Generalized estimating equation

In statistics, a generalized estimating equation (GEE) is used to estimate the parameters of a generalized linear model with a possible unknown correlation between outcomes.

Parameter estimates from the GEE are consistent even when the covariance structure is misspecified, under mild regularity conditions. The focus of the GEE is on estimating the average response over the population ("population-averaged" effects) rather than the regression parameters that would enable prediction of the effect of changing one or more covariates on a given individual. GEEs are usually used in conjunction with Huber–White standard error estimates, also known as "robust standard error" or "sandwich variance" estimates. In the case of a linear model with a working independence variance structure, these are known as "heteroscedasticity consistent standard error" estimators. Indeed, the GEE unified several independent formulations of these standard error estimators in a general framework.

GEEs belong to a class of regression techniques that are referred to as semiparametric because they rely on specification of only the first two moments. They are a popular alternative to the likelihood–based generalized linear mixed model which is more sensitive to variance structure specification. They are commonly used in large epidemiological studies, especially multi-site cohort studies, because they can handle many types of unmeasured dependence between outcomes.

Given a mean model ${\displaystyle \mu _{ij}}$ for subject ${\displaystyle i}$ and time ${\displaystyle j}$ that depends upon regression parameters ${\displaystyle \beta _{k}}$, and variance structure, ${\displaystyle V_{i}}$, the estimating equation is formed via:

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