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.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The normality of continuous variables was assessed by examining skewness statistics and normal probability plots, and skewness and kurtosis values within the range of −1 to +1 were considered acceptable indicators of normality.
“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.”
An inverse association has been consistently found between mindfulness and psychological distress.
“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]
Univariate normality of the data was verified using the guidelines proposed by Muthén and Kaplan (1985).
“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)
Cited by
Sorted by citations
Schermelleh-Engel, K., Moosbrugger, H., & Müller, H. (2003) · Department of Psychology - University of Koblenz-Landau · doi:10.23668/psycharchives.12784 · Cited by 8,975 · see citing works
Practical issues in structural modeling
BENTLER, P. M., & CHOU, C.-P. (1987) · Sociological Methods & Research · doi:10.1177/0049124187016001004 · Cited by 5,804 · see citing works
Curran, P. J., West, S. G., & Finch, J. F. (1996) · Psychological Methods · doi:10.1037/1082-989x.1.1.16 · Cited by 5,512 · see citing works
Bond, F. W., Hayes, S. C., Baer, R. A., Carpenter, K. M., Guenole, N., Orcutt, H. K., Waltz, T., & Zettle, R. D. (2011) · Behavior Therapy · doi:10.1016/j.beth.2011.03.007 · Cited by 3,950 · see citing works
“All items, and AAQ-II total scores, were in acceptable ranges (Muthen & Kaplan, 1985).”
BackgroundByrne, B. M., Shavelson, R. J., & Muthén, B. (1989) · Psychological Bulletin · doi:10.1037/0033-2909.105.3.456 · Cited by 3,928 · see citing works
Self-citationFlora, D. B., & Curran, P. J. (2004) · Psychological Methods · doi:10.1037/1082-989x.9.4.466 · Cited by 3,105 · see citing works
“…& Jöreskog, 1987; Green, Akey, Fleming, Hershberger, & Marquis, 1997; Hutchinson & Olmos, 1998;B. Muthén & Kaplan, 1992), parameters are underestimated (Babakus et al., 1987;B. Muthén & Kaplan, 1992), and standard error estimates tend to be downwardly biased (B. Muthén & Kaplan, 1985, 1992).”
MethodLi, C.-H. (2016) · Behavior Research Methods · doi:10.3758/s13428-015-0619-7 · Cited by 3,031 · see citing works
“…ML in cases of severe nonnormality due to categorization, researchers have found that chi-square statistics may be inflated, factor loadings may be downward-biased, and standard errors may be biased to some degree, as well (Beauducel & Herzberg, 2006; Kaplan, 2009; Muthén & Kaplan, 1985, 1992).”
BackgroundRhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. (2012) · Psychological Methods · doi:10.1037/a0029315 · Cited by 2,816 · see citing works
“…studies pronounce ML parameter estimates to be accurate (Beauducel & Herzberg, 2006; DiStefano, 2002; Dolan, 1994; Johnson & Creech, 1983; B. O. Muthén & Kaplan, 1985; but see Babakus, Ferguson, & Jöreskog, 1987, and Dolan, 1994, for evidence that even five categories may not be enough to…”
BackgroundIntroducing the Short Dark Triad (SD3): A Brief Measure of Dark Personality Traits
Jones, D. N., & Paulhus, D. L. (2014) · Assessment · doi:10.1177/1073191113514105 · Cited by 2,162 · see citing works
El análisis factorial exploratorio de los ítems: una guía práctica, revisada y actualizada
Lloret-Segura, S., Traver, A. F., Hernández, A., & Tomás-Marco, I. (2014) · Anales de Psicología · doi:10.6018/analesps.30.3.199361 · Cited by 1,798 · see citing works
Dimensionality assessment of ordered polytomous items with parallel analysis
Timmerman, M. E., & Lorenzo-Seva, U. (2011) · Psychological Methods · doi:10.1037/a0023353 · Cited by 1,634 · see citing works
Complex Sample Data in Structural Equation Modeling
Muthen, B. O., & Satorra, A. (1995) · Sociological Methodology · doi:10.2307/271070 · Cited by 1,586 · see citing works
“Muthen and Kaplan (1985, 1992 ) carried”
Self-citationCan test statistics in covariance structure analysis be trusted?
