The DOI matches its Crossref record.
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.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
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?
In the citing paper
“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)
Citations
Cited by
Sorted by citations
Items 101–200 of 1,003
Three Approaches to Using Lengthy Ordinal Scales in Structural Equation Models
Yang, C., Nay, S., & Hoyle, R. H. (2009) · Applied Psychological Measurement · doi:10.1177/0146621609338592 · Cited by 254
“Under various distributions, the weighted least squares estimator with degrees of freedom adjusted for means and variances (WLSMV) in Mplus has proven to be fairly robust to various categorical indicators with large sample sizes (B. O. Muthén & Kaplan, 1985, 1992).”
BackgroundJensen, K., & Cross, K. (2021) · Journal of Engineering Education · doi:10.1002/jee.20391 · Cited by 278
“Previous literature suggests absolute value of skewness greater than 2 and kurtosis greater than 7 indicate non-normality (Curran et al., 1996; Harlow, 1986; Muthén & Kaplan, 1985).”
BackgroundFlora, D. B., Labrish, C., & Chalmers, R. P. (2012) · Frontiers in Psychology · doi:10.3389/fpsyg.2012.00055 · Cited by 236
“…by factor analyzing product-moment R can lead to incorrect decisions about the number of common factors or overall model fit, biased parameter estimates, and biased SE estimates (Muthén and Kaplan, 1985, 1992; Babakus et al., 1987; Bernstein and Teng, 1989; Dolan, 1994; Green et al., 1997).”
BackgroundStice, E. M. (1998) · Behaviour Research and Therapy · doi:10.1016/s0005-7967(98)00074-6 · Cited by 236
Estimation of IRT graded response models: Limited versus full information methods.
Forero, C. G., & Maydeu‐Olivares, A. (2009) · Psychological Methods · doi:10.1037/a0015825 · Cited by 234
“…CIFA, more simulation studies have assessed the performance of CIFA methods (e.g., DiStefano, 2002; Dolan, 1994; Flora & Curran, 2004; Kaplan, 1991; Muthén & Kaplan, 1985, 1992; Oranje, 2003; Parry & McArdle, 1991; Potthast, 1993; Rigdon & Ferguson, 1991), and, as a result, we have a more…”
MethodBai, X., Wu, C., Zheng, R., & Ren, X. (2010) · Journal of Happiness Studies · doi:10.1007/s10902-010-9186-x · Cited by 233
“…was small when the number of points was increased to six and the sample size was large; (2) Dolan (1994) suggested that five response categories are the minimum when ML estimation is performed; and (3) Muthén and Kaplan (1985) suggested that if variables have skewness and kurtosis from -1 to ?”
BackgroundTopic Avoidance in Developing Romantic Relationships
Knobloch, L. K., & Carpenter‐Theune, K. E. (2004) · Communication Research · doi:10.1177/0093650203261516 · Cited by 232
“Most of our measures violated the structural equation modeling assumption of multivariate normality, so we used the maximum likelihood method of estimation because it is somewhat robust against such violations (Fan & Wang, 1998; Muthen & Kaplan, 1985).8 We evaluated the statistical fit of our Note.”
MethodApplication of Structural Equation Modeling in Educational Research and Practice
Teo, T., Tsai, L. T., & Yang, C. C. (2013) · SensePublishers eBooks · doi:10.1007/978-94-6209-332-4 · Cited by 250
Albiero, P., Matricardi, G., Speltri, D., & Toso, D. (2008) · Journal of Adolescence · doi:10.1016/j.adolescence.2008.01.001 · Cited by 230
Passion and Gambling: Investigating the Divergent Affective and Cognitive Consequences of Gambling1
Mageau, G. A., Vallerand, R. J., Rousseau, F. L., Ratelle, C. F., & Provencher, P. J. (2005) · Journal of Applied Social Psychology · doi:10.1111/j.1559-1816.2005.tb02095.x · Cited by 224
“Overall, univariate values of kurtosis and skewness were generally adequate, with most values ranging from -1.0 to +1.0 and a mean skewness of .51 and a mean kurtosis of .23 (Muthén & Kaplan, 1985).”
