I want to model Multidimensional Item Response Theory (MIRT) in Mplus but I am struggling with the concept of compensatory and non-compensatory models . Suppose that I have a test comprising 20 items and two dimensions (e.g. f1 and f2). When I assume compensatory model it means that f1 and f2 have additive form in determining probability of a correct answer. In non-compensatory model we assume that f1 and f2 have multiplicative form(i.e. interaction between f1 and f2).

If we assume that all items have loadings on both f1 and f2, how can I model compensatory and non-compensatory models in Mplus?

Any help and idea is appreciated.

Thanks,