I am struggling with conceptual understanding and analytical choice in mixed models.
In a within-subject experiment (2 conditions, factor X), I want to test if the effect of the condition on the outcome response (Y) is influenced by a third variable measured at the subject level (moderator W, at between level).
Thus I coded:
Should I allow the slope of the condition (X) to varying in each of the subjects -->
Would not the variance of the interaction with the between-level moderator (W) be already explained (at least partially) and concealed by the inclusion of the random slope?
If I understood well, the inclusion of the random slope would take from the residual variance all the variance due to unconsidered subject-level variables, including the variance due to the moderator W.
I hope I could explain my doubts clearly... Thank you