something like this or fid I missunderstand your question? y ~ (group*stage) * x + (1|partID) or is your question at stage 1 vs stage2?

Hello @Wim Kaijser. I want to see the effect of x on the Stage*Group interaction in terms of y. But I don't want to include x in the interaction. Because there are other covariates besides x. When I look at the interaction, the model complexity becomes high for me since the sample size is relatively small. I know that if I only look at the main effect when adding it to the model as a fixed factor, it will take into account the average of Stage 1 and Stage 2. I want to take into account x in both stages.

I think you are just proposing looking at the model with main effects and some two-way interactions, which is fine if that's all that is of interest. The x:group effect is often sense as a test of homogeneity of covariance so people often check it and drop that term if it is NS.

A simpler - arguably better model is:

y_post ~ y_pre + group + x

... and I'd usually include the interactions with group and covariates but not between covariates:

y_post ~ y_pre + group + x + group:y_pre + group:x

I'd also centre the covariates to aid interpretation (prior to computing interactions). This makes the estimates from group adjusted means.

Thank you for your comprehensive response. I will use the second model you suggested. So, in the formula you propose, is there a way and sense to include the interaction of x (as well as y) with time rather than an average value? Of course, what I want may not be possible. I would be very happy if you could shed some light on this matter. Additionally, I'm asking to find out, what's wrong with the model I'm thinking of using first? Is it because the stage main effect is used twice? Thank you very much for your interest