I am just wondering about the appropriateness of multivariate regression in my research design. As an example, say I have three different dependent measures of similar constructs (e.g. "academic achievement", such as school marks, GPA scores, SAT scores) and accuracy responses on four different trials types (e.g. accuracy on red, black, blue, and white trials) - in two different schools.
If I'm interested in how the three measures of academic achievement predict accuracy on the four trial types (red,black,blue,white), should I be running one multivariate regression (with the two schools as an interaction variable) or three different regression (with the two schools as an interaction variable, with school marks, GPA, SAT scores in separate models)? I am not really interested in holding the other academic achievement measures constant, as they are all likely similar measures of a similar construct? By holding them all constant, I am worried that I will be wiping out any effects that did exist as they are all measures of similar things.
Any answers with minimal maths/equations would be much appreciated. Thanks!