Fitting Large Factor Analysis Models With Ordinal Data.

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Confirmatory Factor Analysis (CFA) is widely used in psychology and social sciences.
• Ordinal indicators are common in psychological measurement, necessitating specialized CFA techniques.
• The impact of model size (number of items) on ordinal CFA performance is not fully understood.

Purpose of the Study:

• To investigate the model size effect in confirmatory factor analysis (CFA) with numerous ordinal items.
• To determine how sample size, category number, and model misspecification influence CFA results.
• To assess the impact on parameter estimates, standard errors, and model fit indices.

Main Methods:

• A simulation study was performed using confirmatory factor analysis (CFA) models.
• Models included 15 to 120 ordinal items.
• Mean- and variance-adjusted weighted least squares estimation was employed.

Main Results:

• Increasing the number of items improved the accuracy of parameter estimates and the proportion of admissible solutions, even with model misspecification.
• Standard errors of parameter estimates became more accurate as the number of items increased.
• The root mean square error of approximation (RMSEA) tended to be overly optimistic when models were misspecified.

Conclusions:

• Larger models with more ordinal items generally yield more accurate and stable CFA results.
• Researchers should exercise caution when interpreting RMSEA in ordinal CFA, especially under misspecified conditions.
• Findings provide guidance for structural equation modeling with numerous ordinal indicators.