  We propose a class of continuous-time Markov counting processes for analyzing
correlated binary data and establish a correspondence between these models and
sums of exchangeable Bernoulli random variables. Our approach generalizes many
previous models for correlated outcomes, admits easily interpretable
parameterizations, allows different cluster sizes, and incorporates
ascertainment bias in a natural way. We demonstrate several new models for
dependent outcomes and provide algorithms for computing maximum likelihood
estimates. We show how to incorporate cluster-specific covariates in a
regression setting and demonstrate improved fits to well-known datasets from
familial disease epidemiology and developmental toxicology.
