Factor Score Regression in Connected Measurement Models Containing Cross-Loadings

Factor Score Regression (FSR) methods have received increased interest in the quantitative literature, with Croon’s bias-correcting method gaining particular traction. By fixing measurement parameters in place in an initial step, FSR methods aim to stymie the proliferation of bias in larger structural models that may contain misspecification. Although Croon’s approach was originally derived for factor models exhibiting simple structure and conditionally independent unique factors, Hayes and Usami recently extended this method to connected measurement models featuring correlated uniquenesses. In this article, we demonstrate that their formulas also correct bias in models that feature cross-loadings. We begin by discussing bias in SEMs that incorrectly impose simple structure. We then describe Croon’s approach in connected measurement models featuring cross-loadings and compare its performance to two other state-of-the-art FSR approaches both analytically and via a simulated demonstration.