A survey off methods for analyzing clustered binary response data

A comprehensive survey of regression-type models for clusters of correlated binary outcomes, including longitudinal data, is presented. In particular, we focus on models which can accommodate both between- and within-cluster categorical and continuous covariates. Emphasis is given to motivation of the model specification, interrelationships among models, parameter testing and interpretation, estimation methods (including both likelihood and non-likelihood approaches), computational issues, availability of software and other implementation issues, and to the advantages and disadvantages of the various approaches. Models discussed include naïve and response feature models, conditionally specified models, marginal models, and cluster-specific models. Extensions to ordinal data and relationships to graphical representations of models are also discussed.