Hu, L.-T., Bentler, P., & Kano, Y. (1992) · Psychological bulletin · doi:10.1037/0033-2909.112.2.351 · Cited by 1,568 · see citing works
Bandalos, D. L. (2002) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1207/s15328007sem0901_5 · Cited by 1,387 · see citing works
“…violations of normality (Finch, West, & MacKinnon, 1997; Harlow, 1985; Hutchinson & Olmos, 1998; Muthén & Kaplan, 1985, 1992) and coarse categorization (Babakus, Ferguson, & Jöreskog, 1987; Green, Akey, Fleming, Hershberger, & Marquis, 1997; Hutchinson & Olmos, 1998; Muthén & Kaplan, 1985, 1992).”
Environmental risk management and the cost of capital
Sharfman, M. P., & Fernando, C. S. (2008) · Strategic Management Journal · doi:10.1002/smj.678 · Cited by 1,530 · see citing works
Angeles, L. (2002) · Cited by 1,182 · see citing works
Utility of confirmatory factor analysis in test validation research.
Cole, D. A. (1987) · Journal of Consulting and Clinical Psychology · doi:10.1037/0022-006x.55.4.584 · Cited by 1,089 · see citing works
Tanaka, J. S. (1987) · Child Development · doi:10.2307/1130296 · Cited by 982 · see citing works
Enders, C. K. (2001) · Psychological Methods · doi:10.1037/1082-989x.6.4.352 · Cited by 942 · see citing works
On structural equation modeling with data that are not missing completely at random
Muthén, B., Kaplan, D., & Hollis, M. (1987) · Psychometrika · doi:10.1007/bf02294365 · Cited by 883 · see citing works
“In contrast, the FQL estimator merely utilizes the normality of y, an assumption to which parameter estimates have been found rather robust in complete data settings (see e.g., Boomsma, 1983; Muth6n & Kaplan, 1985).”
MethodSelf-citationStructural Equation Modeling: Strengths, Limitations, and Misconceptions
Tomarken, A. J., & Waller, N. G. (2004) · Annual Review of Clinical Psychology · doi:10.1146/annurev.clinpsy.1.102803.144239 · Cited by 892 · see citing works
“Alternative estimators and test statistics can be used with such data (Muthén 1993; Muthén & Kaplan 1985, 1992).”
MethodIntegrative data analysis: The simultaneous analysis of multiple data sets
Curran, P. J., & Hussong, A. M. (2009) · Psychological Methods · doi:10.1037/a0015914 · Cited by 867 · see citing works
“The standard linear confirmatory factor analysis (CFA) model is well suited for items that are (at least approximately) interval scaled, although there is some controversy regarding what constitutes "approximately" (e.g., Muthén & Kaplan, 1985; 1992).”
MethodAssessing Factorial Invariance in Ordered-Categorical Measures
Millsap, R. E., & Tein, J. Y. (2004) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr3903_4 · Cited by 864 · see citing works
“While WLS estimation was used in the examples, this method is known to require very large samples for adequate performance (Boomsma & Hoogland, 2001; Muthén & Kaplan, 1985).”
MethodRisk factors for binge eating onset in adolescent girls: A 2-year prospective investigation.
Stice, E., Presnell, K., & Spangler, D. (2002) · Health Psychology · doi:10.1037/0278-6133.21.2.131 · Cited by 835 · see citing works
Ding, L., Velicer, W. F., & Harlow, L. L. (1995) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705519509540000 · Cited by 791 · see citing works
Do Self-Report Instruments Allow Meaningful Comparisons Across Diverse Population Groups?
Gregorich, S. E. (2006) · Medical Care · doi:10.1097/01.mlr.0000245454.12228.8f · Cited by 784 · see citing works
Analyzing ordinal data with metric models: What could possibly go wrong?
