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This study introduces permutation tests for configural invariance, offering accurate error rates even with imperfect model fit. It proposes multivariate modification indices to guide simultaneous parameter adjustments across groups for robust measurement invariance.

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Multivariate Analysis

Background:

  • Measurement invariance testing is crucial for cross-group comparisons.
  • Traditional methods often conflate overall model fit with configural invariance.
  • Configural invariance ensures equivalent factor structures across groups.

Purpose of the Study:

  • To differentiate the null hypothesis of configural invariance from overall model fit.
  • To propose and evaluate multivariate modification indices for model adjustments.
  • To assess the Type I error control of permutation tests and multivariate indices.

Main Methods:

  • Utilizing permutation tests to assess configural invariance.
  • Applying multivariate modification indices to identify parameters for simultaneous freeing.
  • Conducting Monte Carlo simulations to compare error rates.
  • Illustrating methods with the Holzinger and Swineford (1939) dataset.

Main Results:

  • Permutation tests maintain nominal Type I error rates, even when models do not perfectly fit.
  • Multivariate modification indices offer a structured approach to model modification across groups.
  • Simulations demonstrate the Type I error control of multivariate indices compared to traditional ones.

Conclusions:

  • Configural invariance testing requires distinct evaluation from overall model fit.
  • Multivariate modification indices provide a valuable tool for refining measurement models across groups.
  • Researchers should consider simultaneous parameter adjustments guided by multivariate indices when configural invariance is questioned.