BackgroundInfluentialAn Investigation of the Sample Performance of Two Nonnormality Corrections for RMSEA
Brosseau-Liard, P. É., Savalei, V., & Li, L. (2012) · Multivariate Behavioral Research · doi:10.1080/00273171.2012.715252 · Cited by 245
“Studies have shown that the ML methodology breaks down with increasing multivariate kurtosis (Chou, Bentler, & Satorra, 1991; Curran, West, & Finch, 1996; Hu, Bentler, & Kano, 1992; Muthén & Kaplan, 1985, 1992).”
Adams, L. L., Gatchel, R. J., Robinson, R. C., Polatin, P. B., Gajraj, N. M., Deschner, M., & Noe, C. E. (2004) · Journal of Pain and Symptom Management · doi:10.1016/j.jpainsymman.2003.10.009 · Cited by 216
Markland, D. A., & Hardy, L. (1997) · Research Quarterly for Exercise and Sport · doi:10.1080/02701367.1997.10608863 · Cited by 227
Petkova, A. P., Rindova, V., & Gupta, A. K. (2012) · Organization Science · doi:10.1287/orsc.1120.0759 · Cited by 219
“We used the maximum-likelihood (ML) estimation procedure, which allows for testing both direct and interaction effects and is pretty robust with respect to skewed and kurtotic variables (Hayduk 1987, Muthen and Kaplan 1985).”
MethodThe 10-Item Big Five Inventory
Rammstedt, B. (2007) · European Journal of Psychological Assessment · doi:10.1027/1015-5759.23.3.193 · Cited by 235
Jõesaar, H., Hein, V., & Hagger, M. S. (2011) · Psychology of sport and exercise · doi:10.1016/j.psychsport.2011.04.005 · Cited by 235
Byrne, B. M. (1991) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr2604_2 · Cited by 211
Farrell, A. D. (1994) · Journal of Consulting and Clinical Psychology · doi:10.1037//0022-006x.62.3.477 · Cited by 209
Issues in applied structural equation modeling research
Raykov, T., & Widaman, K. F. (1995) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705519509540017 · Cited by 207
Public Service Motivation Measurement
Coursey, D. H., & Pandey, S. K. (2007) · Administration & Society · doi:10.1177/0095399707303634 · Cited by 207
Maydeu‐Olivares, A., Shi, D., & Rosseel, Y. (2017) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2017.1389611 · Cited by 214
“Because the number of categories is large, it is appropriate to treat the discretized data as continuous when conducting data analysis (Muthén & Kaplan, 1985; Rhemtulla, Brosseau-Liard, & Savalei, 2012).”
MethodMarsh, H. W., Craven, R. G., Hinkley, J. W., & Debus, R. L. (2003) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr3802_3 · Cited by 205
“…estimation procedures are robust in relation to violations of normality – particularly in relation to parameter estimates (factor loadings, factor correlations, path coefficients, etc.) that were our main concern (e.g., Hu, Bentler, & Kano, 1992; Jöreskog & Sörbom, 1993; Múthen & Kaplan, 1985).”
BackgroundInguglia, C., Ingoglia, S., Liga, F., Lo Coco, A., & Lo Cricchio, M. G. (2015) · Journal of Adult Development · doi:10.1007/s10804-014-9196-8 · Cited by 244
“0 (Muthén and Kaplan 1985).”
Person-organization and person-supervisor fits: Employee commitments in a Chinese context
van Vianen, A. V., Shen, C.-T., & Chuang, A.-C. (2011) · Journal of Organizational Behavior · doi:10.1002/job.726 · Cited by 202
“Maximum likelihood (ML) works well under slightly non-normal conditions (Muthén & Kaplan, 1985) and ML is relatively insensitive to variations in sample size and kurtosis (Olsson, Foss, Troye, & Howell, 2000).”
BackgroundThe Application of Latent Curve Analysis to Testing Developmental Theories in Intervention Research
Curran, P. J., & Muthén, B. (1999) · American Journal of Community Psychology · doi:10.1023/a:1022137429115 · Cited by 202
Self-citationThe Development and Validation of the Goal Orientation and Learning Strategies Survey (Goals-S)
Dowson, M. N., & McInerney, D. M. (2004) · Educational and Psychological Measurement · doi:10.1177/0013164403251335 · Cited by 207
“Fortunately, however, maximum likelihood estimation procedures appear to be robust with respect to violations of normality, particularly in relation to parameter estimates and goodness-of-fit indices (Hu et al., 1992; Joreskog & Sorbom, 1993; Muthen & Kaplan, 1985).”
