A NEW PERSPECTIVE ON PRIORS FOR GENERALIZED LINEAR-MODELS

This article deals with specifications of informative prior distributi ons for generalized linear models. Our emphasis is on specifying distr ibutions for selected points on the regression surface; the prior dist ribution on regression coefficients is induced from this specification . We believe that it is inherently easier to think about conditional m eans of observables given the regression variables than it is to think about model-dependent regression coefficients. Previous use of condit ional means priors seems to be restricted to logistic regression with one predictor variable and to normal theory regression. We expand on t he idea of conditional means priors and extend these to arbitrary gene ralized linear models. We also consider data augmentation priors where the prior is of the same form as the likelihood. We show that data au gmentation priors are special cases of conditional means priors. With current Monte Carlo methodology, such as importance sampling and Gibbs sampling, our priors result in tractable posteriors.