We establish a zero-inflated (random-effects) logistic-Gaussian model for clustered binary data in which members of clusters in one latent class have a zero response with probability one, and members of clusters in a second latent class yield correlated outcomes. Response probabilities in terms of random-effects models are formulated, and maximum marginal likelihood estimation procedures based on Gaussian quadrature are developed. Application to esophageal cancer data in Chinese families is presented.
Keywords: Clustered binary data; Gaussian quadratures; logistic-Gaussian model; random-effects models; structured zeros; zero-inflated models.