I've developed somewhat of a theory over the years since its release in 2001.
Many times throughout the films, there's an indication towards Dr. Powell's failed attempt at a marriage, the first time around. I've always wondered as to why this was mentioned, what significance could this possibly hold? That it's questionable as to whether Dr. Powell should be considered to having his life in order?
Sure, Dr. Powell has a beautiful wife and two cute kids, and another whom we don't see till the end of the film played by the fabulous Aaron Paul... but what relevance does this past marriage have?
My opinion, which may be somewhat outlandish, is that Dr. Powell is Robert Porter.
Robert Porter vanished five years ago, and yet Kevin Spacey's role as Prot seems unbelievably close in age to Dr. Powell. Could they have been childhood friends? Apparently, Robert's father was a keen astronomer; something which a member of Dr. Powell's family is also proficient in.
Maybe Prot has returned with complete knowledge of where Robert Porter/Powell had setup his new life - in New York as a psychologist. One could argue how someone would be able to become an obviously well-respected psychologist in 5 years, on top of building a family; but even here - we don't know if Powell's daughters are biologically related to him, and either of them may be under/around the age of 5. Powell also has a dream about the twilight planet of K-PAX, which may be a clue that he's also travelled with Prot at some point or another, and that this warping of time may have afflicted him also.
Powell also had his previous failed marriage, but there's no indication as to what the cause of this was; only that he and his son Michael have developed an alienated relationship.
There were other clues throughout the years I have considered and mulled over, but I don't think it was the intent of the DOP to have people wondering the truth behind it all. I suppose in the end it is quite evident that Prot IS really Robert Porter (the first clue, obviously, being that Prot is an anagram for the first four letters of Porter).