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Factor Analysis of Ordinal Variables: A Comparison of Three Approaches
Abstract
Theory and methodology for exploratory factor analysis have been well developed for continuous variables. In practice, observed or measured variables are often ordinal. However, ordinality is most often ignored and numbers such as 1, 2, 3, 4, representing ordered categories, are treated as numbers having metric properties, a procedure which is incorrect in several ways. In this article we describe four approaches to factor analysis of ordinal variables which take proper account of ordinality and compare three of them with respect to parameter estimates and fit. The comparison is made both in terms of their relative methodological advantages and in terms of an empirical data example and two generated data examples. In particular, we discuss the issue of how to test the model and to measure model fit.
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Cites
Some Methods for Strengthening the Common χ 2 Tests
Cochran, W. G. (1954) · Biometrics · doi:10.2307/3001616 · Cited by 3,718 · cited 1×
“These residuals are simply the square roots of our GF-Fit in Equations 33 and 35, see Cochran (1954).”
BackgroundEstimation of Latent Ability Using a Response Pattern of Graded Scores
Samejima, F. (1969) · Psychometrika · doi:10.1007/bf03372160 · Cited by 2,194
Cited by
Item factor analysis: Current approaches and future directions.
Wirth, R. J., & Edwards, M. C. (2007) · Psychological Methods · doi:10.1037/1082-989x.12.1.58 · Cited by 910
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 805
Asymptotic efficiency of the two-stage estimation method for copula-based models
Joe, H. (2005) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2004.06.003 · Cited by 602
Lubke, G. H., & Muthén, B. O. (2004) · Structural Equation Modeling: A Multidisciplinary Journal · doi:10.1207/s15328007sem1104_2 · Cited by 489
Evaluating the Impact of Partial Factorial Invariance on Selection in Two Populations
Millsap, R. E., & Kwok, O.-M. (2004) · Psychological Methods · doi:10.1037/1082-989x.9.1.93 · Cited by 414
Metadata
- Authors
- Jöreskog, K. G., & Moustaki, I.
- Venue
- Multivariate Behavioral Research
- Publisher
- Informa UK Limited
- Published
- 2001-07
- Volume
- 36
- Issue
- 3
- Pages
- 347-387
- ISSN
- 0027-3171 (ISSN-L)
- 1532-7906
- OpenAlex
- W2007897277
- Cited by
- 374
- References
- 2
- FWCI
- 4.43
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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