Does strict invariance matter? Valid group mean comparisons with ordered-categorical items

• Published in: Behavior research methods 2024-04, Vol.56 (4), p.3117-3139
• Main Authors: Tse, Winnie Wing-Yee, Lai, Mark H. C., Zhang, Yichi
• Format: Article
• Language: English
• Subjects: Behavioral Science and Psychology; Cognitive Psychology; Computer Simulation; Data Interpretation, Statistical; Factor Analysis, Statistical; Humans; Models, Statistical; Monte Carlo Method; Monte Carlo simulation; Original Manuscript; Psychology; Psychometrics - instrumentation; Psychometrics - methods
• ISSN: 1554-3528; 1554-351X; 1554-3528
• DOI: 10.3758/s13428-023-02247-6

Measurement invariance (MI) of a psychometric scale is a prerequisite for valid group comparisons of the measured construct. While the invariance of loadings and intercepts (i.e., scalar invariance) supports comparisons of factor means and observed means with continuous items, a general belief is that the same holds with ordered-categorical (i.e., ordered-polytomous and dichotomous) items. However, as this paper shows, this belief is only partially true—factor mean comparison is permissible in the correctly specified scalar invariance model with ordered-polytomous items but not with dichotomous items. Furthermore, rather than scalar invariance, full strict invariance—invariance of loadings, thresholds, intercepts, and unique factor variances in all items—is needed when comparing observed means with both ordered-polytomous and dichotomous items. In a Monte Carlo simulation study, we found that unique factor noninvariance led to biased estimations and inferences (e.g., with inflated type I error rates of 19.52%) of (a) the observed mean difference for both ordered-polytomous and dichotomous items and (b) the factor mean difference for dichotomous items in the scalar invariance model. We provide a tutorial on invariance testing with ordered-categorical items as well as suggestions on mean comparisons when strict invariance is violated. In general, we recommend testing strict invariance prior to comparing observed means with ordered-categorical items and adjusting for partial invariance to compare factor means if strict invariance fails.