  We propose a versatile and computationally efficient estimating equation
method for a class of hierarchical multiplicative generalized linear mixed
models with additive dispersion components, based on explicit modelling of the
covariance structure. The class combines longitudinal and random effects models
and retains a marginal as well as a conditional interpretation. The estimation
procedure combines that of generalized estimating equations for the regression
with residual maximum likelihood estimation for the association parameters.
This avoids the multidimensional integral of the conventional generalized
linear mixed models likelihood and allows an extension of the robust empirical
sandwich estimator for use with both association and regression parameters. The
method is applied to a set of otolith data, used for age determination of fish.