Liddell, T. M., & Kruschke, J. K. (2018) · Journal of Experimental Social Psychology · doi:10.1016/j.jesp.2018.08.009 · Cited by 773 · see citing works
Exploratory Factor Analysis: A Users’Guide
Ferguson, E., & Cox, T. (1993) · International Journal of Selection and Assessment · doi:10.1111/j.1468-2389.1993.tb00092.x · Cited by 724 · see citing works
Robustness Studies in Covariance Structure Modeling: An Overview and a Meta-Analysis
HOOGLAND, J. J., & BOOMSMA, A. (1998) · Sociological Methods & Research · doi:10.1177/0049124198026003003 · Cited by 734 · see citing works
A Comparison of Diagonal Weighted Least Squares Robust Estimation Techniques for Ordinal Data
DiStefano, C., & Morgan, G. B. (2014) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2014.915373 · Cited by 705 · see citing works
“By inverting only the diagonal, these techniques avoid some of the problems identified with WLS (Bollen, 1989; Muthén & Kaplan, 1985).”
MethodThe Effect of Varying Degrees of Nonnormality in Structural Equation Modeling
Lei, M., & Lomax, R. G. (2005) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1207/s15328007sem1201_1 · Cited by 705 · see citing works
“ML, GLS, and asymptotically distribution free (ADF) are the most common estimators investigated in previous studies (Arminger & Rothe, 1993; Chou et al., 1991; Fan & Wang, 1998; Finch et al., 1997; Muthén, 1989; Muthén & Kaplan, 1985, 1992; Wang et al., 1995).”
BackgroundMethodFromme, K., Stroot, E. A., & Kaplan, D. (1993) · Psychological Assessment · doi:10.1037/1040-3590.5.1.19 · Cited by 704 · see citing works
Self-citationFormulating clinical research hypotheses as structural equation models: A conceptual overview.
Hoyle, R. H., & Smith, G. T. (1994) · Journal of Consulting and Clinical Psychology · doi:10.1037//0022-006x.62.3.429 · Cited by 696 · see citing works
Factor Analysis with Ordinal Indicators: A Monte Carlo Study Comparing DWLS and ULS Estimation
Forero, C. G., Maydeu-Olivares, A., & Gallardo-Pujol, D. (2009) · Structural Equation Modeling: A Multidisciplinary Journal · doi:10.1080/10705510903203573 · Cited by 685 · see citing works
“The WLS estimator turned out to be impractical, however, as it was found to converge very slowly to its asymptotic properties (Muthén & Kaplan, 1985, 1992).”
BackgroundStice, E., & Bearman, S. K. (2001) · Developmental Psychology · doi:10.1037/0012-1649.37.5.597 · Cited by 704 · see citing works
Pelletier, L. G., Fortier, M. S., Vallerand, R. J., & Brière, N. M. (2001) · Motivation and Emotion · doi:10.1023/a:1014805132406 · Cited by 958 · see citing works
“Despite a few high values, univariate values of kurtosis and skewness were considered adequate since mean kurtosis (|M | = 0.77) and mean skewness (|M | = 0.25) were within an acceptable range of 0–1.00 (Muthén & Kaplan, 1985).”
BackgroundInfluentialTwo-dimensional self-esteem: Theory and measurement
Tafarodi, R. W., & Swann, W. B. (2001) · Personality and Individual Differences · doi:10.1016/s0191-8869(00)00169-0 · Cited by 606 · see citing works
“ADF estimation was used here, given evidence for its adequate performance with skewed variables when models are modest in complexity and sample size is >1000 (Hu, Bentler & Kano, 1992; Muthe n & Kaplan, 1985).”
MethodPerceptual measures of performance: fact or fiction?
