Cited by 1,778Psychometric Methodologies and TestingStatistical Methods and Bayesian InferenceStatistical Methods and Applications

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A comparison of some methodologies for the factor analysis of non‐normal Likert variables

Muthén, Bengt, Kaplan, David·1985·British Journal of Mathematical and Statistical Psychology

DOI 10.1111/j.2044-8317.1985.tb00832.x

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Abstract

This paper considers the problem of applying factor analysis to non‐normal categorical variables. A Monte Carlo study is conducted where five prototypical cases of non‐normal variables are generated. Two normal theory estimators, ML and GLS, are compared to Browne's (1982) ADF estimator. A categorical variable methodology (CVM) estimator of Muthén (1984) is also considered for the most severely skewed case. Results show that ML and GLS chi‐square tests are quite robust but obtain too large values for variables that arc severely skewed and kurtotic. ADF, however, performs well. Parameter estimate bias appears non‐existent for all estimators. Results also show that ML and GLS estimated standard errors are biased downward. For ADF no such standard error bias was found. The CVM estimator appears to work well when applied to severely skewed variables that had been dichotomized. ML and GLS results for a kurtosis only case showed no distortion of chi‐square or parameter estimates and only a slight downward bias in estimated standard errors. The results are compared to those of other related studies.

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“After transformation, all skewness and kurtosis indices were between −1.0 and 1.0, implying that not much distortion is to be expected (Muthén and Kaplan, 1985).”
BackgroundInfluential
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“These six items also had skewness and kurtosis values that were well outside the negligible range of 1.00 to −1.00 (Muthén & Kaplan, 1985).”
BackgroundInfluential
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“The majority of kurtosis and skewness values for the Brief COPE sub-scales were within the negligible range of -1.00 to 1.00 (Muthén and Kaplan 1985), and those outside this range were still well below the levels at which deviations from normality become problematic (Curran et al. 1996).”
Influential
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“Confirmatory Factor Structure Analysis A substantial number of items showed values of skewness and kurtosis that fell outside the [ 1; +1] range recommended by Muthén and Kaplan (1985) for using maximum likelihood estimator in factor analyses.”
Method
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“Such a discrepancy can arise from methodological differences between studies due to the diversity in samples (e.g., including or not including somatic diseases), the nature of the scale used (Sienaert et al., 2011), and the method of statistical extraction (Muthén and Kaplan, 1985).”
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“CFA models were estimated using the robust mean- and variance-adjusted Weighted Least Square method (WLSMV), an established statistical procedure recommended for analyzing dichotomous variables [35,36] applied extensively in past studies [37,38].”
Method
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“However, the normal-theory chi-square fit function and the standard errors are not robust (Muthén & Kaplan, 1985), plus the problem of nonpositive definite matrices plaques the use of polychoric correlations in factor analysis.”
Background
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“…studies (e.g., Fahlman et al., 2013; Bőthe et al., 2018): (1) corrected item-total correlations, (2) normality in terms of skewness and kurtosis (Muthén and Kaplan, 1985; Curran et al., 1996), and (3) content validity (Haynes et al., 1995) compared to the other items and competition in general.”
Background
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“While ML estimation with non-normal (kurtotic) data may produce biased chi-square based fit values and standard error estimates, it still tends to yield stable factor coefficients [24-26].”
Method

Authors: Muthén, B., & Kaplan, D.
Affiliations: University of California, Los Angeles (US)
Corresponding author: Muthén, Bengt
ORCID: Muthén, Bengt
Venue: British Journal of Mathematical and Statistical Psychology
Publisher: Wiley
Published: 1985-11
Volume: 38
Issue: 2
Pages: 171-189
ISSN: 0007-1102 (ISSN-L)
2044-8317
DOI: 10.1111/j.2044-8317.1985.tb00832.x
OpenAlex: W1985442257
Cited by: 1,778
References: 0
Citations by year: 2026: 68 · 2025: 67 · 2024: 84 · 2023: 79 · 2022: 99 · 2021: 97 · 2020: 104 · 2019: 79 · 2018: 68 · 2017: 82 · 2016: 55 · 2015: 73 · 2014: 91 · 2013: 85 · 2012: 72
FWCI: 10.44
Type: journal article
Language: en
Open access: closed
Licence: onlinelibrary.wiley.com/termsAndConditions#vor (vor, 9407 d)
Locations: British Journal of Mathematical and Statistical Psychology (publishedVersion)
Funders: National Science Foundation
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 Methods and Applications
Keywords: factor analysis, Likert scale data, kurtosis, maximum likelihood estimation, generalized least squares, standard error bias

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A comparison of some methodologies for the factor analysis of non‐normal Likert variables

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