A comprehensive survey of regression-type models for clusters of corre
lated binary outcomes, Including longitudinal data, is presented, In p
articular, we focus on models which can accommodate both between- and
within-cluster categorical and continuous covariates, Emphasis is give
n to motivation of the model specification, interrelationships among m
odels, parameter testing and interpretation, estimation methods (inclu
ding both likelihood and non-likelihood approaches), computational iss
ues, availability of software and other implementation issues, and to
the advantages and disadvantages of the various approaches, Models dis
cussed include naive and response feature models, conditionally specif
ied models, marginal models, and cluster-specific models, Extensions t
o ordinal data and relationships to graphical representations of model
s are also discussed.