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

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

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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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  1. Jöreskog, K. G., & Sörbom, D. (1996). Prelis 2: User’s reference guide: A program for multivariate data screening and data summarization. Chicago, IL: Scientific Software.
  2. Muthén, L. K., & Muthén, B. O. (2007). Mplus user’s guide. Los Angeles, CA: Muthén & Muthén.

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Metadata

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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