What's the difference in the interpretation of the model parameters (intercept +slope) in the mixed-effects model and GEE model for poisson and logistic regression?
In models with nonlinear link functions there is indeed a difference in the interpretation of the regression coefficients in GEEs and mixed-effects models. In short,
- GEEs give you the more usual interpretation of comparing groups of subjects. E.g., for dichotomous outcomes and the logit link you get the log-odds ratio between the group of males and the group of females.
- Mixed-effects models give an interpretation conditional on the random effects. E.g., again for dichotomous outcomes and the logit link you get the log-odds ratio if a particular subject would changed sex and from a male he/she became a female.
Because of this more strange interpretation of mixed models with categorical outcomes, people have been suggesting that GEEs are more practical. Nonetheless, GEEs suffer more when you have missing data.
Recently, there has been a solution proposed to bridge the two worlds. Namely, from a mixed model to get coefficients with a marginal interpretation as in GEEs. This is available in the function
marginal_coefs() in the GLMMadaptive package; for more information check here.