LATENT VARIABLE MODELS FOR CLUSTERED DICHOTOMOUS DATA WITH MULTIPLE SUBCLUSTERS

Regression models for clustered binary data are derived from nonlinear mixed models in terms of latent normal variables. The marginal response probabilities are functions of covariates through generalized linear models. Within a cluster, the pairwise tetrachoric correlations are all equal and are not restricted by marginal probabilities. This approach accommodates hierarchically nested binary data. An algorithm for estimation using generalized estimating equations is proposed. An example illustrates the application of this approach.