A Generalized Estimating Equations

When inferences focus on population averages, one can directly model all of the marginal expectations E(Yij) = μij in terms of covariates of interest. This is typically done via h(μij) = x ′ ijβ, with h(·) some known link function, such as the logit link for binary responses. The marginal variance depends on the marginal mean according to Var(Yij) = v(μij)φ, where v(·) is a known variance function and φ is a scale (overdispersion) parameter. The correlation between Yij and Yik is expressed via a correlation matrix Ri(α) where α is a vector of nuisance parameters. The covariance matrix Vi of Y i can then be written as Vi = Vi(β,α) = φA 1/2 i RiA 1/2 i , with Ai the matrix with the marginal variances on the main diagonal and zeros elsewhere. Generalized estimating equations take the form