BackgroundLaird, T. F. N., Engberg, M. E., & Hurtado, S. (2005) · The Journal of Higher Education · doi:10.1353/jhe.2005.0028 · Cited by 200
Marsh, H. W., Liem, G. A. D., Martin, A. J., Morin, A. J. S., & Nagengast, B. (2011) · Journal of Psychoeducational Assessment · doi:10.1177/0734282911406657 · Cited by 199
“…tests 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; Muthén & Kaplan, 1985; Rhemtulla, Brosseau-Liard, & Savalei, 2010).”
BackgroundRelationship of family support and ethnic minority students' achievement in science and mathematics
Smith, F. M., & Hausafus, C. O. (1998) · Science Education · doi:10.1002/(sici)1098-237x(199801)82:1 · Cited by 80
Self-citationBrondino, M., da Silva, S. A., & Pasini, M. (2012) · Safety Science · doi:10.1016/j.ssci.2012.04.010 · Cited by 211
Sequencing of cognitive‐behavioral treatments for bulimia nervosa
Davis, R., McVey, G. L., Heinmaa, M., Rockert, W., & Kennedy, S. H. (1999) · International Journal of Eating Disorders · doi:10.1002/(sici)1098-108x(199905)25:4 · Cited by 59
Commuting trips within tours: how is commuting related to land use?
Acker, V. V., & Witlox, F. (2010) · Transportation · doi:10.1007/s11116-010-9309-6 · Cited by 189
Empirical validation of the Gamification User Types Hexad scale in English and Spanish
Tondello, G. F., Mora, A., Marczewski, A., & Nacke, L. E. (2019) · International Journal of Human-Computer Studies · doi:10.1016/j.ijhcs.2018.10.002 · Cited by 185
The hierarchical structure of empathy: Dimensional organization and relations to social functioning
Cliffordson, C. (2002) · Scandinavian Journal of Psychology · doi:10.1111/1467-9450.00268 · Cited by 188
A resource dependence theory perspective of ISO 9000 in managing organizational environment
Singh, P. J., Power, D., & Sum, C. (2010) · Journal of Operations Management · doi:10.1016/j.jom.2010.04.002 · Cited by 190
Impact of Team Integration and Group Cohesion on Project Delivery Performance
Franz, B. W., Leicht, R., Molenaar, K. R., & Messner, J. (2016) · Journal of Construction Engineering and Management · doi:10.1061/(asce)co.1943-7862.0001219 · Cited by 186
OECD (2010) · Teaching and learning international survey · doi:10.1787/9789264079861-en · Cited by 186
Duncan, T. E., Duncan, S. C., & Hops, H. (1994) · Journal of Studies on Alcohol · doi:10.15288/jsa.1994.55.588 · Cited by 184
Steuwe, C., Lanius, R. A., & Frewen, P. (2012) · Depression and Anxiety · doi:10.1002/da.21944 · Cited by 195
“0, respectively, cause significant problems.[54,55] Although the variables used in our analyses showed lower skewness (ranging from −1.”
MethodBond, F. W., Lloyd, J., & Guenole, N. (2013) · Journal of Occupational and Organizational Psychology · doi:10.1111/joop.12001 · Cited by 186
Bernaards, C. A., & Sijtsma, K. (2000) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr3503_03 · Cited by 177
“Dolan (1994) used 200, 300, and 400 simulated respondents; Muthén and Kaplan (1985) were interested in large sample properties and used a sample size of 1000.”
BackgroundMethodSelf-Assessment of Individual Differences in Language Switching
Rodríguez‐Fornells, A., Krämer, U. M., Lorenzo‐Seva, U., Festman, J., & Münte, T. F. (2012) · Frontiers in Psychology · doi:10.3389/fpsyg.2011.00388 · Cited by 206
“If both indices are lower than one in absolute value, then Pearson correlation is advised (Muthén and Kaplan, 1985, Table 1 | Univariate descriptive statistics for the items.”
MethodAssumptions of the Two-Step Approach to Latent Variable Modeling
Fornell, C., & Yi, Y. (1992) · Sociological Methods & Research · doi:10.1177/0049124192020003001 · Cited by 178
The construct validity of the Perceived Stress Scale
Nielsen, M. G., Ørnbøl, E., Vestergaard, M., Bech, P., Larsen, F. B., Lasgaard, M., & Christensen, K. S. (2016) · Journal of Psychosomatic Research · doi:10.1016/j.jpsychores.2016.03.009 · Cited by 209
“The RMSEA fit index showed reasonable fit, and both the CFI and the TFI showed good fit [46,47,55].”
