Statistica Sinica 10(2000), 647-657

HIERARCHICAL BAYESIAN ANALYSIS

OF BINARY MATCHED PAIRS DATA

Malay Ghosh, Ming-Hui Chen, Atalanta Ghosh and Alan Agresti

University of Florida, Worcester Polytechnic Institute and Lilly Corporate Center

Abstract: The paper introduces a hierarchical Bayesian analysis of binary matched pairs data with noninformative prior distributions. Certain properties of the posterior distributions, including their propriety, are established. The Bayesian methods are implemented via Markov chain Monte Carlo integration techniques, and numerical illustrations are provided. For the logit link, the conditional and marginal maximum likelihood estimators of a treatment effect depend only on the off-main-diagonal elements of a contingency table, and the same is true of McNemar's test. By contrast, the hierarchical Bayes estimators and subsequent analyses depend also on the main-diagonal elements in a natural way.

Key words and phrases: Conditional maximum likelihood estimator, Gibbs sampling, improper prior distribution, logit model, log-log model, Markov chain Monte Carlo, McNemar test, probit model.