Invitee speculated on the radio (5)
I believe the answer is:
guest
'invitee' is the definition.
(synonyms)
'speculated on the radio' is the wordplay.
'speculated' becomes 'guessed' (guessing is a kind of speculating).
'on the radio' shows a homophone (sound like).
'guessed' is a homophone of 'GUEST'.
(Other definitions for guest that I've seen before include "Someone invited" , "One who's invited" , "See 2" , "Invited person" , "Visitor, lodger" .)