"Invitation to" or "invitation for"

What is the appropriate preposition to use with invitation, to or for? I have seen two books that used preposition to. Is it right and what is the explanation of using to instead of for?

[Tdol]

I'd invite someone 'to'a place and'for' an activity. There's some grey area, like 'dinner', which could be seen as either.

I mean for the word invitation.
Example:
I got an invitation (to/for) a party.