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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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“More specifically, skewness and kurtosis values greater than |1| indicated significant deviations from univariate normality (Muthén & Kaplan, 1985).”
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Tho, N. D. (2009) · Quality Assurance in Education · doi:10.1108/09684880910992331 · Cited by 24
“Therefore, the maximum likelihood estimation method was used (Muthen and Kaplan, 1985).”
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“1.50 (Muthén and Kaplan 1985).”
InfluentialConfirmatory Factor Analysis, Validation and Revision of a Teacher Stress Inventory
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Guertler, D., Rumpf, H., Bischof, A., Kastirke, N., Meerkerk, G., John, U., & Meyer, C. (2014) · Diagnostica · doi:10.1026/0012-1924/a000127 · Cited by 23
Smorti, M., Ponti, L., & Tani, F. (2019) · Journal of Reproductive and Infant Psychology · doi:10.1080/02646838.2019.1581919 · Cited by 28
“…was tested using the Maximum Likelihood estimator (Muthén & Muthén, 1998–2007), because no serious problemswith skewness or kurtosis were found (see Table 1), suggesting that the datawere close to a normal univariate distribution (Curran,West, & Finch, 1996; Kline, 2015; Muthén & Kaplan, 1985).”
MethodTho, N. D. (2019) · Education + Training · doi:10.1108/et-03-2018-0068 · Cited by 23
Need satisfaction, passion, empathy and helping behaviour in videogame play
Johnson, D. M., Zhao, X., White, K. M., & Wickramasinghe, V. (2021) · Computers in Human Behavior · doi:10.1016/j.chb.2021.106817 · Cited by 29
Alessandri, G., Vecchione, M., Tisak, J., & Barbaranelli, C. (2011) · Multivariate Behavioral Research · doi:10.1080/00273171.2011.589272 · Cited by 23
“…(West, Finch, & Curran, 1995), different simulation studies have found ML to perform well with variables with five or more categories (Bentler & Chou, 1987) when modest departures from normality are observed (Babakus, Ferguson, & Jöreskog, 1987; Bollen & Barb, 1981; Muthén & Kaplan, 1985, 1992).”
BackgroundDeveloping a Comprehensive School Connectedness Scale for Program Evaluation
Chung‐Do, J. J., Goebert, D. A., Chang, J. Y., & Hamagani, F. (2015) · Journal of School Health · doi:10.1111/josh.12237 · Cited by 28
Marital Satisfaction: Psychometric Properties of the PFB and Comparison with the DAS
Rossier, J., Rigozzi, C., Charvoz, L., & Bodenmann, G. (2006) · Swiss Journal of Psychology · doi:10.1024/1421-0185.65.1.55 · Cited by 23
Miaskowski, C. A., Conley, Y. P., Mastick, J., Paul, S. M., Cooper, B. A., Levine, J. D., Knisely, M. R., & Kober, K. M. (2017) · Journal of Pain and Symptom Management · doi:10.1016/j.jpainsymman.2017.05.007 · Cited by 23
“, reduce bias).(35) Factor loadings were considered meaningful if they exceeded 0.”
BackgroundCultural Factors, Perceived Barriers, and Asian American Career Development
Kantamneni, N., Dharmalingam, K., Orley, G. J., & Kanagasingam, S. K. (2017) · Journal of Career Assessment · doi:10.1177/1069072717723097 · Cited by 27
“Maximum likelihood estimation is robust to multivariate nonnormality (Muthén & Kaplan, 1985), particularly in cases where univariate variables fall within acceptable ranges for normality (skewness values 3; kurtosis values 10; Weston & Gore, 2006).”
BackgroundFactor-analytic Procedures for Assessing Response Pattern Scalability
Ferrando, P. J. (2007) · Multivariate Behavioral Research · doi:10.1080/00273170701382583 · Cited by 23
“Next, the item responses were categorized at five response points by using Muthén and Kaplan’s thresholds (1985) for obtaining non-skewed distributions.”
MethodMoscovitch, D. A., Rowa, K., Paulitzki, J. R., Antony, M. M., & McCabe, R. E. (2015) · Cognitive Therapy and Research · doi:10.1007/s10608-014-9645-5 · Cited by 22
“…toward more frequent endorsement of lower responses on NSPS items, kurtosis and skew characteristics for each respective item were all less than 1.4 and 1.3, respectively, suggesting the item data were represented roughly by normal distributions (see Muthén and Kaplan 1985; West et al. 1995).”
BackgroundInfluentialRenz, S., Kalimeris, J., Hofreiter, S., & Spörrle, M. (2024) · Technological Forecasting and Social Change · doi:10.1016/j.techfore.2024.123760 · Cited by 27
Chamot, E., Kister, I., & Cutter, G. (2014) · BMC Neurology · doi:10.1186/s12883-014-0192-1 · Cited by 22
“Preliminary analyses After performing traditional descriptive statistics for the 11 PS, we conducted exploratory factor analysis (EFA) in the development sample to obtain initial information as to whether the PS should be aggregated into one or more than one disability measures (Additional file 2) [17,18].”
MethodKrishnakumar, S., Hopkins, K., & Robinson, M. D. (2016) · Motivation and Emotion · doi:10.1007/s11031-016-9588-0 · Cited by 23
Morales-Vives, F., Cosí, S., Lorenzo‐Seva, U., & Vigil‐Colet, A. (2019) · Frontiers in Psychology · doi:10.3389/fpsyg.2019.00713 · Cited by 23
“…were done using Pearson correlation coefficients instead of polychoric correlations, which are more advisable with Likert-type items (Muthen and Kaplan, 1985), and most of them used procedures such as the scree test to determine the number of factors to retain instead of more appropriate…”
MethodReverberi, E., Gozzoli, C., D’Angelo, C., Lanz, M., & Sorgente, A. (2021) · Frontiers in Psychology · doi:10.3389/fpsyg.2021.604852 · Cited by 16
“Both steps were performed using Mplus software (version 7.11) and adopting robust maximum likelihood (MLR) as the estimation method to address the items’ non-normal distribution (i.e., skewness and/or kurtosis higher than |1|; Muthen and Kaplan, 1985).”
MethodInfluentialState-Based Estimates of Mammography Screening Rates Based on Information from Two Health Surveys
Davis, W. W., Parsons, V. L., Xie, D., Nathaniel Schenker, A., Town, M., Raghunathan, T. E., & Feuer, E. J. (2010) · Public Health Reports · doi:10.1177/003335491012500412 · Cited by 22
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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