Composite-level Measurement Invariance
Year: 2026
Type: preprint
Abstract: In applied research comparison of observed group scores is often the primary interest. To ensure valid group comparisons, researchers test for measurement invariance (MI) to see if the items on a scale function equivalently across groups. Item-level MI is defined as the equality of item parameters across groups. We argue item-level MI is overly restrictive when researchers are only interested in comparing scale scores. Non-invariance at the item level does not imply that scale scores are non-invariant, and may represent a more stringent test than is necessary in many situations. Therefore, we introduce composite-level measurement invariance, which is the invariance of parameter totals, rather than of the individual item parameters. Composite-level MI can be tested in lieu of item-level MI when researchers are only interested in the comparison of composite or scale scores. With the aid of a Shiny app, we illustrate theoretical properties (Type I error rates and power) of the composite-level MI tests and compare them to those of item-level MI. We then illustrate the composite-level MI approach on an empirical example. We conclude with a discussion, focusing on the appropriate use of the proposed procedure, possible disadvantages, and limitations.
Source: PsyArXiv (OSF Preprints)
Institution: Oklahoma State University
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7225612522
Cites:
Cited by:
Related to: