(1) This paper is like the papers we have worked in factorial DIF, but it focuses on the performance of LR and MANOVA to detect the influence of interaction. I would be more interested in the evaluation of MG-CFA performance in detecting the impact of grouping memberships and their interactions.
(2) Is four indicators enough to yield stable results?
(3) How was MANOVA be used in CFA models? I thought that such comparsions should be made via model comparisons.