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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.”
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“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]
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“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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“What if a sample with a moderate size does not have a multivariate normal distribution and the ML estimation is used? Theoretically, non-normality leads to an overestimation of the chi-squared statistic (indicating the degree of discrepancy between the model-implied and sample-derived covariance matrices), potentially…”
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Leversen, I., Danielsen, A. G., Birkeland, M. S., & Samdal, O. (2012) · Journal of Youth and Adolescence · doi:10.1007/s10964-012-9776-5 · Cited by 301
“Univariate skewness of 2.0 and higher and kurtosis of 7.0 and higher is considered moderate to high nonnormality and has been found to create problems in analyses (Curran et al. 1996; Muthen and Kaplan 1985, 1992).”
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Fernández, S., & Moldogaziev, T. T. (2013) · Public Administration Review · doi:10.1111/puar.12049 · Cited by 254
Doubly Latent Multilevel Analyses of Classroom Climate: An Illustration
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Kaplan, D. (1990) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr2502_1 · Cited by 249
Self-citationLloret, S., Traver, A. F., Hernández, A., & Tomás-Marco, I. (2017) · Anales de Psicología · doi:10.6018/analesps.33.2.270211 · Cited by 306
Pelletier, L. G., Dion, S. C., Tuson, K. M., & Green‐Demers, I. (1999) · Journal of Applied Social Psychology · doi:10.1111/j.1559-1816.1999.tb00122.x · Cited by 246
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“Studies suggest that polychoric correlations should used when dealing with ordinal data, or in the presence of strong skewness or kurtosis (Muthèn and Kaplan 1985; Gilley and Uhlig 1993), as is often the case of Likert items.”
BackgroundPavlov, G., Maydeu‐Olivares, A., & Shi, D. (2020) · Educational and Psychological Measurement · doi:10.1177/0013164420926231 · Cited by 272
“To achieve the designed skewness and kurtosis, the continuous data were discretized using selected threshold values (Maydeu-Olivares, 2017b; Muthén & Kaplan, 1985).”
MethodLajunen, T. J., & Räsänen, M. (2004) · Journal of Safety Research · doi:10.1016/j.jsr.2003.09.020 · Cited by 242
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“…SCALES 581 to produce more semicontinuous or normally distributed variables may be of minimal consequence given the other methods available to ameliorate these problems (for a review see Hau & Marsh, 2004; Hoyle, 1995; Muthén & Kaplan, 1985; Sharma et al., 1989; West, Finch, & Curran, 1995).”
BackgroundMethod
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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