Factor Score Regression in the Presence of Correlated Unique Factors

Recently, quantitative researchers have shown increased interest in two-step factor score regression (FSR) approaches to structural model estimation. A particularly promising approach proposed by Croon involves first extracting factor scores for each latent factor in a larger model, then correcting the variance-covariance matrix of the factor scores for bias before using this matrix as input data in a subsequent regression analysis or path model. Although not immediately obvious, Croon's bias correction formulas are predicated upon the standard assumption of conditionally independent uniquenesses (measurement residuals). To our knowledge, the method's performance has never been evaluated under conditions in which this assumption is violated. In the present research, we rederive Croon's formulas for the case of correlated uniqueness and present the results of two Monte Carlo simulations comparing the method's performance with standard methods when the unique factors were correlated in the population model. In our simulations, our proposed Croon FSR approaches outperformed methods that blindly assumed conditionally independent uniquenesses (e.g., uncorrected FSR, traditional Croon FSR, structural equation modeling [SEM] using standard specification), performed comparably to a correctly specified SEM, and outperformed SEMs that correctly specified the unique factor covariances but misspecified the structural model. We discuss the implications of our results for substantive researchers.