MethodMarsh, H. W., Abduljabbar, A. S., Abu-Hilal, M. M., Morin, A. J. S., Abdelfattah, F. A., Leung, K. C., Xu, M. K., Nagengast, B., & Parker, P. D. (2012) · Journal of Educational Psychology · doi:10.1037/a0029907 · Cited by 195
“Our decision was based on the growing body of work (e.g., Beauducel & Herzberg, 2006; DiStefano, 2002; Dolan, 1994; Muthén & Kaplan, 1985; Rhemtulla, Brosseau-Liard, & Savalei, 2012) suggesting that categorical estimation procedures make little or no difference to the parameter point estimates that…”
MethodMoreau, E., & Mageau, G. A. (2011) · Motivation and Emotion · doi:10.1007/s11031-011-9250-9 · Cited by 214
“1.0 (mean kurtosis = 0.7 and mean skewness = - 0.2; Muthe´n and Kaplan 1985).”
BackgroundInfluentialSpirituality in the Workplace: Theory and Measurement
Liu, C. H., & Robertson, P. J. (2010) · Journal of Management Inquiry · doi:10.1177/1056492610374648 · Cited by 175
“…from treating ordered-categorical data as continuous data (e.g., Flora & Curran, 2004; Lubke & Muthen, 2004; Millsap & Jenn, 2004; Muthen, 1984; Muthen & Kaplan, 1985) Future research can treat survey data collected using Likert-type scales as ordered-categorical variables to test whether the…”
MethodRiso, D. D., Salcuni, S., Chessa, D., Raudino, A., Lis, A., & Altoè, G. (2010) · Personality and Individual Differences · doi:10.1016/j.paid.2010.05.005 · Cited by 173
“An absolute value of Kurtosis ple (N = 1394) and age group. greater than one indicates a substantial deviance from the normal distribution (Muthén & Kaplan, 1985).”
BackgroundSharma, S., Durvasula, S., & Dillon, W. R. (1989) · Journal of Marketing Research · doi:10.2307/3172607 · Cited by 173
Behavior of descriptive fit indexes in confirmatory factor analysis using ordered categorical data
Hutchinson, S. R., & Olmos, A. (1998) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705519809540111 · Cited by 172
Whiteside-Mansell, L., AYOUB, C. C., McKelvey, L. M., Faldowski, R. A., Hart, A. D., & Shears, J. (2007) · Parenting · doi:10.1080/15295190709336775 · Cited by 172
“WLS is appropriate for use with categorical data and where serious violations of normality occur (Muthen & Kaplan, 1985).”
MethodTian, L., Tian, Q., & Huebner, E. S. (2015) · Social Indicators Research · doi:10.1007/s11205-015-1021-7 · Cited by 216
Family Factors Associated With Sixth‐Grade Adolescents' Math and Science Career Interests
Turner, S. L., Steward, J., & Lapan, R. T. (2004) · The Career Development Quarterly · doi:10.1002/j.2161-0045.2004.tb00654.x · Cited by 171
An Empirical Examination of the Construct Validity of Two Alternative Self-Control Measures
Marcus, B. (2003) · Educational and Psychological Measurement · doi:10.1177/0013164403251329 · Cited by 170
“…maximum likelihood (ML) technique, and it has been demonstrated to be robust against deviations from multivariate normality as long as the skewness and kurtosis of each observed variable does not exceed an absolute value of 1 (Muthén & Kaplan, 1985; see also Bollen, 1989; Hoogland & Boomsma, 1998).”
BackgroundUsing Exploratory Factor Analysis to Determine the Dimensionality of Discrete Responses
Barendse, M. T., Oort, F. J., & Timmerman, M. E. (2014) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2014.934850 · Cited by 189
“ML analysis of covariances or correlations between discrete responses is often applied but yields biased parameters as well as incorrect standard errors and fit statistics (Dolan, 1994; Johnson & Creech, 1983; Muthén & Kaplan, 1985, 1992; Rhemtulla, Brosseau-Liard, & Savalei, 2012).”
