Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-01-07T19:07:31.014Z Has data issue: false hasContentIssue false
  • English
  • Français

Factor Analysis via Components Analysis

Published online by Cambridge University Press:  01 January 2025

Peter M. Bentler  and
Jan de Leeuw
Peter M. Bentler*
Affiliation:
University of California, Los Angeles
Jan de Leeuw
Affiliation:
University of California, Los Angeles
*
Requests for reprints should be sent to Peter M. Bentler, Departments of Psychology and Statistics, UCLA, Box 951563, Los Angeles, CA 90095-1563, USA. E-mail: bentler@ucla.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

When the factor analysis model holds, component loadings are linear combinations of factor loadings, and vice versa. This interrelation permits us to define new optimization criteria and estimation methods for exploratory factor analysis. Although this article is primarily conceptual in nature, an illustrative example and a small simulation show the methodology to be promising.

Keywords

factor loadingsfactor scorescomponent loadingscomponent scores
Type
Original Paper
Information
Psychometrika , Volume 76 , Issue 3 , July 2011 , pp. 461 - 470
Copyright
Copyright © 2011 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bentler, P.M., Kano, Y. (1990). On the equivalence of factors and components. Multivariate Behavioral Research, 25, 67–74.CrossRefGoogle ScholarPubMed
de Leeuw, J. (2004). Least squares optimal scaling of partially observed linear systems. In van Montfort, K., Oud, J., Satorra, A. (Eds.), Recent developments on structural equation models: theory and applications (pp. 121–134). Dordrecht: Kluwer Academic. See also http://preprints.stat.ucla.edu, Preprint #360.CrossRefGoogle Scholar
Guttman, L. (1956). Best possible systematic estimates of communalities. Psychometrika, 21, 273–285.CrossRefGoogle Scholar
Harman, H.H. (1976). Modern factor analysis, (3rd ed.). Chicago: University of Chicago Press.Google Scholar
Jennrich, R.I. (2002). A simple general method for oblique rotation. Psychometrika, 67, 7–20.CrossRefGoogle Scholar
Johnstone, I.M., Lu, A.Y. (2009). On consistency and sparsity for principal components analysis in high dimensions. Journal of the American Statistical Association, 104(486), 682–693.CrossRefGoogle ScholarPubMed
Mulaik, S.A. (2010). Foundations of factor analysis, (2nd ed.). Boca Raton: Chapman & Hall/CRC.Google Scholar
Nadler, B. (2008). Finite sample approximation results for principal component analysis: a matrix perturbation approach. Annals of Statistics, 36(6), 2791–2817.CrossRefGoogle Scholar
Schönemann, P.H. (1966). A general solution of the orthogonal Procrustes problem. Psychometrika, 31, 1–10.CrossRefGoogle Scholar
Shapiro, A. (1984). A note on the consistency of estimators in the analysis of moment structures. British Journal of Mathematical and Statistical Psychology, 37, 84–88.CrossRefGoogle Scholar
Shen, H., Huang, J.Z. (2008). Sparse principal component analysis via regularized low rank matrix approximation. Journal of Multivariate Analysis, 99(6), 1015–1034.CrossRefGoogle Scholar
Slutsky, E. (1925).Über stochastische Asymptoten und Grenzwerte. Metron, 5(3), 3–89 (in German).Google Scholar
Witten, D.M., Tibshirani, R., Hastie, T. (2009). A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis. Biostatistics, 10(3), 515–534.CrossRefGoogle ScholarPubMed