Are factor scores measurement invariant?

Abstract

There has been increased interest in practical methods for integrative analysis of data from multiple studies or samples, and using factor scores to represent constructs has become a popular and practical alternative to latent variable models with all individual items. Although researchers are aware that scores representing the same construct should be on a similar metric across samples-namely they should be measurement invariant-for integrative data analysis, the methodological literature is unclear whether factor scores would satisfy such a requirement. In this note, we show that even when researchers successfully calibrate the latent factors to the same metric across samples, factor scores-which are estimates of the latent factors but not the factors themselves-may not be measurement invariant. Specifically, we prove that factor scores computed based on the popular regression method are generally not measurement invariant. Surprisingly, such scores can be noninvariant even when the items are invariant. We also demonstrate that our conclusions generalize to similar shrinkage scores in item response models for discrete items, namely the expected a posteriori scores and the maximum a posteriori scores. Researchers should be cautious in directly using factor scores for cross-sample analyses, even when such scores are obtained from measurement models that account for noninvariance. (PsycInfo Database Record (c) 2024 APA, all rights reserved).