Your model specification involves two key aspects.
First, what is the response (outcome) variable, and how does MathAbility
relate to the other variables? For some effects of interest, including MathAbility
in the model may require justification, as discussed in this blog post.
Second, the key difference between the two models you mentioned is in their assumptions about MathAbility
. In the first model, its effect is assumed to be constant across hemispheres and regions, whereas in the second model, it is allowed to vary across these factors.
Gang Chen