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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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“…distributions can inflate maximum likelihood χ2 values and thus bias researchers to erroneously reject correct models (Curran, West, & Finch, 1996; Muthén & Kaplan, 1985; Satorra, 1991), we removed the aforementioned eight severely skewed and conceptually flawed items and performed three…”
Depressive mood and social maladjustment: Differential effects on academic achievement
Aluja, A., & Blanch, À. (2004) · European Journal of Psychology of Education · doi:10.1007/bf03173227 · Cited by 14
Anguiano‐Carrasco, C., & Vigil‐Colet, A. (2011) · PubMed · Cited by 13
Yang, Y. X., Jing, F., & Nguyen, B. (2016) · Journal of China Tourism Research · doi:10.1080/19388160.2016.1223776 · Cited by 13
“Hence, SEM is applicable to this study (Muthén & Kaplan, 1985).”
MethodTueller, S., Johnson, K. L., Grimm, K. J., Desmarais, S. L., Sellers, B. G., & Dorn, R. A. V. (2016) · International Journal of Methods in Psychiatric Research · doi:10.1002/mpr.1549 · Cited by 13
“…practice of collapsing categories has received mixed reactions in the literature; some maintain that collapsing categories will not adversely affect results (Hsueh, Wang, Sheu, & Hsieh, 2004; Meulman & Heiser, 2001; Muthén & Kaplan, 1985), whereas others note potential limitations of the practice.”
BackgroundLundmark, R., Schwarz, U. V. T., Hasson, H., Stenling, A., & Tafvelin, S. (2017) · Stress and Health · doi:10.1002/smi.2770 · Cited by 14
“…scalewere conductedbased on itemmean centring aroundmiddle value, a relatively large variance (SD > 0.50), skewness and kurtosis between −1 and 1 (Muthén & Kaplan, 1985), interitem correlations over .40, interscale correlations above .30 and squared multiple correlations ≈ 0.50 (Clark & Watson,…”
BackgroundInfluentialEsnaola, I., Benito, M., Antonio‐Agirre, I., Ballina, E., & de Reizábal, M. L. (2019) · Child Indicators Research · doi:10.1007/s12187-018-9616-6 · Cited by 13
QUASUS: A Tool for Measuring the Parents’ School Satisfaction
Mossi, P., Ingusci, E., Tonti, M., & Salvatore, S. (2019) · Frontiers in Psychology · doi:10.3389/fpsyg.2019.00013 · Cited by 13
Racz, S. J., McMahon, R. J., King, K. M., Pinderhughes, E. E., & Bendezú, J. J. (2019) · Development and Psychopathology · doi:10.1017/s0954579419000993 · Cited by 20
“…rules variables revealed a preponderance of “5’s” (i.e., the majority of children and parents indicated that children “almost always” had a curfew); therefore, we modeled these variables as censored, requiring the use of a weighted least squares (WLSMV) estimator in Mplus (Muthén & Kaplan, 1985).”
MethodShort report: Perceptions of causes and common beliefs of autism spectrum disorder in the U.S
Castillo, A., Cohen, S. R., Miguel, J., & Warstadt, M. F. (2019) · Research in Autism · doi:10.1016/j.rasd.2019.101472 · Cited by 14
Quang, H. T., Sampaio, P. A. D. C. A., Carvalho, M. S., Fernandes, A. C., & An, D. T. B. (2014) · Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT) · Cited by 13
Horwitz, S. K., & Horwitz, I. B. (2012) · Human Resource Management · doi:10.1002/hrm.20465 · Cited by 13
The Unidimensionality and Reliability of the Preschool and Kindergarten Behavior Scales
Edwards, M. C., Whiteside-Mansell, L., Conners, N. A., & Deere, D. (2003) · Journal of Psychoeducational Assessment · doi:10.1177/073428290302100102 · Cited by 13
Exploring bipolarity of affect ratings by using polychoric correlations
Schmukle, S. C., & Egloff, B. (2008) · Cognition & Emotion · doi:10.1080/02699930801987330 · Cited by 13
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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