Can you compare a two-factor solution from CFA to a three-factor solution via Chi²-tests? I got a questionnaire with 30 items and our theory proposes two different factor solutions for this questionnaire. I want to run CFA based on this theory. Solution 1 would include 2 factors on which 15 items load, respectively. Solution 2 would include 3 factors on which different subsets of items would load.
My question is now whether these models would qualify as nested and I can thus compare their model-fit using Chi²-test or a likelihood ratio test.
Thanks!

No.
For model B to be nested within model A, it has to be the case that model A can be made to be the same as model B by fixing some of A's parameters to a set value, typically 0 (removing a loading from CFA is equivalent to fixing it to 0).
What's more, you're not even using the same data for both models in this case, so they're definitely not nested!
