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

The DOI matches its Crossref record; 49 of the 53 references it cites were found in a registry or an index.

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
Open this paper in CoChat — free accountOpen PDF

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.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.3758/s13428-015-0619-7

Cites

49 of 49 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Show all 53 references

Research works printed but not linked: 2

  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.

Cited by

Sorted by citations

Items 801–900 of 1,002

Related

See all

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

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review