Informative g -Priors for Mixed Models

Yu-Fang Chien, Haiming Zhou (), Timothy Hanson and Theodore Lystig
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Yu-Fang Chien: Department of Statistics and Actuarial Science, Northern Illinois University, DeKalb, IL 60115, USA
Haiming Zhou: Department of Statistics and Actuarial Science, Northern Illinois University, DeKalb, IL 60115, USA
Timothy Hanson: Structural Heart & Aortic, Medtronic, Minneapolis, MN 55432, USA
Theodore Lystig: BridgeBio, Palo Alto, CA 94304, USA

Stats, 2023, vol. 6, issue 1, 1-23

Abstract: 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 y i . 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.

Keywords: prior elicitation; g -priors; linear regression; Bayesian model selection; mixed models; variable selection; Bayes factor (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2023
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