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

Efficient and Robust Estimation for a Class of Generalized Linear Longitudinal Mixed Models