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

• Published in: Journal of the Royal Statistical Society. Series B, Statistical methodology Statistical methodology, 1999, Vol.61 (1), p.223-242
• Main Authors: Chen, M.-H., Ibrahim, J. G., Yiannoutsos, C.
• Format: Article
• Language: English
• Subjects: AIDS; Clinical trials; Density estimation; Experimentation; Gibbs sampling; Logistic regression; Modeling; Monte Carlo methods; Normal prior; Parametric models; Posterior distribution; Prior distribution; Probabilities; Regression analysis; Selection of variables
• ISSN: 1369-7412; 1467-9868
• DOI: 10.1111/1467-9868.00173

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 prediction y0 for the response vector and a quantity a0 quantifying the uncertainty in y0. Then, y0 and a0 are used to specify a prior for the regression coefficients semi-automatically. Examples using real data are given to demonstrate the methodology.