Ketokivi, M. A., & Schroeder, R. G. (2004) · Journal of Operations Management · doi:10.1016/j.jom.2002.07.001 · Cited by 607 · see citing works
Structural Equation Modeling in Practice
Johnson, K. (1999) · Journal of Social Service Research · doi:10.1300/j079v24n03_06 · Cited by 597 · see citing works
Issues and recommendations for exploratory factor analysis and principal component analysis
Schreiber, J. B. (2021) · Research in Social and Administrative Pharmacy · doi:10.1016/j.sapharm.2020.07.027 · Cited by 565 · see citing works
Wu, H., & Estabrook, R. (2016) · Psychometrika · doi:10.1007/s11336-016-9506-0 · Cited by 541 · see citing works
“Data collected with such measures had been analyzed as normal data until proper models for ordered categorical outcomes were introduced (Jöreskog and Moustaki, 2001; Mislevy, 1986; Muthén, 1984) and proved to be superior (Babakus, Ferguson and Jöreskog, 1987; Bernstein and Teng, 1989; Lubke and Muthén, 2004; Muthén an…”
MethodMarsh, H. W., & Hocevar, D. (1988) · Journal of Applied Psychology · doi:10.1037/0021-9010.73.1.107 · Cited by 529 · see citing works
Empowering leadership: Construct clarification, conceptualization, and validation of a new scale
Amundsen, S., & Martinsen, Ø. L. (2013) · The Leadership Quarterly · doi:10.1016/j.leaqua.2013.11.009 · Cited by 560 · see citing works
“Univariate skewness and kurtosis values were all well within the cutoff values of ±1.0 recommended by Muthén and Kaplan (1985).”
BackgroundInfluentialLajunen, T. J., & Summala, H. (2003) · Transportation Research Part F Traffic Psychology and Behaviour · doi:10.1016/s1369-8478(03)00008-1 · Cited by 505 · see citing works
Chang, L. (1994) · Applied Psychological Measurement · doi:10.1177/014662169401800302 · Cited by 502 · see citing works
Lubke, G. H., & Muthén, B. (2004) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1207/s15328007sem1104_2 · Cited by 489 · see citing works
“Data arising from Likert-type items are often analyzed as multivariate normal outcomes, although the data are ordered categorical (Muthén & Kaplan, 1985).”
Self-citationA Tutorial on Hierarchically Structured Constructs
Brunner, M., Nagy, G., & Wilhelm, O. (2012) · Journal of Personality · doi:10.1111/j.1467-6494.2011.00749.x · Cited by 459 · see citing works
Cross-Cultural Comparisons and the Presumption of Equivalent Measurement and Theoretical Structure
Byrne, B. M., & Campbell, T. L. (1999) · Journal of Cross-Cultural Psychology · doi:10.1177/0022022199030005001 · Cited by 472 · see citing works
“For scores that are normally distributed, the skewness and kurtosis values will equal zero, although values ranging from –1.50 to +1.50 may be considered to approximate a normal distribution (Muthén & Kaplan, 1985).”
BackgroundInfluentialSmith, R. E., Smoll, F. L., & Schutz, R. W. (1990) · Anxiety Research · doi:10.1080/08917779008248733 · Cited by 455 · see citing works
Validation and Psychometric Evaluation of the Italian Version of the Fear of COVID-19 Scale
Soraci, P., Ferrari, A., Abbiati, F. A., Del Fante, E., De Pace, R., Urso, A., & Griffiths, M. D. (2022) · International Journal of Mental Health and Addiction · doi:10.1007/s11469-020-00277-1 · Cited by 427 · see citing works
“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…”
BackgroundMethodHertzog, C., Van Alstine, J., Usala, P. D., Hultsch, D. F., & Dixon, R. (1990) · Psychological Assessment: A Journal of Consulting and Clinical Psychology · doi:10.1037/1040-3590.2.1.64 · Cited by 452 · see citing works
Why Are You Doing Things for the Environment? The Motivation Toward the Environment Scale (MTES)1
Pelletier, L. G., Tuson, K. M., Green‐Demers, I., Noels, K., & Beaton, A. M. (1998) · Journal of Applied Social Psychology · doi:10.1111/j.1559-1816.1998.tb01714.x · Cited by 444 · see citing works
Jedidi, K., Jagpal, H. S., & DeSarbo, W. S. (1997) · Marketing Science · doi:10.1287/mksc.16.1.39 · Cited by 435 · see citing works
“This design and choice of factor levels are consistent with those used in previous simulations (e.g., Muthen and Kaplan 1985).”
InfluentialWelpe, I. M., Spörrle, M., Grichnik, D., Michl, T., & Audretsch, D. B. (2011) · Entrepreneurship Theory and Practice · doi:10.1111/j.1540-6520.2011.00481.x · Cited by 428 · see citing works
Svetina, D., Rutkowski, L. A., & Rutkowski, D. (2019) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2019.1602776 · Cited by 429 · see citing works
“Ignoring the categorical distribution of these variables in a CFA context can have severe consequences on parameters, model fit, and cross-group comparisons (Beauducel & Herzberg, 2006; Lubke & Muthén, 2004; Muthén & Kaplan, 1985).”
