I am on F1 visa and I am inviting and sponsoring my parents to visit USA. While applying for online Visa, there is a column 'Relative's status' and options are 1) U.S. citizen, 2) LPR, 3) Nonimmigrant and 4) Other/I don't know.
What should they fill up over here ?

LPR means green card holder... as F-1, you are nonimmigrant.