Like as a preposition and prepositional phrase sub categorization rules

I'm trying to figure out how the sentence "My hands are shaking like crazy," breaks down into lexical categories. I know "like" can function as a preposition, meaning "similar to", but I'm not sure if "like" can be a preposition since I don't think "crazy" is a noun/object in this sentence, and from what I know, PP's require noun phrases as a sub-categorization rule in syntax.

I would say "crazy" is an adverb since it seems to be modifying "shaking", but that leaves me clueless as to how like functions in the sentence.

Please explain the different parts of speech for "like" and "crazy" in this sentence.

Thank you!

Like crazy is an idiom and should be treated as a single word; an adverb describing how my hands were shaking.