Confirmatory factor analysis of ordinal variables: A simulation study comparing the main estimation methods

Abstract

In order to obtain evidences about construct validity through Confirmatory Factor Analysis, it has been usual treating Likert-type scales as if they were continuous variables measured on an interval scale. Therefore, Maximum Likelihood estimation method has been broadly applied, but in turn it implies problems concerning both Pearson correlations and skewness in the distribution of responses to items. In this simulation study we analyse —through χ2, Type I error, and power— correctly specified and misspecified models comparing five estimation methods (Maximum Likelihood —ml—, Robust Maximum Likelihood —rml—, Weighted Least Squares —wls—, Unweighted Least Squares —uls— and Robust Unweighted Least Squares —ruls—) in relation to the models features: number of factors, number of response categories, items’ skewness, and sample size. We advise using ruls estimation method, in which polychoric correlations are implied.