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Estimated Factor Scores Are Not True Factor Scores.

Mijke Rhemtulla1, Victoria Savalei2

  • 1Department of Psychology, University of California, Davis, Davis, CA, USA.

Multivariate Behavioral Research
|January 22, 2025
PubMed
Summary

This tutorial distinguishes true factor scores from estimated factor scores, like regression factor scores. It demonstrates how measurement error impacts factor score reliability using simulated data.

Keywords:
Factor scoreslatent variablessum scores

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Data Analysis

Background:

  • Factor scores are crucial in psychometrics for representing latent variables.
  • Distinguishing between true and estimated factor scores is essential for accurate interpretation.
  • Regression factor scores are widely used but their properties require careful consideration.

Purpose of the Study:

  • To clarify the distinction between true factor scores and estimated factor scores.
  • To illustrate the properties of regression factor scores using a linear regression analogy.
  • To examine the impact of measurement error on the reliability of factor score estimates.

Main Methods:

  • Utilizing an analogy with linear regression to explain factor score estimation.
  • Employing simulated data from one- and two-factor models.
  • Comparing the performance of regression factor scores with unweighted sum scores.

Main Results:

  • Predicted values in linear regression share properties with regression factor scores.
  • The reliability of regression factor scores is demonstrably affected by the level of measurement error.
  • Regression factor scores showed varying performance compared to unweighted sum scores depending on the model.

Conclusions:

  • Understanding the nature of estimated factor scores, particularly regression factor scores, is vital for robust statistical analysis.
  • Measurement error significantly influences the reliability of factor score estimates.
  • The choice between different factor score estimation methods should consider the impact of measurement error and model characteristics.