The Relationship Between the Standardized Root Mean Square Residual and Model Misspecification in Factor Analysis...

Area of Science:

• Statistics
• Psychometrics
• Quantitative Psychology

Background:

• Model misspecification is a common issue in statistical modeling.
• Existing fit indices may not adequately detect certain types of misspecification.
• The concept of substantially ignorable misspecification (SIM) offers a new perspective.

Purpose of the Study:

• To investigate the relationship between population standardized root mean square residual (SRMR) values and model misspecifications in factor analysis.
• To propose new population reference values for assessing close and acceptable model fit.
• To introduce criteria that account for localized misspecifications.

Main Methods:

• Examined the population SRMR values in relation to various misspecifications in factor analysis models.
• Analyzed the sensitivity of SRMR to localized misspecifications using standardized residual covariances.
• Developed a two-index strategy for evaluating model fit.

Main Results:

• SRMR can be insensitive to localized misspecifications in large models.
• Largest absolute standardized residual covariance is a key indicator of localized misspecification.
• Proposed population reference values for close fit (≤0.10 for residual covariance, ≤0.05 × average R² for SRMR) and acceptable fit (≤0.15 and ≤0.10 × average R², respectively).

Conclusions:

• The definition of close fitting models should incorporate substantially ignorable misspecifications (SIM).
• A two-index strategy combining standardized residual covariance and SRMR provides improved criteria for model fit assessment in factor analysis.
• These findings offer practical guidelines for evaluating the fit of structural equation models.