Model conditions for asymptotic robustness in the analysis of linear relations
Satorra, A., & Bentler, P. M. (1990) · Computational Statistics & Data Analysis · doi:10.1016/0167-9473(90)90004-2 · Cited by 170
Wu, C., & Yao, G. (2008) · Personality and Individual Differences · doi:10.1016/j.paid.2008.02.003 · Cited by 169
“The maximum likelihood method was used for model estimation, since Muthén and Kaplan (1985) suggest that if variables have skewness and kurtosis from 1 to +1, then, estimating parameters for non-normal categorical variables with the maximum likelihood method was acceptable.”
Bruhn, M., Schnebelen, S., & Schäfer, D. B. (2013) · Industrial Marketing Management · doi:10.1016/j.indmarman.2013.08.008 · Cited by 178
Psychological Antecedents of Risk-Taking Behavior in Construction
Tixier, A. J. ‐., Hallowell, M. R., Albert, A., Leaf Van Boven, A., & Kleiner, B. M. (2014) · Journal of Construction Engineering and Management · doi:10.1061/(asce)co.1943-7862.0000894 · Cited by 175
“Although PCA is primarily intended for continuous data, Muthen and Kaplan (1985) showed that PCA performs quite well with ordered categorical variables such as Likert scales, especially for data reduction and clustering.”
MethodResult(Why) Should We Use SEM? Pros and Cons of Structural Equation Modeling
Nachtigall, C., Kroehne, U., Funke, F., & Steyer, R. (2003) · doi:10.23668/psycharchives.12783 · Cited by 173
Dichotomous Factor Analysis of Symptom Data
Muthén, B. (1989) · Sociological Methods & Research · doi:10.1177/0049124189018001002 · Cited by 168
Self-citationRecklitis, C. J., Parsons, S. K., Shih, M.-C., Mertens, A., Robison, L. L., & Zeltzer, L. (2006) · Psychological Assessment · doi:10.1037/1040-3590.18.1.22 · Cited by 209
Lam, E. T. C., Zhang, J. J., & Jensen, B. E. (2005) · Measurement in Physical Education and Exercise Science · doi:10.1207/s15327841mpee0902_2 · Cited by 184
“Extensive research on the robustness of the ML method indicated that this method is almost always acceptable even when data are nonnormally distributed (Harlow, 1985; Hoyle & Panter, 1995; Muthén & Kaplan, 1985; Tanaka & Bentler, 1985; West et al., 1995).”
MethodRescaling Ordinal Data to Interval Data in Educational Research
Harwell, M. R., & Gatti, G. (2001) · Review of Educational Research · doi:10.3102/00346543071001105 · Cited by 169
El análisis factorial exploratorio de los ítems: algunas consideraciones adicionales
Ferrando, P. J., & Lorenzo‐Seva, U. (2014) · Anales de Psicología · doi:10.6018/analesps.30.3.199991 · Cited by 165
“…punto, las estimaciones de los pesos proporcionadas por el modelo lineal estarán sesgadas hacia abajo (i.e. atenuadas) con respecto a los pesos verdaderos y, además, esté efecto no será constante: la atenuación será mayor cuanto más extremos y discriminativos los ítems (Muthén y Kaplan, 1985).”
BackgroundKaplan, D. (1988) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr2301_4 · Cited by 165
Self-citationFinite Sampling Properties of the Point Estimates and Confidence Intervals of the RMSEA
Curran, P. J., Bollen, K. A., Chen, F., Paxton, P. M., & Kirby, J. B. (2003) · Sociological Methods & Research · doi:10.1177/0049124103256130 · Cited by 165
COGNITIVE AND NON-COGNITIVE FACTORS RELATED TO STUDENTS’ STATISTICS ACHIEVEMENT
Chiesi, F., & Primi, C. (2010) · Statistics Education Research Journal · doi:10.52041/serj.v9i1.385 · Cited by 179
Qin, G., & Prybutok, V. R. (2008) · Quality Management Journal · doi:10.1080/10686967.2008.11918065 · Cited by 169
Predictors of adolescent dieting behaviors: A longitudinal study.
Stice, E. M., Mazotti, L. A., Krebs, M., & Martin, S. B. (1998) · Psychology of Addictive Behaviors · doi:10.1037/0893-164x.12.3.195 · Cited by 164
Garrido, L. E., Abad, F. J., & Ponsoda, V. (2015) · Psychological Methods · doi:10.1037/met0000064 · Cited by 188
Police Officers as Warriors or Guardians: Empirical Reality or Intriguing Rhetoric?
