A New Perspective on Priors for Generalized Linear Models

Edward J. Bedrick, Ronald Christensen, Wesley Johnson

Research output: Contribution to journalArticlepeer-review

187 Scopus citations

Abstract

This article deals with specifications of informative prior distributions for generalized linear models. Our emphasis is on specifying distributions for selected points on the regression surface; the prior distribution on regression coefficients is induced from this specification. We believe that it is inherently easier to think about conditional means of observables given the regression variables than it is to think about model-dependent regression coefficients. Previous use of conditional means priors seems to be restricted to logistic regression with one predictor variable and to normal theory regression. We expand on the idea of conditional means priors and extend these to arbitrary generalized linear models. We also consider data augmentation priors where the prior is of the same form as the likelihood. We show that data augmentation 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.

Original languageEnglish (US)
Pages (from-to)1450-1460
Number of pages11
JournalJournal of the American Statistical Association
Volume91
Issue number436
DOIs
StatePublished - Dec 1 1996
Externally publishedYes

Keywords

  • Conditional means priors
  • Data augmentation priors
  • Exponential regression
  • Gamma regression
  • Linear models
  • Log-linear models
  • Logistic regression
  • Poisson regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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