Psychological profile like anything concerning psychology is subjective. For every diagnosis one psychologist or psychiatrist makes there will be others that disagree.
A IQ test I'm not sure would be of any benefit. There has been several studies that try to determine past president IQ and there is bias involved in that as well. There are many examples in history of high IQ leaders that made terrible blunders or atrocities.
Maybe a better indication is trying to determine if the candidates are truthful.