In the movie donnie darko why is frank imaginary to donnie in the beginning but real at the end of the movie?

in the beginning donnie see's him like a vision or something. but when gretchen is dead frank is real and says why were they in the middle of the road and than donnie shoots him and kills him. how would he kill frank if he was only imaginary? and than when the airplane killed donnie how is frank real in his room?