Mixtures of marginal models

In this paper, we adapt a mixture model originally developed for regression models with independent data for the more general case of correlated outcome data, which includes longitudinal data as a special case. The estimation is performed by a generalisation of the EM algorithm which we call the Expectation-Solution (Es) algorithm. In this Es algorithm the M-step of the EM algorithm is replaced by a step requiring the solution of a series of generalised estimating equations. The Es algorithm, a general algorithm for solving generalised estimating equations with incomplete data, is then applied to the present problem of mixtures of marginal models. In addition to allowing for correlation inherent in correlated outcome data, the systematic component of this mixture of marginal models is more flexible than the conventional linear function. The methodology is applied in the contexts of normal and Poisson response data. Some theory regarding the Es algorithm is presented.