Composite-level Measurement Invariance

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.