Greetings, I am trying to estimate a common factor model for 6 items that show some degree of zero-inflation. I am using MLR. I have 2 questions:
1. When using a zero-inflated model (ZIP or ZINB), should there be separate (and correlated) latent factors for the inflated part and for the count part?
2. Would it be correct to use AIC and BIC to compare the fit of common factor models assuming alternative response distributions (normal, poisson, ZIP, two-part) to get a sense of which fits best? The two-part model comparison seems especially problematic given that the 6 items are converted into 12 items and 2 factors are fitted instead of 1.
Thank you in advance for any direction or references you can provide.
1. That's up to your theorizing. A straightforward model would just let the inflation part be a set of unrestricted means. But Mplus allows a wide set of alternatives, including specifying one or more factors behind the inflation part - and they might be correlated with the factors of the Poisson part.
2.Different distributions have BIC in different metrics, so not comparable. You can compare Poisson and ZIP.