Evaluating SEM Model Fit with Small Degrees of Freedom

Area of Science:

• Structural Equation Modeling
• Psychometrics
• Statistical Modeling

Background:

• Root Mean Square Error of Approximation (RMSEA) performance is suboptimal for structural equation models with small degrees of freedom (df).
• This can lead to the incorrect rejection of correctly specified or closely fitted models.
• Existing research highlights limitations of RMSEA in specific modeling contexts.

Purpose of the Study:

• To investigate the performance of Standardized Root Mean Square Residual (SRMR) and Comparative Fit Index (CFI) in small df structural equation models.
• To compare SRMR and CFI against RMSEA under varying conditions of factor loadings, sample sizes, and model misspecifications.
• To provide guidance on selecting appropriate fit indices for models with limited degrees of freedom.

Main Methods:

• Simulation study examining structural equation models with small df.
• Manipulation of factor loadings, sample sizes, and levels of model misspecification.
• Evaluation of population SRMR, CFI, and RMSEA performance.
• Assessment of sample SRMR and CFI's ability to differentiate model misfit.
• Analysis of confidence intervals and p-values for close fit.

Main Results:

• Population SRMR and CFI demonstrate greater robustness against small df compared to RMSEA.
• Sample SRMR and CFI provide more informative differentiation of model misfit in small df scenarios.
• Confidence intervals and p-values for close fit remained accurate across all three indices.
• RMSEA's susceptibility to low df can lead to inaccurate model evaluations.

Conclusions:

• Exercise caution when interpreting RMSEA for structural equation models with small df.
• Prioritize the use of SRMR and CFI for assessing model fit in low df conditions.
• SRMR and CFI offer more reliable insights into model adequacy when df is limited.