Models for Generalized Estimating Equation?

Question

From Wikipedia, Generalized Estimating Equation (GEE) is a method to estimate the parameters of a generalized linear model (with an exponential family distribution for the response).

By reading other references online, I am confused whether GEE is an estimation method, or a statistical model like the generalized linear model, but I am inclined to think of GEE as an estimation method, as an alternative to MLE. Am I right?

But it only relies on the mean model (as a function of the parameter), and the variance function (as a function of the mean). If I am correct, it is a maximum quasi-likelihood method (although I also want to ask what a maximum quasi-likelihood method is?).

So GEE doesn't use the entire likelihood offered by the generalized linear model, but only part of it. Is it correct that GEE should be able to apply to bigger models than the generalized linear model?

Thanks and regards!

Answer 1

I prefer to call GEE an estimation method compared to ML or REML, since it combines quasi-likelihood estimation with robust variance estimation to estimate generalized linear marginal models for longitudinal data. Some texts and papers also call "GEE models", e.g. Hedeker, D., & Gibbons, R. D. (2006). Longitudinal data analysis. Wiley-Interscience. I guess it is to separate it from subject-specific (fixed and random effects) models, since GEE is mainly regarded as or marginal (population average) models.

We have no idea about the distribution function of the outcome, but we know its mean ($\mu$) and variance ($V$). So we cannot do ML but we can turn to the quasi-likelihood,

$$Q(\mu,y)=\int^{\mu}_y(y-t)^TV^{-1}dt,$$

and the quasi-likelihood estimating equations (quasi-score function) is

$$\sum_i\frac{\partial{\mu_i^{'}}}{\partial{\beta}}V_i^{-1}(y_i-\mu_i)=0.$$

Thus the estimating equations are derived without specifying the joint distribution of a outcomes but they reduce to the score equations (marginal distributions). The approach based on maximum likelihood (ML) estimation specifies the joint multivariate normal distribution of outcome variables, while the approach of GEE based on the quasi-likelihood specifies only the marginal distributions.

I have seen GEE was applied in statistical genetics, but I am afraid it is also under the framework of generalized linear models.