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

Research output: Journal contributionsComments / Debate / ReportsResearch


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.

Original languageEnglish
JournalSociological Methods and Research
Number of pages18
Publication statusAccepted/In press - 2022

    Research areas

  • compositional Substitutability, emancipative Values, measurement Equivalence, nomological Performance, Non-Invariance
  • Politics