I haven't seen the movie yet, but from wikipedia it says -
The original concept for the book featured horses instead of monsters. According to Sendak, his publisher suggested the switch when she discovered that he could not draw horses, but thought that he "could at the very least draw 'a thing'!" He replaced the horses with caricatures of his aunts and uncles, whom he had studied critically in his youth as an escape from their weekly visits to his family's Brooklyn home. When working on the opera adaptation of the book with Oliver Knussen, Sendak gave the monsters the names of his relatives: Tzippy, Moishe, Bruno, Emile, and Bernard.
So they are based on real people, but whether or not they are the people in Max's life / emotions is uncertain.