Confirmatory factor analysis with ordinal data: Comparing robust maximum likelihood and diagonally weighted least...

Area of Science:

• Psychometrics
• Statistical Modeling
• Quantitative Psychology

Background:

• Confirmatory Factor Analysis (CFA) commonly uses Maximum Likelihood (ML) estimation, assuming continuous, multivariate normal data.
• Ordinal variables violate ML assumptions, necessitating alternative methods like Robust Maximum Likelihood (MLR) or Diagonally Weighted Least Squares (WLSMV).
• WLSMV is designed for ordinal data, assuming a normal latent distribution, while MLR addresses normality violations.

Purpose of the Study:

• To compare the performance of WLSMV and MLR in CFA with ordinal data.
• To evaluate the impact of latent distribution normality, category number, and sample size on parameter estimates, standard errors, and model fit.
• To identify optimal estimation methods under various conditions for ordinal CFA.

Main Methods:

• A Monte Carlo simulation study was conducted.
• A correlated two-factor model was specified.
• Evaluated estimation methods included WLSMV and MLR.
• Varied conditions included latent response distributions, number of categories, and sample sizes.

Main Results:

• WLSMV demonstrated less bias and higher accuracy in estimating factor loadings compared to MLR across most conditions.
• WLSMV showed moderate overestimation of interfactor correlations with small sample sizes or nonnormal latent distributions.
• MLR provided more accurate standard error estimates than WLSMV under nonnormal latent distributions and small sample sizes (N=200).
• Chi-square statistics tended to over-reject the model under both MLR and WLSMV with small sample sizes (N=200).

Conclusions:

• WLSMV is generally preferred for factor loading estimation with ordinal data in CFA.
• Researchers should be cautious of potential interfactor correlation overestimation with WLSMV in small samples or nonnormal data.
• MLR may be advantageous for standard error estimation when latent distributions are nonnormal and sample sizes are small.
• Small sample sizes (N=200) pose challenges for model fit testing with both WLSMV and MLR.