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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.

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One approach from the classical statistics domain (which will be your friend, especially if you don't have a big data set) is to run ordinal regression with GPA quartiles as the dependent variables, and with interaction terms between major dummies/factor and the SAT components. The coefficients on the interaction terms will tell you the relative importance of the sub-group. For example, the coefficient on the sat_math*major_math term will give you insight into the relative importance of the math SAT scores for math majors in predicting GPA.

Be careful with how you code the ordinal variables, you don't want your statistical software to think that they are continuous or categorical variables (unless you explicitly want to do that).

p.s. if you have access to continuous versions of GPA and test scores, I would use those and run OLS regression with interaction terms.

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