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A small sample correction for factor score regression

Jasper Bogaert (UGent) , Wen Wei Loh (UGent) and Yves Rosseel (UGent)
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Abstract
Factor score regression (FSR) is widely used as a convenient alternative to traditional structural equation modeling (SEM) for assessing structural relations between latent variables. But when latent variables are simply replaced by factor scores, biases in the structural parameter estimates often have to be corrected, due to the measurement error in the factor scores. The method of Croon (MOC) is a well-known bias correction technique. However, its standard implementation can render poor quality estimates in small samples (e.g. less than 100). This article aims to develop a small sample correction (SSC) that integrates two different modifications to the standard MOC. We conducted a simulation study to compare the empirical performance of (a) standard SEM, (b) the standard MOC, (c) naive FSR, and (d) the MOC with the proposed SSC. In addition, we assessed the robustness of the performance of the SSC in various models with a different number of predictors and indicators. The results showed that the MOC with the proposed SSC yielded smaller mean squared errors than SEM and the standard MOC in small samples and performed similarly to naive FSR. However, naive FSR yielded more biased estimates than the proposed MOC with SSC, by failing to account for measurement error in the factor scores.
Keywords
Applied Mathematics, Applied Psychology, Developmental and Educational Psychology, Education, factor score regression, method of Croon, structural equation modeling, small sample estimation, measurement error, MULTIPLE-REGRESSION, IMPROPER SOLUTIONS, PATH-ANALYSIS, VARIABLES, ERROR

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Citation

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MLA
Bogaert, Jasper, et al. “A Small Sample Correction for Factor Score Regression.” EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT, vol. 83, no. 3, 2023, pp. 495–519, doi:10.1177/00131644221105505.
APA
Bogaert, J., Loh, W. W., & Rosseel, Y. (2023). A small sample correction for factor score regression. EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT, 83(3), 495–519. https://doi.org/10.1177/00131644221105505
Chicago author-date
Bogaert, Jasper, Wen Wei Loh, and Yves Rosseel. 2023. “A Small Sample Correction for Factor Score Regression.” EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT 83 (3): 495–519. https://doi.org/10.1177/00131644221105505.
Chicago author-date (all authors)
Bogaert, Jasper, Wen Wei Loh, and Yves Rosseel. 2023. “A Small Sample Correction for Factor Score Regression.” EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT 83 (3): 495–519. doi:10.1177/00131644221105505.
Vancouver
1.
Bogaert J, Loh WW, Rosseel Y. A small sample correction for factor score regression. EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT. 2023;83(3):495–519.
IEEE
[1]
J. Bogaert, W. W. Loh, and Y. Rosseel, “A small sample correction for factor score regression,” EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT, vol. 83, no. 3, pp. 495–519, 2023.
@article{8760483,
  abstract     = {{Factor score regression (FSR) is widely used as a convenient alternative to traditional structural equation modeling (SEM) for assessing structural relations between latent variables. But when latent variables are simply replaced by factor scores, biases in the structural parameter estimates often have to be corrected, due to the measurement error in the factor scores. The method of Croon (MOC) is a well-known bias correction technique. However, its standard implementation can render poor quality estimates in small samples (e.g. less than 100). This article aims to develop a small sample correction (SSC) that integrates two different modifications to the standard MOC. We conducted a simulation study to compare the empirical performance of (a) standard SEM, (b) the standard MOC, (c) naive FSR, and (d) the MOC with the proposed SSC. In addition, we assessed the robustness of the performance of the SSC in various models with a different number of predictors and indicators. The results showed that the MOC with the proposed SSC yielded smaller mean squared errors than SEM and the standard MOC in small samples and performed similarly to naive FSR. However, naive FSR yielded more biased estimates than the proposed MOC with SSC, by failing to account for measurement error in the factor scores.}},
  author       = {{Bogaert, Jasper and Loh, Wen Wei and Rosseel, Yves}},
  issn         = {{0013-1644}},
  journal      = {{EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT}},
  keywords     = {{Applied Mathematics,Applied Psychology,Developmental and Educational Psychology,Education,factor score regression,method of Croon,structural equation modeling,small sample estimation,measurement error,MULTIPLE-REGRESSION,IMPROPER SOLUTIONS,PATH-ANALYSIS,VARIABLES,ERROR}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{495--519}},
  title        = {{A small sample correction for factor score regression}},
  url          = {{http://doi.org/10.1177/00131644221105505}},
  volume       = {{83}},
  year         = {{2023}},
}

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