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I read about generalized estimating equations (GEE) here, here and at other sites.

It is mentioned in first of above links that "the parameter estimates are nearly identical" for linear models but not for non-linear models.

In most situations, we are not able to predict if the relation will be linear. Then, why not perform GEE all the time rather than linear mixed method?

Thanks for your insight.

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I think there could be some confusion caused by those links. I believe the statement about "not for nonlinear models" is actually referring to generalised linear mixed models (GLMMs), for example when the response is binary or a count or generally whenever a non-gaussian link function is used; and not a nonlinear mixed model, such as those that can be fitted with nlme like the logistic growth model $f(x)={\frac {L}{1+e^{-k(x-x_{0})}}}$ where we would no longer have a linear predictor. GLMMs still have a linear predictor, but a lot of the literature on GLMMs talks about them being nonlinear models due to the link function, but not the functional form of the model iteslf. This inevitably can lead to some confusion.

So, usually the debate about GEE vs mixed models is actually about GEE vs GLMM.

GLMMs typically produce estimates that are conditional on the random effects, whereas GEEs average over the random effects to produce marginal estimates. The fundamental difference between the two is in this interpretation of the (fixed) effects. GEEs produce population-averaged effects, while GLMMs produce subject specific effects.

So there is indeed an argument for the use of GEE rather than GLMM when the marginal (population averaged) interpretation is wanted. GEEs are also useful when the correlation structure is mispecified, as the standard errors are robust. On the other hand GEE is know to require larger sample sizes and is not robust to data missing at random whereas GLMMs generally are. Finally, the GLMMAdaptive package in R can produced marginal as well as conditional estimates.

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GEE is an asymptotic method and is less robust than it would appear from its derivation. It may not be accurate in small samples, and it doesn't extend to multiple levels of clustering. It assumes that missing data are missing completely at random and is not robust to non-random dropouts in a longitiudinal study. Finally, GEE invites a disjointed way of thinking because not using a full likelihood means that you can't do a Bayesian GEE, you can only do frequentist GEE.

There are marginal models (i.e., models that don't condition on subject-specific random effects) that are full likelihood that are not GEE. The oldest example is growth curve analysis, now called generalized least squares. This assumes multivariate normality with a parametric correlation structure, and I have a full case study here. But this approach does not extend easily to ordinal and binary Y.

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