McLean, K. D., Wolfe, S. E., Rojek, J. J., Alpert, G. P., & Smith, M. R. (2019) · Justice Quarterly · doi:10.1080/07418825.2018.1533031 · Cited by 164
“Typically, the maximum-likelihood estimator is preferred when items have ordered responses of five or more categories and are normally distributed (Bollen, 1989; Dolan, 1994; Finney & DiStefano, 2013; Muthen & Kaplan, 1985).”
van den Oord, E. J. C. G., Boomsma, D. I., & Verhulst, F. C. (1994) · Behavior Genetics · doi:10.1007/bf01067187 · Cited by 158
The stress-negative affect model of adolescent alcohol use: disaggregating negative affect.
Hussong, A. M., & Chassin, L. (1994) · Journal of Studies on Alcohol · doi:10.15288/jsa.1994.55.707 · Cited by 157
Cyberbullying: The hidden side of college students
Francisco, S. M., Simão, A. M. V., Ferreira, P. C., & Martins, M. J. D. (2014) · Computers in Human Behavior · doi:10.1016/j.chb.2014.10.045 · Cited by 155
“We used polychoric correlations, as suggested in the literature, when univariate distributions of ordinal items are asymmetric for polytomous items (Brown, 2006; Muthén & Kaplan, 1985, 1992).”
MethodMoshagen, M., Hilbig, B. E., & Zettler, I. (2014) · Diagnostica · doi:10.1026/0012-1924/a000112 · Cited by 155
Flexible cutoff values for fit indices in the evaluation of structural equation models
Niemand, T., & Mai, R. (2018) · Journal of the Academy of Marketing Science · doi:10.1007/s11747-018-0602-9 · Cited by 174
la Du, T. J., & Tanaka, J. S. (1989) · Journal of Applied Psychology · doi:10.1037/0021-9010.74.4.625 · Cited by 163
Wu, C., & Yao, G. (2006) · Personality and Individual Differences · doi:10.1016/j.paid.2005.11.012 · Cited by 160
“However, Muthén and Kaplan (1985) suggested that if variables have skewness and kurtosis from 1 to +1, using likelihood estimators for non-normal categorical variables is acceptable.”
BackgroundPagliaccio, D., Luking, K. R., Anokhin, A. P., Gotlib, I. H., Hayden, E. P., Olino, T. M., Peng, C.-Z., Hajcak, G., & Barch, D. M. (2015) · Psychological Assessment · doi:10.1037/pas0000186 · Cited by 161
Aluja, A., Garcı́a, O., Rossier, J., & Garcı́a, L. F. (2005) · Personality and Individual Differences · doi:10.1016/j.paid.2004.05.014 · Cited by 150
“Values outside the )1 to +1 interval have been suggested as indicators of normality violation (Muth en & Kaplan, 1985).”
BackgroundReinecke, L., Klimmt, C., Meier, A., Reich, S., Hefner, D., Knop-Huelss, K., Rieger, D., & Vorderer, P. (2018) · PLoS ONE · doi:10.1371/journal.pone.0205384 · Cited by 197
Cudeck, R. A., & Browne, M. W. (1992) · Psychometrika · doi:10.1007/bf02295424 · Cited by 148
Depressive symptoms in children and adolescents: changing aetiological influences with development
Scourfield, J., Rice, F. J., Thapar, A., Harold, G. T., Martin, N. C., & McGuffin, P. (2003) · Journal of Child Psychology and Psychiatry · doi:10.1111/1469-7610.00181 · Cited by 148
Measurement of Affective States in Adults: Evaluation of an Adjective Rating Scale Instrument
Usala, P. D., & Hertzog, C. (1989) · Research on Aging · doi:10.1177/0164027589114001 · Cited by 146
The Development of a School-Based Measure of Child Mental Health
Deighton, J., Tymms, P. B., Vostanis, P., Belsky, J., Fonagy, P., Brown, A., Martin, A., Patalay, P., & Wolpert, M. (2012) · Journal of Psychoeducational Assessment · doi:10.1177/0734282912465570 · Cited by 144
Morata-Ramirez, M. Á., Tello, F. P. H., García, M. I. B., & Méndez, G. (2015) · Acción Psicológica · doi:10.5944/ap.12.1.14362 · Cited by 147
Zygmont, C. S., & Smith, M. R. (2014) · The Quantitative Methods for Psychology · doi:10.20982/tqmp.10.1.p040 · Cited by 149
“…like the Minimal Residuals (MINRES), Asymptotically Distribution Free (ADF) generalized least-squares for large sample sizes, or Continuous/Categorical Variable Methodology (CVM) techniques should be compared to the performance of the default ML procedure (Jöreskog, 2003; Muthén & Kaplan, 1985).”
