Informative g-Priors for Mixed Models

Zellner's objective g-prior has been widely used in linear regression models due to its simple interpretation and computational tractability in evaluating marginal likelihoods. However, the g-prior further allows portioning the prior variability explained by the linear predictor versus that of pure noise. In this paper, we propose a novel yet remarkably simple g-prior specification when a subject matter expert has information on the marginal distribution of the response yi. The approach is extended for use in mixed models with some surprising but intuitive results. Simulation studies are conducted to compare the model fitting under the proposed g-prior with that under other existing priors.