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From my understanding, glm(not glmer) and GEE both handle binary values. But GEE is a marginal model and glmer is a random effects model (mixed model). So then what is the main difference between GLM (Not glmer) and GEE? Is GEE a longitudinal data version of GLM? Does it mean you can run 'glm' to only cross-sectional data?

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  • $\begingroup$ Welcome to CV. I'm not an expert in this field, but GLM and GEE are related topics. GLM are a way to extend linear regression, but don't state a way how to determine the generalized parameters. GEE are one possible way to do it. Maybe you could state the question a bit more explicit. $\endgroup$ – cherub Dec 13 '18 at 14:33
  • $\begingroup$ have a look here: stats.stackexchange.com/questions/62939/… $\endgroup$ – chRrr Dec 13 '18 at 14:36
  • $\begingroup$ glm per se uses a specific assumption on the data, for instance, it assumes that the (conditional) distribution of $y$ belongs to the exponential-family of distribution. estimation of the model parameters is then done by maximum likelihood. the estimators solve the so called score functions. a generalization of GLM is quasi-maximum-likelihood, where you just start with the score equations from GLM but don't assume that $y$ belongs to the exponential-family. QML score equations corresponds to the estimation equations in GEE. the latter wording is often used in cross-sectional context. $\endgroup$ – chRrr Dec 13 '18 at 14:52
  • $\begingroup$ more specifically: in QML/GEE you weaken your assumptions on the data. you just assume that it still holds that $E(Y)= g(\alpha + \sum_{r=1}^K \beta_r X_r)$ as well as $Var(Y)= \sigma^2(g(\alpha + \sum_{r=1}^K \beta_r X_r))$, but don't assume that the distribution of $y$ is known anymore. $\endgroup$ – chRrr Dec 13 '18 at 15:04
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    $\begingroup$ Check out McNeish et al (2017) [doi:10.1037/met0000078] for a discussion of the differences among MLM, GEE, and GLM for longitudinal data. $\endgroup$ – Noah Dec 13 '18 at 15:40
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Indeed, GLMs do not account for correlations you may have in your outcome data. Hence, they are more suitable for cross-sectional data, because in longitudinal data you expect that measurements over time from the same subject are correlated.

With regard to the interpretation of the coefficients you obtain, the GEEs can be seen as the equivalent of GLMs because they will also have a marginal intepretation. This is different than generalized linear mixed models, in which the fixed effects coefficients have an interpretation conditional on the random effects (though based on recent developments it is possible to get coefficients with a marginal intepretation from a GLMM; for more info check here).

With regard to the estimation, as mentioned in one of the comments above, GEEs are not based on a model that has a specific likelihood. On the one hand this makes them semi-parametric and you do not need to specify the distribution of your data, but on the other hand (i) you can only use Wald tests and not likelihood ratio tests, (ii) they are less efficient than a likelihood-based model in which you have appropriately specified the correlation structure, and (iii) in their basic form and with regard to missing data, they are only valid under the missing completely at random missing data mechanism, whereas a likelihood-based approach under the missing at random mechanism.

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