Comparison: which one is correct

Question

Which of the following sentences is correct or more idiomatic for comparison between two things:

1. The AUC (the area under curve) for the model A is greater than of the model B
2. The AUC (the area under curve) for the model A is greater than for the model B
3. The AUC (the area under curve) for the model A is greater than of that for the model B
4. The AUC (the area under curve) of the model A is greater than of the model B
5. The AUC (the area under curve) of the model A is greater than the model B

I feel the third one is more precise. However, I wonder if the first and second also are idiomatic and convey the desired meaning.

Answer 1

Either "for" or "of" is fine, just use the same preposition for both. It's fine not to repeat the preposition, as in your fifth example, but this is a style choice. "Of that for", in your third example is incorrect (or at least awkward).

Personally, I wouldn't use "the", since these are the names of the models:

The AUC of Model A is greater than that of Model B.

Notice I use "that of Model B". This is because I feel it's good style to compare "like to like", especially in a scientific publication. Other people might think shorter is better:

The AUC of Model A is greater than (of) Model B.

Again, this is about writing style, not grammar.