Fitting Large Factor Analysis Models With Ordinal Data

A simulation study was conducted to investigate the model size effect when confirmatory factor analysis (CFA) models include many ordinal items. CFA models including between 15 and 120 ordinal items were analyzed with mean- and variance-adjusted weighted least squares to determine how varying sample size, number of ordered categories, and misspecification affect parameter estimates, standard errors of parameter estimates, and selected fit indices. As the number of items increased, the number of admissible solutions and accuracy of parameter estimates improved, even when models were misspecified. Also, standard errors of parameter estimates were closer to empirical standard deviation values as the number of items increased. When evaluating goodness-of-fit for ordinal CFA with many observed indicators, researchers should be cautious in interpreting the root mean square error of approximation, as this value appeared overly optimistic under misspecified conditions