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I got two interaction terms: One is "female_minority" which is 1 if the person is a female and forms part of an ethnical minority.

"Male_minority" is 1 if the person is a male and forms part of an ethnical minority. If I include both interaction terms in my regression (which already contains gender) will I run into a problem of perfect multicollinearity between both interaction term or is it imperfect multicollinearity? If it's imperfect can somebody explain me why? Down below you find an example of the data in R.

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Thank you in advance

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Yes it is perfect multicollinearity. This is classic dummy variable trap. There will always be perfect -1 correlation between being male and female minority (conditional of having minority as a separate dummy). Hence you cannot put both of them in the same regression with minority dummy.

Moreover, note there is absolutely no reason to put them both in same regression, the baseline regression with minority dummy will already tell you what is the effect of minority males, and then minority females effect is just the minority + minority female effect.

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