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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“…1998-2008), using the robust maximum likelihood estimator (MLR), which has been found to be efficient in the estimation of latentvariable models based on items rated on answer scales incorporating five or more response categories (Beauducel & Herzberg, 2006; DiStefano, 2002; Muthén & Kaplan, 1985).”
Method
Categorizing h-index variants
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“But according to Muthen & Kaplan (1985) , some degree of skew and kurtosis in the data is acceptable for conducting EFA, especially when the skew and kurtosis coefficients are below the value of 2.”
BackgroundInfluential
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“For variables with skewness and kurtosis not far from the range of 21 and +1, estimating the parameter of non-normal variables via the maximum likelihood (ML) method would get acceptable values (Muthen & Kaplan, 1985).”
Method
An evaluation of the factor structure of the Problem Gambling Severity Index
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“…ordered category data and which does not, therefore, assume that the intervals between the categories are equal is, thus, the most appropriate coefficient for use with these data (Holgado-Tello, Chacón-Moscoso, Barbero-Garcı́a, & Vila-Abad, 2010; Muthén & Kaplan, 1985; Wang & Cunningham, 2005).”
Method
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“We can consider the degree of non-normality thought the skewness and kurtosis values (Harlow, 1985; Lei & Lomax, 2005; Muthén & Kaplan, 1985).”
Background
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“Treating nominal and ordinal data as interval or ratio data, may lead to unreliable parameter estimates as well as to poor goodness of fit, especially in presence of highly skewed non Gaussian data or polarized/bimodal distributions (Muthén and Kaplan, 1985).”
BackgroundMethod
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Zagalaz, J. C., Lara-Sánchez, A. J., Sánchez, M. L. Z., Manrique, I. L., & de Mesa, C. G. G. (2018) · Suma Psicológica · doi:10.14349/sumapsi.2018.v25.n2.3 · Cited by 18
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“Some authors [51] also argue that kurtosis values within the range of ± 2 are sufficient to assume normality for structural equation modelling.”
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Tracey, D. (2002) · Cited by 17
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“Muthen and Kaplan (1985) have suggested that if the variables have skewness and kurtosis from +1 to -1, then estimating parameters with maximum likelihood is acceptable.”
Background
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“Skewness and kurtosis were within the acceptable range (+1.00; Muthén & Kaplan, 1985).”
BackgroundInfluential
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“A number of researchers have recently argued, sometimes vociferously (Bradley, 1980), that the assumption of normality is often untenable with biometric and/or social science data (Andrews et al., 1972; Ansell, 1973; Boomsma, 1983; Browne, 1982, 1984, 1987; Harlow, 1985; Hill and Dixon, 1982; Muth6n, 1984, 1987b; Muth…”
BackgroundSelf-citation
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Reliability for Tests With Items Having Different Numbers of Ordered Categories
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“For the five-response category tests, the thresholds used to generate the normal and moderate skew distributions were taken from Muthén and Kaplan (1985).”
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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