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A stochastic model is proposed for the study of the influence of time-dependent covariates on the marginal distribution of the binary response in serially correlated binary data. Markov chains are expressed in terms of transitional rather than marginal probabilities. We show how to construct the model so that the covariates relate only to the mean value of the process, independently of the association parameter. After formulating the stochastic model for a simple sequence of data with possibly missing data, the same approach is applied to a repeated measures setting and illustrated with a real data example.
Adelchi Azzalini (Sat,) studied this question.