Testing Measurement Invariance and Comparing Latent Factor Means Within a Confirmatory Factor Analysis Framework

Researchers commonly compare means and other statistics across groups with little concern for whether the measure possesses strong factorial invariance (i.e., equal factor loadings and intercepts/thresholds). When this assumption is violated, inaccurate inferences associated with statistical and practical significance can occur. This manuscript emphasizes the importance of testing for measurement invariance (MI) and provides guidance when conducting these tests. Topics discussed are potential causes of noninvariant items, the difference between measurement bias and invariance, remedies for noninvariant measures, and considerations associated with model estimation. Using a sample of 491 teachers, a demonstration is also provided that evaluates whether a newly constructed behavior and instructional management scale is invariant across elementary and middle school teachers. Analyses revealed that the results differ slightly based on the estimation method utilized although these differences did not greatly influence the latent factor mean difference conclusions. Additional implications and considerations related to invariance testing are discussed.