If the author mentioned DIF detection as one of purposes, the setting of matching variable should be concerned more. But the author just described the detection of interaction effect by using the multigroup model. Therefore I think this study might be extended simply to DIF issue.
After the detection of interaction effect, is it necessary to detect which level of groups the difference occurred? I mean it is like that after test of interaction of ANOVA, we need to test the simple main effect. Whether we should further to detect the simple main effect by using multigroup model?