modification index in Amos

Modification indexes assume that the model is correct (Cheung & Rensvold, 1999). Hence, indexes calculated for the fully invariant model are more or less biased depending on the extent of noninvariance. Practically, this implies that the modification index for a respective parameter may not be trustworthy. Furthermore, the sequence by which constraints for  parameters with high modification indexes are relaxed affect the modification indexes for the remaining constrained parameters. It is, for instance, possible that a modification index is substantial in a certain step of the sequence and becomes negligible after relaxing the constraint for another parameter with a larger modification index. Similarly, parameters that have passed one step of the sequence again show a high modification index when elements of a different parameter matrix are constrained (e.g., after successfully passing the test for metric invariance, some loadings show high modification indexes when restricting the intercepts to be equal). 

Steenkamp and Baumgartner (1998), “model respecifications should be conducted cautiously and […] we recommend that invariance constraints be relaxed only when MIs [modification indexes] are highly significant (both in absolute magnitude and in comparison with the majority of others MIs) and EPCs [expected parameters change] are substantial” (p. 81)