Factor Analysis of Ordinal Items: Old Questions, Modern Solutions?

Abstract

Factor analysis, a staple of correlational psychology, faces challenges with ordinal variables like Likert scales. The validity of traditional methods, particularly maximum likelihood (ML), is debated. Newer approaches, like using polychoric correlation matrices with weighted least squares estimators (WLS), offer solutions. This paper compares maximum likelihood estimation (MLE) with WLS for ordinal variables. While WLS on polychoric correlations generally outperforms MLE on Pearson correlations, especially with nonbell-shaped distributions, it may yield artefactual estimates with severely skewed data. MLE tends to underestimate true loadings, while WLS may overestimate them. Simulations and case studies highlight the importance of item psychometric distributions. Despite advancements, MLE remains robust, underscoring the complexity of analyzing ordinal data in factor analysis. There is no one-size-fits-all approach, emphasizing the need for distributional analyses and careful consideration of data characteristics.

Keywords

• factor analysis
• ordinal items
• maximum likelihood
• polychoric correlations
• weighted least squares