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

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.