In my task, there are 8 levels of a within-subjects/repeated measure factor. The overall relationship that this factor has with the DV is in the shape of an inverted-U, such that their DV scores at levels 1 and 8 are generally lowest, and those at 4 and 5 are highest.
What I want to test is whether my individual difference measure interacts with the within-subjects factor to make the inverted U (quadratic) shape fit better or worse. My hypothesis is that those high on my indiv diff measure will have more of a straight line than the curvey one in the overall sample. And I'd like to keep the indiv diff measure continuous.
Input and insights on good statistical approaches to this question are greatly appreciated!