What do you mean X? vs What do you mean by X? - Is the omission of the preposition "by" grammatical?

People sometimes say "What do you mean X", e.g. "What do you mean I’m funny?", "What do you mean I’m not going to the party? Of course I’m going!", etc. I completely understand these sentences, but I get the sense that the preposition by is being omitted. Is the construction "what do you mean X" grammatical, and how is it any different to the construction "what do you mean by X"? Are there specific contexts in which one construction is preferred over the other?