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Area of Science:

  • Psychometrics
  • Statistical Modeling

Background:

  • Multigroup structural equation modeling (SEM) is crucial for measurement invariance and group comparisons.
  • Sequential testing of invariance (configural, loadings, intercepts, means) relies on chi-square difference tests.

Purpose of the Study:

  • To highlight the limitations of chi-square difference tests in controlling Type I and Type II errors in multigroup SEM.
  • To propose equivalence testing as a superior alternative for robust invariance testing.

Main Methods:

  • Analysis of existing methods, a case example, and Monte Carlo simulations.
  • Demonstration of the misuse of chi-square difference tests.
  • Proposal and illustration of equivalence testing in multigroup SEM.

Main Results:

  • Chi-square difference tests are prone to misuse and do not adequately control error rates.
  • The assumption of a well-fitting base model for chi-square difference tests is often violated.
  • Equivalence testing offers better control over model misspecification.

Conclusions:

  • Null hypothesis testing in multigroup SEM should be replaced by equivalence testing.
  • Equivalence testing enhances the reliability of measurement invariance assessment.
  • Provided R code facilitates the adoption of equivalence testing for researchers.