While he claims to have seen THE WIZARD OF OZ over 50 times while writing the movie, you shouldn’t expect any similar parallels between the home world and the fantasy world. Says Eggers:
We sort of sought actively not to have any direct parallels. That way, it lends itself to the way a brain might work at eight years old, where it’s more dreamlike and there’s a good deal of confusion of who’s who and who in your life represents what. There’s one primary sympathetic female Wild Thing, but you can’t really say it’s Max’s sister. Is it Max’s mom? It’s not really just one; it’s sort of in between. Is Carol Max’s dad? Sort of, in a way, but it’s Max, too.
Eggers adds later that one of his main goals was to keep the film from being “a puzzle that needed to be solved or would click tidily into place.” If you loved the movie, you should absolutely read this article and it will give you an extra layer of insight while at the same time giving you even more to think about.