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Generalized estimating equations are introduced in an ad hoc fashion for the covariance matrix of a multivariate response. These equations are to be solved jointly with score equations from a generalized linear model for mean parameters. A class of quadratic exponential models is used to develop joint estimating equations for mean and covariance parameters in a more systematic fashion, and proposals for the use of such equations are developed. Comments on the relative merits of the ad hoc and model-based approaches to estimation are given and a regression illustration with a bivariate response is provided.
Prentice et al. (Sun,) studied this question.