Relative Performance of Categorical Diagonally Weighted Least Squares and Robust Maximum Likelihood Estimation
Abstract
Robust maximum likelihood (ML) and categorical diagonally weighted least squares (cat-DWLS) estimation have both been proposed for use with categorized and nonnormally distributed data. This study compares results from the 2 methods in terms of parameter estimate and standard error bias, power, and Type I error control, with unadjusted ML and WLS estimation methods included for purposes of comparison. Conditions manipulated include model misspecification, level of asymmetry, level and categorization, sample size, and type and size of the model. Results indicate that cat-DWLS estimation method results in the least parameter estimate and standard error bias under the majority of conditions studied. Cat-DWLS parameter estimates and standard errors were generally the least affected by model misspecification of the estimation methods studied. Robust ML also performed well, yielding relatively unbiased parameter estimates and standard errors. However, both cat-DWLS and robust ML resulted in low power under conditions of high data asymmetry, small sample sizes, and mild model misspecification. For more optimal conditions, power for these estimators was adequate.
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DWLS does not assume multivariate normality of indicators and provides more accurate parameter estimates for ordinal data compared with maximum likelihood-based estimators.
“DWLS does not assume multivariate normality of indicators and provides more accurate parameter estimates for ordinal data compared with maximum likelihood-based estimators.”
From Enhancing Digital Financial Literacy and Digital Trust for Sustainable Online Loan Adoption among Micro-Entrepreneurs in Developing Economies (2026) · cites this paper as [51]
The Diagonally Weighted Least Squares estimator with robust standard errors and a scaled/shifted test statistic was selected, as recommended for ordered categorical (Likert-scale) data.
“The Diagonally Weighted Least Squares (DWLS) estimator with robust standard errors and a scaled/shifted test statistic was selected, as recommended for ordered categorical (Likert-scale) data [50], [51].”
From Enhancing Digital Financial Literacy and Digital Trust for Sustainable Online Loan Adoption among Micro-Entrepreneurs in Developing Economies (2026) · cites this paper as [51]
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 [44]
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 [44]
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Giancaspro, M. L., Manuti, A., Presti, A. L., & Rosa, A. D. (2021) · Sustainability · doi:10.3390/su132111834 · Cited by 18 · see citing works
The Factor Structure and External Validity of the COPE 60 Inventory in Slovak Translation
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Lewis, N., & Martinez, L. S. (2020) · Journal of Health Communication · doi:10.1080/10810730.2020.1797247 · Cited by 16 · see citing works
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Moreira, P., & Inman, R. A. (2021) · Humor - International Journal of Humor Research · doi:10.1515/humor-2021-0039 · Cited by 15 · see citing works
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The factor structure of Big Five personality trait measures at the between- and within-person levels
Grosz, M. P. (2023) · European Journal of Personality · doi:10.1177/08902070231213805 · Cited by 14 · see citing works
- Authors
- Bandalos, D. L.
- Affiliations
- James Madison University (US)
- Corresponding author
- Bandalos, Deborah L.
- ORCID
- Bandalos, Deborah L.
- Venue
- Structural Equation Modeling: A Multidisciplinary Journal
- Publisher
- Informa UK Limited
- Published
- 2014-01-02
- Volume
- 21
- Issue
- 1
- Pages
- 102-116
- ISSN
- 1070-5511 (ISSN-L)
- 1532-8007
- OpenAlex
- W2085399079
- Cited by
- 381
- References
- 25
- Citations by year
- 2026: 43 · 2025: 54 · 2024: 53 · 2023: 53 · 2022: 44 · 2021: 33 · 2020: 40 · 2019: 20 · 2018: 19 · 2017: 13 · 2016: 5 · 2015: 3 · 2014: 1
- FWCI
- 9.24
- 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 › Advanced Statistical Methods and Models
- Keywords
- categorical data, non-normal data, standard error bias, statistical power, type I error control, model misspecification, data asymmetry, sample size effects, weighted least squares
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