Article
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Factor Analysis of Ordinal Items: Old Questions, Modern Solutions?
Version 1
: Received: 5 August 2024 / Approved: 6 August 2024 / Online: 6 August 2024 (06:19:34 CEST)
How to cite: Marôco, J. Factor Analysis of Ordinal Items: Old Questions, Modern Solutions?. Preprints 2024, 2024080388. https://doi.org/10.20944/preprints202408.0388.v1 Marôco, J. Factor Analysis of Ordinal Items: Old Questions, Modern Solutions?. Preprints 2024, 2024080388. https://doi.org/10.20944/preprints202408.0388.v1
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 ML with WLS for ordinal variables. While WLS generally outperforms ML, especially with non-bell-shaped distributions, it may yield artefactual estimates with severely skewed data. ML tends to underestimate true loadings, while WLS may overestimate them. Simulations and case studies highlight the importance of item psychometric distributions. Despite advancements, ML remains robust, underscoring the complexity of analyzing ordinal data in factor analysis. There's no one-size-fits-all approach, emphasizing the need for sensitivity analyses and careful consideration of data characteristics.
Keywords
Factor Analysis; Ordinal items; Maximum Likelihood; Polychoric correlations; Weighted Least Squares
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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