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Evaluating Equivalence Testing Methods for Measurement Invariance.

Alyssa Counsell1, Robert A Cribbie1, David B Flora1

  • 1Department of Psychology, York University, Toronto, ON, Canada.

Multivariate Behavioral Research
|August 8, 2019
PubMed
Summary
This summary is machine-generated.

The equivalence test (EQ) maintains accurate error rates for measurement invariance (MI) testing, unlike traditional methods. However, EQ requires larger sample sizes for sufficient statistical power compared to other approaches.

Keywords:
Equivalence testsconfirmatory factor analysismeasurement invariancemodel comparisonstructural equation modeling

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Area of Science:

  • Psychometrics
  • Statistical modeling
  • Structural Equation Modeling (SEM)

Background:

  • Measurement invariance (MI) is crucial for comparing latent variables across groups.
  • Traditional methods like chi-square difference tests and goodness-of-fit indices (GOFs) for testing MI have limitations.
  • Equivalence testing (EQ) has been proposed as an alternative to address these limitations.

Purpose of the Study:

  • To evaluate the Type I error and statistical power of the equivalence test (EQ) and its adjusted version (EQ-A).
  • To compare the performance of EQ and EQ-A against traditional chi-square difference tests and GOFs for MI testing.
  • To provide guidance on the practical application of EQ in measurement invariance research.

Main Methods:

  • Simulation study evaluating Type I error rates and statistical power.
  • Comparison of four procedures: chi-square difference test, GOFs, EQ, and EQ-A.
  • Analysis across various sample sizes and effect sizes relevant to MI.

Main Results:

  • The equivalence test (EQ) was the only procedure that consistently maintained empirical error rates below the nominal alpha level.
  • EQ demonstrated adequate power only with larger sample sizes or when using more lenient equivalence bounds (e.g., RMSEA > .05).
  • The adjusted version (EQ-A) did not offer advantages over the standard EQ and is not recommended.

Conclusions:

  • The equivalence test (EQ) is a reliable method for testing measurement invariance, controlling Type I error effectively.
  • Researchers should consider larger sample sizes or adjusted equivalence bounds to ensure adequate power when using EQ.
  • The EQ-A is not recommended, and further research may be needed to optimize power for the EQ procedure.