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Cited by 3,031Psychometric Methodologies and TestingStatistical Methods and Bayesian InferenceStatistical Distribution Estimation and Applications

Confirmatory factor analysis with ordinal data: Comparing robust maximum likelihood and diagonally weighted least squares

Open access
Li, Cheng-Hsien·2016·Behavior Research Methods
DOI 10.3758/s13428-015-0619-7
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Abstract

In confirmatory factor analysis (CFA), the use of maximum likelihood (ML) assumes that the observed indicators follow a continuous and multivariate normal distribution, which is not appropriate for ordinal observed variables. Robust ML (MLR) has been introduced into CFA models when this normality assumption is slightly or moderately violated. Diagonally weighted least squares (WLSMV), on the other hand, is specifically designed for ordinal data. Although WLSMV makes no distributional assumptions about the observed variables, a normal latent distribution underlying each observed categorical variable is instead assumed. A Monte Carlo simulation was carried out to compare the effects of different configurations of latent response distributions, numbers of categories, and sample sizes on model parameter estimates, standard errors, and chi-square test statistics in a correlated two-factor model. The results showed that WLSMV was less biased and more accurate than MLR in estimating the factor loadings across nearly every condition. However, WLSMV yielded moderate overestimation of the interfactor correlations when the sample size was small or/and when the latent distributions were moderately nonnormal. With respect to standard error estimates of the factor loadings and the interfactor correlations, MLR outperformed WLSMV when the latent distributions were nonnormal with a small sample size of N = 200. Finally, the proposed model tended to be over-rejected by chi-square test statistics under both MLR and WLSMV in the condition of small sample size N = 200.

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  • 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 [50]

    The Abstract identifies DWLS/WLSMV as an estimator with corrected standard errors and chi-square statistics for ordinal data. The Diagonally weighted least squares section describes robust standard errors and a mean- and variance-adjusted chi-square statistic, but does not specify a scaled-and-shifted test statistic. Thus the general choice is supported, while that precise test-statistic specification is not established by this source. (LLM, conf=0.84)

    Experimental — accuracy not yet measured

  • 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 [50]

    The Abstract says WLSMV, a robust DWLS estimator, makes no distributional assumption about observed variables, though it assumes a normal latent distribution underlying each ordinal variable. The Parameter estimates section finds WLSMV more accurate than robust ML (MLR) for factor loadings, but the Summary and conclusions says MLR performs better for some other estimates, including interfactor correlations. The claim overgeneralizes the accuracy finding to parameter estimates as a whole. (LLM, conf=0.91)

    Experimental — accuracy not yet measured

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4 of the 53 references couldn’t be matched to a known paper.

Research works printed but not linked: 2

  1. Bradley, J. V. (1978). Robustness? British Journal of Mathematical and Statistical Psychology, 58, 430-450.
  2. Muthén, B. O. (1993). Goodness of fit with categorical and other non- normal variables. In K. A. Bollen & J. S. Long (Eds.), Testing struc- tural equation models (pp. 205-243). Newbury Park, CA: Sage.

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Authors
Li, C.-H.
Affiliations
The University of Texas Health Science Center at Houston (US)
Corresponding author
Li, Cheng-Hsien
Venue
Behavior Research Methods
Publisher
Springer Science and Business Media LLC
Published
2015-07-15
Volume
48
Issue
3
Pages
936-949
ISSN
  • 1554-351X (ISSN-L)
  • 1554-3528
DOI
10.3758/s13428-015-0619-7
OpenAlex
W1819467863
Cited by
3,031
References
53
Citations by year
2026: 555 · 2025: 391 · 2024: 407 · 2023: 402 · 2022: 353 · 2021: 366 · 2020: 242 · 2019: 145 · 2018: 94 · 2017: 56 · 2016: 17
FWCI
69.36
Type
journal article
Language
en
Open access
Licence
www.springer.com/tdm (tdm)
Locations
  • Behavior Research Methods (publishedVersion)
  • PubMed (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
confirmatory factor analysis, ordinal data, non-normality, factor loadings, chi-square test, small sample size, categorical indicators
MeSH terms
Data Interpretation, Statistical, Factor Analysis, Statistical, Humans, Monte Carlo Method, Models, Statistical, Chi-Square Distribution, Likelihood Functions, Least-Squares Analysis, Sample Size

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