methods for computing the marginal distribution of the data. The new computational algorithms only require Gibbs samples from the full model to facilitate the computation of the prior and posterior model probabilities for all possible models. Several properties of the algorithms are also derived. The prior specification for the first challenge focuses on the observables in that the elicitation is based on a prior predictiony0for the response vector and a quantitya0quantifying the uncertainty iny0. Then,y0anda0are used to specify a prior for the regression coefficients semi-automatically. Examples using real data are given to demonstrate the methodology.

Keywords

Gibbs sampling, Logistic regression, Normal prior, Posterior distribution, Prior distribution, Selection of variables

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