Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series A, Pt. 1, pp. 57--85

NECESSARY AND SUFFICIENT CONDITIONS ON THE PROPERIETY OF POSTERIOR DISTRIBUTIONS FOR GENERALIZED LINEAR MIXED MODELS

By

MING-HUI CHEN, University of Connecticut, Storrs
QI-MAN SHAO and DAMING XU, University of Oregon, Eugene

SUMMARY. This paper investigates the properties of the posterior distribution for a generalized linear mixed model (GLMM) using an improper uniform prior for the regression parameters. Necessary and sufficient conditions for the propriety of the posterior distribution with a general link function and a general covariance structure for random effects are obtained. Several special cases, including GLMM's with structured covariances for random effects and binary matched pairs data models, are also considered. Necessary theories are provided, and a real data example is used to demonstrate that the theorems can be applied to obtain proper posteriors.

AMS (1991) subject classification. Primary 62A15, secondary 62E15, 62J12.

Key words and phrases. Improper prior, logit model, log-log model, probit model.

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