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The Role of Measurement Quality on Practical Guidelines for Assessing Measurement and Structural Invariance.

Yoonjeong Kang1, Daniel M McNeish2, Gregory R Hancock2

  • 1American Institutes for Research, Washington, DC, USA.

Educational and Psychological Measurement
|May 26, 2018
PubMed
Summary

Measurement quality significantly impacts tests of invariance. While McDonald

Keywords:
factor indicator reliabilityfit indexinvariance testingmultiple group modelstructural equation modeling

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Area of Science:

  • Psychometrics
  • Structural Equation Modeling
  • Multivariate Statistics

Background:

  • Goodness-of-fit indices (ΔGOFs) are used to assess measurement invariance.
  • Previous studies used limited indicator variable quality (loading magnitudes) to set ΔGOF cutoffs.
  • Measurement quality is known to affect data-model fit in single-group models.

Purpose of the Study:

  • To investigate how measurement quality influences ΔGOFs for invariance testing in multiple-group models.
  • To determine the reliability of existing ΔGOF cutoffs under varying measurement quality.

Main Methods:

  • Simulation methods were employed.
  • Population analysis was conducted.
  • The impact of loading magnitude on ΔGOFs was examined.

Main Results:

  • ΔMcDonald's NCI showed minimal sensitivity to loading magnitude and sample size for measurement invariance.
  • ΔComparative Fit Index (ΔCFI) demonstrated substantial variation with changing measurement quality for both measurement and structural invariance.
  • Establishing a universal cutoff for reasonable invariance is challenging due to these variations.

Conclusions:

  • The reliability of ΔCFI for assessing measurement invariance is questionable under varying measurement quality.
  • ΔMcDonald's NCI appears more robust for testing measurement invariance across different loading magnitudes.
  • Researchers should carefully consider measurement quality when interpreting ΔGOFs for invariance testing.