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We need to change how we compute RMSEA for nested model comparisons in structural equation modeling.

Victoria Savalei1, Jordan C Brace2, Rachel T Fouladi3

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Comparing nested models using the root mean square error of approximation (RMSEA) can be misleading. A new RMSEA-difference (RMSEA_D) index is proposed to accurately assess model fit, especially in structural equation modeling (SEM).

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Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • Nested model comparison is prevalent in structural equation modeling (SEM).
  • Approximate fit indices, like RMSEA, are commonly used alongside chi-square difference tests.
  • Current RMSEA comparison methods may mask model misspecification, particularly with large degrees of freedom.

Purpose of the Study:

  • To highlight the limitations of the standard RMSEA difference for nested model comparison.
  • To advocate for the use of RMSEA_D, an RMSEA index derived from the chi-square difference test.
  • To encourage adoption of RMSEA_D in SEM practice, especially for measurement invariance.

Main Methods:

  • Review of methodological articles on RMSEA comparison.
  • Introduction and explanation of the RMSEA_D index.
  • Empirical illustration using three examples, including measurement invariance and factor comparisons.

Main Results:

  • The direct difference of RMSEA values for nested models can obscure model misfit.
  • RMSEA_D provides a more accurate assessment of approximate fit for nested models.
  • Illustrative examples demonstrate the practical differences between current and proposed methods.

Conclusions:

  • The standard RMSEA difference method is problematic for nested model comparisons in SEM.
  • RMSEA_D offers a superior approach for evaluating nested model fit, particularly in complex applications.
  • Further research and adoption of RMSEA_D are recommended to improve SEM practices.