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Rotation to a partially specified target matrix in exploratory factor analysis in practice.

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Using target rotation in exploratory factor analysis can improve accuracy but may decrease stability. The number of targets has a small effect, while target error has a negligible impact on results.

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Area of Science:

  • Psychometrics
  • Statistical analysis

Background:

  • Exploratory factor analysis (EFA) is crucial for understanding complex data structures.
  • Substantive measurement theory guides EFA, but is often incomplete.
  • Target rotation methods leverage existing theory, but their performance with imperfect targets is debated.

Purpose of the Study:

  • To investigate how the number of specified targets impacts EFA solution quality.
  • To evaluate target rotation against a default method (geomin) under realistic conditions.
  • To examine the influence of specification errors in both the model and target matrix.

Main Methods:

  • A Monte Carlo simulation study was employed.
  • Key variables manipulated included target error, number of targets, model error, overdetermination, communality, and sample size.
  • Outcomes assessed were bias (accuracy) and variability (stability) of the rotated pattern matrix.

Main Results:

  • Target error showed negligible effects on both accuracy and stability.
  • The number of targets had small but observable effects on accuracy and stability.
  • Target rotation enhanced accuracy compared to geomin rotation.
  • Geomin rotation generally offered better stability than target rotation.

Conclusions:

  • Extant measurement theory can inform rotation criteria, but caution is advised regarding stability.
  • Target rotation offers accuracy benefits, while geomin provides greater stability.
  • The number of targets is a minor consideration, whereas target accuracy is less critical than previously assumed.