I have tried many ways, even removing the glt.
I am interested in testing the difference between the covariation of the two levels of the within-subject factor (A,B) and the Covariate of interest (IntCov) while controlling for a covariate of no interest (NoIntCov).
Any idea?

What kind of variables are Int_Cov and NoInt_Cov? Are they truly between-individual quantitative variables are declared above? If they vary within individuals, they should be treated as within-individual variables. In that case, you should use 3dLMEr:

Let me take one step back. I have started with a model that had an additional within subject factor (Velocity, two levels: fast, slow).
So I ran a 3dLMEr with

This worked, glt included. I am still not sure though why I should choose this model over, let's say, (1+IntCov+NoIntCov|Subj) or (IntCov|Subj).
Then I have a regressor in the first level which is not varying across Velocity, for which I would like to run a similar analysis, therefore the original question and model. Just removing Velocity from the model and running:

in your suggestion you specify the interaction between Session and NoIntCov, which I am not interested in. Why is that?

A statistical model should be constructed to closely reflect the underlying data-generating process, rather than the investigator's interests. As the data owner, you possess prior knowledge that allows you to determine the presence of any interaction effects.

I have started with a model that had an additional within subject factor (Velocity, two levels: fast, slow).

One possibility is to specify the individual-varying (random) effects as the following:

Depending on whether NoIntCov varies across the levels of Session/Velocity, you may want to include NoIntCov as a varying slope in some of the random-effects terms.

Gang Chen

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