In the sentence:
He considered himself wise.
I would parse this as
He - subject
considered - transitive verb
himself - direct object
wise = object complement adjective
My kids ask me why himself is not a predicate noun. I am not sure how to answer them except that considered is not a linking verb and you need a linking verb to have a predicate noun/adjective.
It still doesn't make sense to them. Is there a rule or just common knowledge about reflexive pronouns that can help me out?