Confirmatory factor analysis with ordinal variables: A comparison of different estimation methods

In social science research, data is often collected using questionnaires with Likert scales, resulting in ordinal data. Confirmatory factor analysis (CFA) is the most common type of analysis, which assumes continuous data and multivariate normality, the assumptions violated for ordinal data. Simulation studies have shown that Robust Maximum Likelihood (RML) works well when the normality assumption is violated. Diagonally Weighted Least Squares (DWLS) estimation is especially recommended for categorical data. Bayesian estimation (BE) methods are also potentially effective for ordinal data. The current study employs a CFA model and Monte Carlo simulation to evaluate the performance of three estimation methods with ordinal data under various conditions in terms of the levels of asymmetry, sample sizes, and number of categories. The results indicate that, for ordinal data, DWLS outperforms RML and BE. RML is effective for ordinal data when the category numbers are sufficiently large. Bayesian methods do not demonstrate a significant advantage with different values of factor loadings, and category distributions had minimal impact on the estimation results.