Factor Analysis with Ordinal Indicators: A Monte Carlo Study Comparing DWLS and ULS Estimation
Abstract
Factor analysis models with ordinal indicators are often estimated using a 3-stage procedure where the last stage involves obtaining parameter estimates by least squares from the sample polychoric correlations. A simulation study involving 324 conditions (1,000 replications per condition) was performed to compare the performance of diagonally weighted least squares (DWLS) and unweighted least squares (ULS) in the procedure's third stage. Overall, both methods provided accurate and similar results. However, ULS was found to provide more accurate and less variable parameter estimates, as well as more precise standard errors and better coverage rates. Nevertheless, convergence rates for DWLS are higher. Our recommendation is therefore to use ULS, and, in the case of nonconvergence, to use DWLS, as this method might converge when ULS does not.
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A sample size of >200 seems sufficient for robust parameter estimations with ordinal data.
“A sample size of > 200 seems sufficient for robust parameter estimations with ordinal data according to Bandalos and Forero and colleagues [44, 45].”
From Dimensionality of the system usability scale among professionals using internet-based interventions for depression: a confirmatory factor analysis (2020) · cites this paper as [45]
Sample sizes between 200 and 500 are recommended for CFA with ordinal data.
“In which sample sizes between 200 and 500 are recommended.”
From Dimensionality of the system usability scale among professionals using internet-based interventions for depression: a confirmatory factor analysis (2020) · cites this paper as [45]
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- Authors
- Forero, C. G., Maydeu-Olivares, A., & Gallardo-Pujol, D.
- Affiliations
- Universitat de Barcelona (ES)
- ORCID
- Forero, Carlos G.
- Venue
- Structural Equation Modeling: A Multidisciplinary Journal
- Publisher
- Informa UK Limited
- Published
- 2009-10-06
- Volume
- 16
- Issue
- 4
- Pages
- 625-641
- ISSN
- 1070-5511 (ISSN-L)
- 1532-8007
- OpenAlex
- W2161517243
- Cited by
- 685
- References
- 38
- Citations by year
- 2026: 65 · 2025: 70 · 2024: 71 · 2023: 60 · 2022: 61 · 2021: 66 · 2020: 57 · 2019: 29 · 2018: 39 · 2017: 32 · 2016: 24 · 2015: 37 · 2014: 23 · 2013: 22 · 2012: 19
- FWCI
- 12.65
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Structural Equation Modeling A Multidisciplinary Journal (publishedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Keywords
- factor analysis, ordinal indicators, unweighted least squares, polychoric correlation, parameter estimation, standard error estimation, coverage rate, convergence
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