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Our original 2021 SMR article “Non-Invariance? An Overstated Problem with Misconceived Causes” disputes the conclusiveness of non-invariance diagnostics in diverse cross-cultural settings. Our critique targets the increasingly fashionable use of Multi-Group Confirmatory Factor Analysis (MGCFA), especially in its mainstream version. We document—both by mathematical proof and an empirical illustration—that non-invariance is an arithmetic artifact of group mean disparity on closed-ended scales. Precisely this arti-factualness renders standard non-invariance markers inconclusive of measurement inequivalence under group-mean diversity. Using the Emancipative Values Index (EVI), OA-Section 3 of our original article demonstrates that such artifactual non-invariance is inconsequential for multi-item constructs’ cross-cultural performance in nomological terms, that is, explanatory power and predictive quality. Given these limitations of standard non-invariance diagnostics, we challenge the unquestioned authority of invariance tests as a tool of measurement validation. Our critique provoked two teams of authors to launch counter-critiques. We are grateful to the two comments because they give us a welcome opportunity to restate our position in greater clarity. Before addressing the comments one by one, we reformulate our key propositions more succinctly.

Against the Mainstream: On the Limitations of Non-Invariance Diagnostics: Response to Fischer et al. and Meuleman et al.