BackgroundGlaesmer, H., Grande, G., Braehler, E., & Roth, M. (2011) · European Journal of Psychological Assessment · doi:10.1027/1015-5759/a000058 · Cited by 485 · see citing works
ASSESSING AGE AND GENDER DIFFERENCES IN PERCEIVED RISK AND FEAR OF CRIME*
LaGrange, R. L., & Ferraro, K. F. (1989) · Criminology · doi:10.1111/j.1745-9125.1989.tb01051.x · Cited by 404 · see citing works
Marsh, H. W. (2007) · Wiley eBooks · doi:10.1002/9781118270011.ch35 · Cited by 395 · see citing works
Rogers, W. M., & Schmitt, N. (2004) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr3903_1 · Cited by 391 · see citing works
“In addition, violations of CSA normality assumptions at the item level have been shown to produce bias in model fit indices (Bandalos, 2002; Muthén & Kaplan, 1985, 1992).”
BackgroundBringing the Candidate into Models of Candidate Evaluation
Funk, C. L. (1999) · The Journal of Politics · doi:10.2307/2647824 · Cited by 389 · see citing works
Using Confirmatory Factor Analysis for Construct Validation: An Empirical Review
DiStefano, C., & Hess, B. (2005) · Journal of Psychoeducational Assessment · doi:10.1177/073428290502300303 · Cited by 385 · see citing works
Have Multilevel Models Been Structural Equation Models All Along?
Curran, P. J. (2003) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr3804_5 · Cited by 384 · see citing works
Sample Size and Power Estimates for a Confirmatory Factor Analytic Model in Exercise and Sport
Myers, N. D., Ahn, S., & Jin, Y. (2011) · Research Quarterly for Exercise and Sport · doi:10.1080/02701367.2011.10599773 · Cited by 306 · see citing works
“The probability of observing untrustworthy results when categorical data are modeled with a NT estimator depends strongly on the degree of nonnormality and the number of ordered response options (e.g., DiStefano, 2002; Dolan, 1994; Muthén & Kaplan, 1985).”
BackgroundMaydeu‐Olivares, A. (2017) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2016.1269606 · Cited by 381 · see citing works
“To conduct analyses, data with five ordered categories were generated, given that this is the minimum number of categories found to be acceptable for considering item-level ordinal data as continuous (Muthén & Kaplan, 1985; Rhemtulla, BrosseauLiard, & Savalei, 2012).”
MethodResultExamination of the Weighted Root Mean Square Residual: Evidence for Trustworthiness?
DiStefano, C., Liu, J., Jiang, N., & Shi, D. (2018) · Structural Equation Modeling: A Multidisciplinary Journal · doi:10.1080/10705511.2017.1390394 · Cited by 372 · see citing works
“As with previous studies (e.g., DiStefano & Morgan, 2014; Muthén & Kaplan, 1985), item-level nonnormal data were generated by discretizing continuous, normal data through the application of set threshold values.”
MethodHohenberger, C., Spörrle, M., & Welpe, I. M. (2016) · Transportation Research Part A Policy and Practice · doi:10.1016/j.tra.2016.09.022 · Cited by 362 · see citing works
The Impact of Categorization With Confirmatory Factor Analysis
DiStefano, C. (2002) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1207/s15328007sem0903_2 · Cited by 361 · see citing works
“As with previous studies, the WLS estimator showed its sensi- tivity to smaller sample sizes, with higher chi-square values and two SRMR values that were beyond their cutoff level (.05; Hutchinson & Olmos; 1998; Muthén & Kaplan, 1985; Potthast, 1993).”
