There are mainly 3 commonly used ways of analysing repeated observations via model: linear model via GLS estimation, generalized linear model via GEE estimation and mixed models (G)LMM.
Let's forget, for a second, that LMM are conditional and GLS/GEE are marginal ones, let's focus on the general linear model only, when they are equivalent.
I noticed, that people in the biosciences use a lot so called MMRM - mixed effect model for repeated measures. This is not, actually, a "true" mixed model, the name is confusing. Instead it's something that is modelled by SAS mixed-model procedure with the REPEAT part specified and without the RANDOM part (no random effects). I noticed also, that it's often pointed that the corresponding analysis in R is the GLS - nlme::gls()
When I tried to mimic the simplest paired t test, it turned out, that the mixed model correctly handled the degrees of freedom, "understanding" that the same subject was examined multiple times. At the same time, the gls() procedure took... all the observations into consideration, which is called "fake replication". I had to switch to analysis pairs of data to halve the DFs.
When I started analysing data with more than 2 time points, the difference between mixed models (which correctly reported the DF, "guessing" each subject is analysed multiple times) and the gls() were only bigger.
GLS still used all the DFs, as if it was just ordinary linear model, taking all the data into the account, only allowing for different variances at each time point (relaxing the homoscedasticity assumption). Well, that's what GLS does.
But then - how can we use the GLS to analyse repeated observations? This model totally ignores the fact the data come from the same subjects, increasing the DF and thus affecting the p-values.
Could anyone tell me how is that possible and justified, to use the LMM model with, say, random intercepts (which only partially mimics the compound symmetry), where the DFs are correctly reported and GLS (with compound symmetry for example), where the DFs are... twice (or three, ... four) times larger than in GLMM to analyse repeated data?
If we clearly know, that GLS cannot replicate even the simples case, the paired t test (without switching to change scores), but LMM can, how can the GLS be called a suitabble tool to handle repeated data?
Linked topics I started: Is there a way to force nlme::gls to use the same degrees of freedom as the nlme::lme or lme4::lmer?