title: A unifying framework for marginalized random intercept models of correlated binary outcomes.
abstract: We demonstrate that many current approaches for marginal modeling of correlated binary outcomes produce likelihoods that are equivalent to the copula-based models herein. These general copula models of underlying latent threshold random variables yield likelihood-based models for marginal fixed effects estimation and interpretation in the analysis of correlated binary data with exchangeable correlation structures. Moreover, we propose a nomenclature and set of model relationships that substantially elucidates the complex area of marginalized random intercept models for binary data. A diverse collection of didactic mathematical and numerical examples are given to illustrate concepts.
authors.affiliation: Johns Hopkins Bloomberg School of Public Health, 615 N. Wolfe Street, Baltimore, MD 21205.
authors.forename: Bruce J
authors.initials: BJ
authors.lastname: Swihart
authors.affiliation: Johns Hopkins Bloomberg School of Public Health, 615 N. Wolfe Street, Baltimore, MD 21205.
authors.forename: Brian S
authors.initials: BS
authors.lastname: Caffo
authors.affiliation: Johns Hopkins Bloomberg School of Public Health, 615 N. Wolfe Street, Baltimore, MD 21205.
authors.forename: Ciprian M
authors.initials: CM
authors.lastname: Crainiceanu
keywords: Binary outcomes; Copulas; Marginal likelihood; Multivariate logit; Multivariate probit