"I have a feeling that you are like me."
Translation:Jag har en känsla av att du är som jag.
This is because when 2 objects are compared, both are treated as the subjects of the sentence, ie, nominative. the grammatically correct english sentence should be, "you are like I". other similar examples are 'I am like he/she', 'you are better than I' and 'I am as good as he'. they all sound weird, but are nevertheless correct grammatically, and still said that way in languages like german and swedish. but it might change in the future (just like in english), no doubt as seen in the comment below, as English has a huge influence on modern swedish.