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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“…included between a range Europe's Journal of Psychology 2020, Vol. 16(2), 331–351 https://doi.org/10.5964/ejop.v16i2.1876 of -1 and +1 are considered acceptable (Muthén & Kaplan, 1985) and the histogram, as well as the Normal Q-Q Plot, showed that responses were reasonably normally distributed.”
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“Maximum likelihood procedures are robust for moderate departures from normality (Muthén & Kaplan, 1985).”
DİJİTAL EBEVEYNLİĞİN, AİLE İÇİ İLETİŞİM VE VELİNİN EĞİTİME KATILIMI ÜZERİNE ETKİSİ: YAPISAL EŞİTLİK MODELİ
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“Maximum Likelihood was selected as the estimator given that all the items were normally distributed (kurtosis and skewness ≤ │1.2│; Muthén & Kaplan, 1985).”
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“Since a substantial number of items in both subgroups showed values of skewness and kurtosis that fell outside the [ 1; +1] range recommended by Muthén and Kaplan (1985) for using maximum likelihood estimator (see Table 1), factor analyses were performed in Mplus 6.1 using the mean and variance…”
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“We also used polychoric correlations which are advised when univariate distributions of ordinal items are asymmetric for polytomous items (Brown, 2006; Muthén & Kaplan, 1985; 1992).”
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“Several researchers (e.g., Achenbach, 1978; Muthén & Kaplan, 1985; West et al., 1995) suggest that 4-point Likert data are inherently nonnormal.”
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“42 Consistent with Floyd and Widaman’s recommendations, 24 all values of the communalities were greater than 0.50.”
Influential
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Self-citation
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“The data had a normal univariate distribution, skewness, and kurtosis values being approximately in the range −1 and+1 (Muthén and Kaplan, 1985) (Table 1).”
Background
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“…robustness of ML estimators to violations of distributional assumptions when the observed variables are discrete (e.g., Boomsma, 1983; Harlow, 1985; Muthén & Kaplan, 1985; Olsson, 1979), pointed out that not much distortion of the ML chi-square, and very little or nonexistent parameter estimate…”
Background
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“However, Bollen (1989) argued that the assumption of multivariate normality need not apply to exogenous variables, and Muthén and Kaplan (1985) showed that maximum likelihood and generalized least squares estimators remain stable with categorical data.”
Background
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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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