Analysis of marginally specified semi-nonparametric models for clustered binary data

Generalized linear mixed models are widely used for analyzing clustered data. If the primary interest is in regression parameters, one can proceed alternatively, through the marginal mean model approach. In the present study, a joint model consisting of a marginal mean model and a cluster-specific conditional mean model is considered. This model is useful when both time-independent and time-dependent covariates are available. Furthermore our model is semi-parametric, as we assume a flexible, smooth semi-nonparametric density of the cluster-specific effects. This semi-nonparametric density-based approach outperforms the approach based on normality assumption with respect to some important features of 'between-cluster variation'. We employ a full likelihood-based approach and apply the Monte Carlo EM algorithm to analyze the model. A simulation study is carried out to demonstrate the consistency of the approach. Finally, we apply this to a study of long-term illness data.