Generalized estimating equations: A hybrid approach for mean parameters in multivariate regression models

We propose an extension of the generalized estimating equation approach to multivariate regression models (Liang and Zeger, 1986) which allows the estimation of dispersion and association parameters in the covariance matrix partly using estimating equations as in Prentice and Zhao (1991), and partly by the direct use of consistent estimators. The advantages of this hybrid approach over that of Prentice and Zhao (1991) are a reduction in the number of fourth moment assumptions that must be made, and the consequent reduction in numerical complexity. We show that the type of estimation used for covariance parameters does not affect the asymptotic efficiency of the mean parameter estimates. The advantages of the hybrid model are illustrated by a simulation study. This work was motivated by problems in statistical genetics, and we illustrate our approach using a twin study examining association between the osteocalcin receptor and various osteoporisis-related traits.