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A comparison of some methodologies for the factor analysis of non‐normal Likert variables
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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“The normality of continuous variables was assessed by examining skewness statistics and normal probability plots. Following the suggestion by Muthen and Kaplan [65], skewness and kurtosis values within the range of −1 to +1 were considered acceptable indicators of normality.”
In the citing paper
“In the empirical field, an inverse association has been consistently found between the capacity for full awareness of the present moment (mindfulness) and the presence of psychological distress [20, 24].”
From Psychological inflexibility mediates the relationship between mindfulness and psychological distress in Peruvian parents with school age children. (2026) · cites this paper as [24]
In the citing paper
“Univariate normality of the data was verified using the guidelines proposed by Muthén and Kaplan (1985) before the analysis of the sample’s results (i.e., to check if acceptable values for asymmetry/asymmetry and kurtosis were in the range from − 1 to + 1 in the case of normal univariate data distribution).”
From Validation and Psychometric Evaluation of the Italian Version of the Fear of COVID-19 Scale (2022) · cites this paper as Muthén and Kaplan (1985)
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“…empirical studies showing that resulting biases are small provided that the number of item categories is no less than five (see, e.g., Bollen, 1989; Dolan, 1994; Muthén & Kaplan, 1985) and provided that excess kurtosis in the manifest items is not severe (see, e.g., Browne, 1984; Jöreskog, 1973).”
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“…r It em # Pe rp et ra te d R ec ei ve d M en W om en t M en W om en t M ( SD ) % n ev er M ( SD ) % n ev er M ( SD ) % n ev er M ( SD ) % n ev er the underlying distribution, rather than assume a normal distribution, this analytic strategy is ideal for the present data (Muthén & Kaplan, 1985).”
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“…ordered 5-category items by imposing a set of categorization thresholds (cf., Babakus et al., 1987; Flora & Curran, 2004; Lubke & Muthén, 2004; B. Muthén & Kaplan, 1985): ~Xig = 0 if Xig\t1 1 if t1 Xig\t2 2 if t2 Xig\t3 3 if t3 Xig\t4 4 if Xig t4 8>>< >>: , ð16Þ where the thresholds were…”
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“Absolute values of skewness and kurtosis were less than or equal to 1, indicating that the univariate normality of all items, across all groups, was within the acceptable level for applying maximum likelihood (ML)2 estimation in confirmatory factor analysis (Muthén & Kaplan, 1985).”
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“On the other hand, it has also been demonstrated that dichotomizing skewed indicators and using a categorical variable estimator in factor analysis can have significant benefits over using a normal theory estimator with skewed continuous indicators (Muth en & Kaplan, 1985).”
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“After sleep parameters were winsorized to 3 standard deviations above or below the mean, no variables except latency exceeded recommended cutoffs for skewness (±2.00) or kurtosis (±7.00; Muthén & Kaplan, 1985).”
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Metadata
- 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
- 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
- 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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