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Hayes T, Usami S. Factor Score Regression in the Presence of Correlated Unique Factors. Educ Psychol Meas. 2019;80(1):5-40doi: 10.1177/0013164419854492.
Hayes, T., & Usami, S. (2020). Factor Score Regression in the Presence of Correlated Unique Factors. Educational and psychological measurement, 80(1), 5-40. https://doi.org/10.1177/0013164419854492
Hayes, Timothy, and Usami, Satoshi. "Factor Score Regression in the Presence of Correlated Unique Factors." Educational and psychological measurement vol. 80,1 (2020): 5-40. doi: https://doi.org/10.1177/0013164419854492
Hayes T, Usami S. Factor Score Regression in the Presence of Correlated Unique Factors. Educ Psychol Meas. 2020 Feb;80(1):5-40. doi: 10.1177/0013164419854492. Epub 2019 Jun 17. PMID: 31933491; PMCID: PMC6943992.
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Educ Psychol Meas. 2020 Feb;80(1):5-40. doi: 10.1177/0013164419854492. Epub 2019 Jun 17.

Factor Score Regression in the Presence of Correlated Unique Factors.

Educational and psychological measurement

Timothy Hayes, Satoshi Usami

Affiliations

  1. Florida International University, Miami, FL, USA.
  2. University of Tokyo, Tokyo, Japan.

PMID: 31933491 PMCID: PMC6943992 DOI: 10.1177/0013164419854492

Abstract

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.

© The Author(s) 2019.

Keywords: correlated uniquenesses; factor score regression; measurement; structural equation modeling

Conflict of interest statement

Declaration of Conflicting Interests: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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