I have a mixed effects model with 3 explanatory factors and a full interaction set (including 3 way interaction). This is the full model. Factor 1 is time and I am interested in the change in the response variable over time. Therefore, only factors or interactions where time is present are biologically relevant.
My questions are: 1) Is it better to begin model simplification by removing the highest order (3-way) interaction first, or by removing the least significant term first (which in this case is factor 2)? The 3 way interaction does actually have a relevant interpretation. I have seen both options proposed.
2)Is it okay to include interactions but remove their basic factors (IE include time x treatment when treatment alone is removed from the model)? Several of the basic factors make no sense when not interacting with time. IE measuring the effect of treatment when you are excluding time doesn't make much sense since starting conditions inside each treatment level are identical.
If my hypothesis is correct the final model should include several factor interactions but should not include basic factor 2 or 3 (as they make no sense in the absence of the time factor).
Thank you for your help. I am happy to clarify if my question is ambiguous.