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Are factor scores measurement invariant?

Mark H C Lai1, Winnie W-Y Tse1

  • 1Department of Psychology, University of Southern California.

Psychological Methods
|May 6, 2024
PubMed
Summary

Factor scores, used for integrative data analysis, may not be measurement invariant even when latent factors are calibrated. This means researchers should be cautious when using these scores for cross-sample comparisons.

Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Data Analysis

Background:

  • Integrative data analysis (IDA) increasingly uses factor scores as practical alternatives to traditional latent variable models.
  • Ensuring measurement invariance of factor scores across samples is crucial for valid IDA, but methodological guidance remains unclear.

Purpose of the Study:

  • To investigate whether factor scores, even when derived from calibrated latent factors, satisfy measurement invariance requirements for IDA.
  • To demonstrate the potential noninvariance of factor scores and generalize findings to related scores in item response theory.

Main Methods:

  • Theoretical proof demonstrating the conditions under which factor scores, specifically regression-based scores, exhibit noninvariance.
  • Extension of the analysis to shrinkage scores like expected a posteriori (EAP) and maximum a posteriori (MAP) scores in item response models.

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Main Results:

  • Factor scores computed using the regression method are generally not measurement invariant, even if the underlying latent factors are on the same metric.
  • Score noninvariance can occur even when the individual items used to compute the scores demonstrate measurement invariance.
  • Conclusions extend to EAP and MAP scores in item response models, indicating a broader issue with shrinkage scores.

Conclusions:

  • Researchers must exercise caution when directly using factor scores for cross-sample comparisons in IDA.
  • Even factor scores from measurement models that address noninvariance may not be suitable for direct cross-sample analysis.
  • The findings highlight a critical limitation in the application of factor scores for integrative analyses across different studies or samples.