Measurement Invariance is Not Sufficient for Meaningful and Valid Group Comparisons: A Note on Robitzsch and Lüdtke

Abstract

This note demonstrates that measurement invariance does not guarantee meaningful and valid group comparisons in multiple-population settings. The article follows on a recent critical discussion by Robitzsch and Lüdtke, who argued that measurement invariance was not a pre-requisite for such comparisons. Within the framework of common factor analysis, we show that measurement invariance is in general not a sufficient condition for evaluating comparable constructs in all groups under consideration. We conclude with a discussion of related issues pertaining to population invariant measurement and the examination of latent differences and similarities in multi-group studies.

Keywords:

• Conditional distribution
• construct
• measurement invariance
• sufficient condition

Notes

1 The indicated substantive meaning “alignment” of the observed measures employed in multiple population settings, may well be of critical importance for cross-cultural studies (as well as in multi-group research in other scientific fields), when the expertise possibly also of linguists, ethnologists, and/or social anthropologists—in addition potentially to other disciplines experts—may well be required for its achievement.