Non-R&D SMEs: external knowledge, absorptive capacity and product innovation
Moilanen, M., Østbye, S., & Woll, K. (2014) · Small Business Economics · doi:10.1007/s11187-014-9545-9 · Cited by 144
“Although we are using a categorical variable to measure firms’ innovation performance, the literature appears to support the notion that when the number of categories is large and the data approximate a normal distribution, failure to address the ordinality of the data is likely negligible (Atkinson 1988; Babakus et a…”
MethodSample Size Requirements of the Robust Weighted Least Squares Estimator
Moshagen, M., & Musch, J. (2013) · Methodology · doi:10.1027/1614-2241/a000068 · Cited by 155
How Serendipity Improves User Satisfaction with Recommendations? A Large-Scale User Evaluation
Chen, L., Yang, Y., Wang, N., Yang, K., & Yuan, Q. (2019) · International World Wide Web Conference (WWW) · doi:10.1145/3308558.3313469 · Cited by 146
“0 to 0 respectively (so not likely to inflate the Chi-squared statistics of path analysis according to [31]).”
BackgroundTho, N. D., & Trang, N. T. M. (2014) · Journal of Business Research · doi:10.1016/j.jbusres.2014.12.003 · Cited by 143
Psychological Capital, Quality of Work Life, and Quality of Life of Marketers
Tho, N. D., & Nguyen, T. T. M. (2011) · Journal of Macromarketing · doi:10.1177/0276146711422065 · Cited by 142
“Therefore, maximum likelihood estimation was used (Muthen and Kaplan 1985).”
Effect of the number of scale points on chi‐square fit indices in confirmatory factor analysis
Green, S. B., Akey, T. M., Fleming, K., Hershberger, S. L., & Marquis, J. G. (1997) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705519709540064 · Cited by 141
Lavergne, K. J., Sharp, E. C., Pelletier, L. G., & Holtby, A. (2009) · Journal of Environmental Psychology · doi:10.1016/j.jenvp.2009.11.002 · Cited by 160
“Descriptive statistics (Table 1) revealed that skewness and kurtosis were within acceptable ranges (Muthen & Kaplan, 1985) and correlations revealed no major concerns of multicollinearity.”
BackgroundAttitude Organization in the General Public: Evidence for a Bidimensional Structure
Fleishman, J. A. (1988) · Social Forces · doi:10.1093/sf/67.1.159 · Cited by 140
Personality, problem drinking, and drunk driving: Mediating, moderating, and direct-effect models.
Stacy, A. W., Newcomb, M. D., & Bentler, P. M. (1991) · Journal of Personality and Social Psychology · doi:10.1037//0022-3514.60.5.795 · Cited by 139
CORRELACIONES POLICÓRICAS Y TETRACÓRICAS EN ESTUDIOS FACTORIALES EXPLORATORIOS Y CONFIRMATORIOS
Hoffmann, A. F., Stover, J. B., de la Iglesia, G., & Liporace, M. F. (2013) · Ciencias Psicológicas · doi:10.22235/cp.v7i1.1057 · Cited by 157
Tóth‐Király, I., Bőthe, B., Rigó, A., & Orosz, G. (2017) · Frontiers in Psychology · doi:10.3389/fpsyg.2017.01968 · Cited by 152
“For univariate normality, considering the guidelines of Muthén and Kaplan (1985) with a ±1 threshold, neither skewness (ranging from −1.03 to +1.61), nor kurtosis (ranging −1.12 to +2.04) values suggested that the data has univariate normality.”
MethodInfluentialMarsh, H. W., Kuyper, H., Seaton, M., Parker, P. D., Morin, A. J. S., Møller, J., & Abduljabbar, A. S. (2014) · Contemporary Educational Psychology · doi:10.1016/j.cedpsych.2014.08.003 · Cited by 137
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
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
