Using Markov chains for marginal modelling for binary longitudinal data in an exact likelihood approach

The analysis of longitudinal data where the response variable is binary is considered from the point of view of likelihood inference, which requires complete specification of a stochastic model for the individual profile. The problem is tackled using binary Markov chains as the basic stochastic mechanism; this must however be suitably parametrised in order to model the marginal behaviour of the observations. Random effects are also considered, in addition to the above form of serial dependence. The methodology is illustrated with a numerical example.