I know that mixed-effect models produce subject-specific answers and the GEE produces marginal effect. But I don't get it very well still, I'm sorry for a silly question. Let me explain what exactly bothers me.
Let's assume we have a
mixed model: Response ~ Covariate_A + Time_point + (Time_point | SubjectID). (random slopes and residuals, more or less the unstructured covariance)
GEE Response ~ Covariate_A + Time_point + (1 | SubjectID)
So, a subject is assessed multiple times (t1, t2... tN). The responses can be correlated across the subject.
from the mixed model I get 2 outputs:
the standard fixed effects part with SE "corrected' for the covariance + random effects (variances). Are they the subject-level or population-averaged effects? If not, what are they?
the individual slopes + intercepts (per each subject). Are they the subject-level effects?
from the GEE I get only 1 output:
- the standard fixed effects (adjusted for the intra-covariance in GLS and raw estimates but with sandwich SEs in GEE). Are they the marginal (population-averaged) effects?
Do I interpret those "fixed parts" in a mixed model like subject-specific? So what are the subject-specific slopes and intercepts, returned as a long list (row per subject) by lmer() in R?
Am I right, that in linear models (and not in GLM) the GEE is equivalent to a mixed model in that the population-averaged effects are equivalent to the subject-level ones, only the estimation method changes (and standard errors, as GEE is robust and LMM are model-based)?
What is the sense in having a single number (fixed effect) in LMM and say it's subject-specific, then have also a single number in GEE and say it's population-averaged? Isn't this single number in LMM already averaged over all subjects?