BackgroundMethodResultInfluentialThe conceptualization and empirical validation of web site user satisfaction
Muylle, S., Moenaert, R. K., & Despontin, M. (2003) · Information & Management · doi:10.1016/s0378-7206(03)00089-2 · Cited by 358 · see citing works
Monte Carlo Experiments: Design and Implementation
Paxton, P. M., Curran, P. J., Bollen, K. A., Kirby, J., & Chen, F. (2001) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1207/s15328007sem0802_7 · Cited by 347 · see citing works
The Development and Validation of the Game User Experience Satisfaction Scale (GUESS)
Phan, M. H., Keebler, J. R., & Chaparro, B. S. (2016) · Human Factors The Journal of the Human Factors and Ergonomics Society · doi:10.1177/0018720816669646 · Cited by 368 · see citing works
“Additionally, researchers have noted that, in practice, factor analysis is often conducted on severely skewed and kur-totic data (Muthén & Kaplan, 1985; Wang, Fan, & Willson, 1996).”
BackgroundBest methods for the analysis of change: Recent advances, unanswered questions, future directions.
Collins, L. M., & American Psychological Association (1991) · American Psychological Association eBooks · doi:10.1037/10099-000 · Cited by 337 · see citing works
A new look at Horn’s parallel analysis with ordinal variables.
Garrido, L. E., Abad, F. J., & Ponsoda, V. (2012) · Psychological Methods · doi:10.1037/a0030005 · Cited by 346 · see citing works
“Thresholds for the asymmetric conditions were created so that as the skewness level increased, the observations were piled up in one of the extreme categories (Muthén & Kaplan, 1985).”
BackgroundInfluentialRetail service quality and perceived value
Sweeney, J., Soutar, G. N., & Johnson, L. W. (1997) · Journal of Retailing and Consumer Services · doi:10.1016/s0969-6989(96)00017-3 · Cited by 350 · see citing works
Byrne, B. M. (1994) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr2903_5 · Cited by 327 · see citing works
Marsh, H. W., Vallerand, R. J., Lafrenière, M.-A. K., Parker, P., Morin, A. J. S., Carbonneau, N., Jowett, S., Bureau, J. S., Fernet, C., Guay, F., et al. (2013) · Psychological Assessment · doi:10.1037/a0032573 · Cited by 420 · see citing works
“…of fit that are robust in relation to nonnormality of observations and the use of categorical variables when there are at least four or more response categories (e.g., Beauducel & Herzberg, 2006; DiStefano, 2002; Dolan, 1994; B. O. Muthén & Kaplan, 1985; Rhemtulla, Brosseau-Liard, & Savalei, 2010).”
BackgroundStatistical Issues in the Study of Temporal Data: Daily Experiences
West, S. G., & Hepworth, J. T. (1991) · Journal of Personality · doi:10.1111/j.1467-6494.1991.tb00261.x · Cited by 307 · see citing works
Confirmatory Factor Analysis of Ordinal Variables With Misspecified Models
Yang‐Wallentin, F., Jöreskog, K. G., & Luo, H. (2010) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2010.489003 · Cited by 317 · see citing works
“Methods developed for continuous variables are not suitable for such ordinal variables (see B. O. Muthén & Kaplan, 1985, 1992).”
BackgroundMarsh, H. W., Ellis, L. A., & Craven, R. G. (2002) · Developmental Psychology · doi:10.1037/0012-1649.38.3.376 · Cited by 302 · see citing works
Giromini, L., Velotti, P., de Campora, G., Bonalume, L., & Cesare Zavattini, G. (2012) · Journal of Clinical Psychology · doi:10.1002/jclp.21876 · Cited by 301 · see citing works
The Development and Validation of the State Self-Compassion Scale (Long- and Short Form)
Neff, K. D., Tóth-Király, I., Knox, M. C., Kuchar, A., & Davidson, O. (2021) · Mindfulness · doi:10.1007/s12671-020-01505-4 · Cited by 309 · see citing works
Fernández, J. G., Gálvez-Ruíz, P., Gavira, J. F., Vélez-Colón, L., Pitts, B. G., & García, A. B. (2017) · Sport Management Review · doi:10.1016/j.smr.2017.07.003 · Cited by 309 · see citing works
Genberg, B. L., Hlávka, Z., Konda, K. A., Maman, S., Chariyalertsak, S., Chingono, A., Mbwambo, J. K. K., Modiba, P., van Rooyen, H., & Celentano, D. D. (2009) · Social Science & Medicine · doi:10.1016/j.socscimed.2009.04.005 · Cited by 296 · see citing works
“Confirmatory factor analysis was conducted using LISREL with a structural equation model with a polychoric correlation matrix specifying a priori three correlated factors measured with 19 items on the total sample (Muthen & Kaplan, 1985; Muthen, 1984).”
