Bayesian Methods for Correlated Binary Data
Dipak K. Dey, Sujit K. Ghosh, Bani K. Mallick · 2000
ABSTRACT This paper reviews some of the recent developments in the fitting and comparison of Bayesian models for correlated binary data. The importance of the multivariate probit model is highlighted and Markov chain simulation algorithms for the fitting of the multivariate probit, probit normal and hierarchical probit models (the last two for longitudinal data) are discussed. The fitting of each model is illus- trated with the Six Cities Data on the health effects of pollution. The computations are conducted using the new Windows™ software package BAYESTAT that has been developed by the author for the fitting of these and many other Bayesian mod- els. The paper also shows how alternative Bayesian models for correlated binary data can be compared. Marginal likelihoods from Chib&s;s (1995) method are computed for each of five models that reflect different assumptions about the correlation structure and the extent of heterogeneity in the sample. Details of the fitting algorithms are reported in the Appendix.