I am not sure what you mean by "one variable of seven likert scale variables..." How many distinct levels of the dependent variable do you have? If your final scale combines 7 variables with 7 levels and this results in say 49 distinct levels you probably would be better off running linear regression than logistic regression.

You can use ordered logistic regression with 7 levels (although the assumptions inherent in ordered might not be met forcing you to use multinomial that is unordered logistic regression instead). As always you have to test the assumptions including the ones specific to ordered logistic regression.

I don't know Stata unfortunately (sort of strange your professor required a specific software).