MethodPolakowski, M. (1994) · Journal of Quantitative Criminology · doi:10.1007/bf02221008 · Cited by 277 · see citing works
Destination loyalty: Effects of wine tourists’ experiences, memories, and satisfaction on intentions
Quadri-Felitti, D., & Fiore, A. M. (2013) · Tourism and Hospitality Research · doi:10.1177/1467358413510017 · Cited by 276 · see citing works
Service Problems and Recovery Stratégies: An Experiment
Levesque, T. J., & McDougall, G. H. G. (2000) · Canadian Journal of Administrative Sciences / Revue Canadienne des Sciences de l Administration · doi:10.1111/j.1936-4490.2000.tb00204.x · Cited by 273 · see citing works
Marsh, H. W., Martin, A. J., & Jackson, S. A. (2010) · Journal of Sport and Exercise Psychology · doi:10.1123/jsep.32.4.438 · Cited by 274 · see citing works
“…relatively unbiased when based on approximately normally distributed, ordered categorical data with at least five categories (Babakus, Ferguson, & Jöreskog, 1987; Beauducel & Herzberg, 2006; DiStefano, 2002; Dolan, 1994; Johnson & Creech, 1983; Muthén & Kaplan, 1985; West, Finch, & Curran, 1995).”
BackgroundInfluentialGreen‐Demers, I., Pelletier, L. G., & Ménard, S. (1997) · Canadian Journal of Behavioural Science/Revue canadienne des sciences du comportement · doi:10.1037/0008-400x.29.3.157 · Cited by 273 · see citing works
Reis, D., Xanthopoulou, D., & Tsaousis, I. (2015) · Burnout Research · doi:10.1016/j.burn.2014.11.001 · Cited by 271 · see citing works
Suicide risk in trans populations: An application of minority stress theory.
Tebbe, E. A., & Moradi, B. (2016) · Journal of Counseling Psychology · doi:10.1037/cou0000152 · Cited by 268 · see citing works
Nonnormality of Data in Structural Equation Models
Gao, S., Mokhtarian, P. L., & Johnston, R. A. (2008) · Transportation Research Record Journal of the Transportation Research Board · doi:10.3141/2082-14 · Cited by 257 · see citing works
“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…”
BackgroundInfluentialBasic Psychological Need Satisfaction in Leisure Activities and Adolescents’ Life Satisfaction
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 262 · see citing works
“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).”
BackgroundInfluentialEmployee Empowerment, Employee Attitudes, and Performance: Testing a Causal Model
Fernández, S., & Moldogaziev, T. T. (2013) · Public Administration Review · doi:10.1111/puar.12049 · Cited by 254 · see citing works
Doubly Latent Multilevel Analyses of Classroom Climate: An Illustration
Morin, A. J. S., Marsh, H. W., Nagengast, B., & Scalas, L. F. (2013) · The Journal of Experimental Education · doi:10.1080/00220973.2013.769412 · Cited by 256 · see citing works
Evaluating and Modifying Covariance Structure Models: A Review and Recommendation
Kaplan, D. (1990) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr2502_1 · Cited by 249 · see citing works
Self-citationLloret, S., Traver, A. F., Hernández, A., & Tomás-Marco, I. (2017) · Anales de Psicología · doi:10.6018/analesps.33.2.270211 · Cited by 266 · see citing works
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 · see citing works
An SPSS R -Menu for Ordinal Factor Analysis
Basto, M., & Pereira, J. M. (2012) · Journal of Statistical Software · doi:10.18637/jss.v046.i04 · Cited by 247 · see citing works
“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 271 · see citing works
“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 · see citing works
Sass, D. A., & Smith, P. L. (2006) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1207/s15328007sem1304_4 · Cited by 241 · see citing works
“…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
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
