I have little experience in Pyschology so I can't comment on that aspect
of it, however if you look at the context of the story it seems to me
you come to the conclusion that each of Ranma's separate personalities
are different people.  I came to this conclusion merely using the fact
that that each of them, most significantly Master, had a variety of
abilities which none of the others did, and Master had these abilities
with no training whatsoever.  Perhaps this isn't as strong an argument
for each of the personalities being a separate person as I think but I
believe it does have some weight.

Adrian Gemini