Suppose I have data at the individual student level on different components of standardized test scores (e.g. verbal, math, and writing components of SAT), college major chosen, and performance in the college major. The data I have indicates whether a student is in the top quartile, second quartile, third quartile, or fourth quartile for each standardized test component, their specific college major (e.g. chemistry), and their GPA quartile.
I want to determine whether different components have different importance in different college majors. For example, is math score more important to a mechanical engineering major compared to an economics major?
How can I do so? I know how to predict how successful a given student may be (build a machine learning model), but comparing relative importance in different situations seems a bit less obvious to me.