We are analyzing data comparing model fit for men and women using a 2-group SEM analysis and MLR (because of non-normal data). In their 2003 Psychological Methods article, Widaman & Thompson argue that, when one does a 2-group model and imposes constraints to test decrements in model fit, the ordinary null model is not appropriate for calculation of incremental fit indices like CFI. Instead, they maintain that one must use an alternative null model, which varies according to what constraints one puts for invariance in parameters across groups. Further, they indicate that one can't trust SEM software to take care of this issue for him or her. Our question is this: Does MPlus automatically use the appropriate alternative null model when calculating incremental fit indices for 2-group models, or does it use the standard null model? We'd appreciate any light you might provide on this subject.