  We introduce a flexible parametric mixed effects model for correlated binary
data, with parameters that can be directly interpreted as marginal odds ratios.
This leads to a robust estimation equation with an optimal weighting matrix
being the inverse of a genuine model-based covariance matrix. Flexible
correlation structures can be imposed by correlated random effects, and
correlation parameters can be estimated by solving a composite likelihood score
function. Marginal parameters are consistently estimated even when the
conditional parametric model is misspecified, and the robust estimation
procedure has low estimation efficiency loss compared to the maximum likelihood
estimation under a correct model specification. Simulations, analyses of the
Madras longitudinal schizophrenia study and British social attributes panel
survey were carried out to demonstrate our method.
