Exploratory factor analysis of data matrices with more variables than observations

Journal of Computational and Graphical Statistics

Volumn 20, Issue 4, 2011, Pages 874-891

  Trendafilov, Nickolay T ^a   Unkel, Steffen ^a  

^a OPEN UNIVERSITY   (United Kingdom)

Author keywords

Factor analysis; P > n; Procrustes problem; Singular value decomposition

Indexed keywords

EID: 83455220743     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/jcgs.2011.09211     Document Type: Article

References (23)

1. Anderson, T. W. (1984), An Introduction to Multivariate Statistical Analysis (2nd ed.), New York: Wiley. [879]
2. Anderson, T. W., and Rubin, H. (1956), "Statistical Inference in Factor Analysis, " in Proceedings of the 3rd Berkeley Symposium onMathematical Statistics and Probability, Vol. V, ed. J. Neyman, Berkeley: University of California Press, pp. 111-150. [880]
3. Bartholomew, D. J., and Knott, M. (1999), Latent Variable Models and Factor Analysis (2nd ed.), London: Edward Arnold. [874,877,879]
4. De Leeuw, J. (2004), "Least Squares Optimal Scaling of Partially Observed Linear Systems, " in Recent Developments on Structural Equation Models: Theory and Applications, eds. K. van Montfort, J. Oud, and A. Satorra, Dordrecht, NL: Kluwer Academic Publishers, pp. 121-134. [875,877]
5. Golub, G. H., and Van Loan, C. F. (1996), Matrix Computations (3rd ed.), Baltimore, MD: The John Hopkins University Press. [875]
6. Hannachi, A., Jolliffe, I. T., and Stephenson, D. B. (2007), "Empirical Orthogonal Functions and Related Techniques in Atmospheric Science: A Review, " International Journal of Climatology, 27, 1119-1152. [886,888,889]
7. Harman, H. H. (1976), Modern factor analysis (3rd ed.), Chicago, IL: University of Chicago Press. [874,876,877, 883]
8. Horn, R., and Johnson, C. (1986), Matrix Analysis, Cambridge, U.K.: Cambridge University Press. [878,879]
9. Horst, P. (1965), Factor Analysis of Data Matrices, New York: Holt, Rinehart, and Winston. [875]
10. Jennrich, R. I., and Trendafilov, N. T. (2005), "Independent Component Analysis as a Rotation Method: A Very Different Solution to Thurstone's Box Problem, " British Journal of Mathematical and Statistical Psychology, 58, 199-208. [883]
11. Jolliffe, I. T. (2002), Principal Component Analysis (2nd ed.), New York: Springer. [875,886]
12. Jöreskog, K. G. (1962), "On the Statistical Treatment of Residuals in Factor Analysis, " Psychometrika, 27, 335-354. [875]
13. Lawley, D. N. (1942), "Further Investigations in Factor Estimation, " Proceedings of the Royal Society of Edinburgh: Section A, 61, 176-185. [875,876]
14. McDonald, R. P. (1979), "The Simultaneous Estimation of Factor Loadings and Scores, " British Journal of Mathematical and Statistical Psychology, 32, 212-228. [875]
15. Mulaik, S. A. (1972), The Foundations of Factor Analysis, New York: McGraw-Hill. [874,876,877]
16. Mulaik, S. A. (2005), "Looking Back on the Indeterminacy Controversies in Factor Analysis, " in Contemporary Psychometrics: A Festschift for Roderick P. McDonald, eds. A. Maydeu-Olivares and J. J. McArdle, Mahwah: Lawrence Erlbaum, pp. 173-206. [890]
17. Ortega, J. M., and Rheinboldt, W. C. (1970), Iterative Solution of Nonlinear Equations in Several Variables, New York: Academic Press. [882]
18. Robertson, D., and Symons, J. (2007), "Maximum Likelihood Factor Analysis With Rank-Deficient Sample Covariance Matrices, " Journal of Multivariate Analysis, 98, 813-828. [878]
19. The MathWorks, Inc. (2009), "MATLAB R2009a. " [883]
20. Thurstone, L. L. (1947), Multiple Factor Analysis, Chicago, IL: University of Chicago Press. [874,875,883]
21. Trendafilov, N. T. (2003), "Dynamical System Approach to Factor Analysis Parameter Estimation, " British Journal of Mathematical and Statistical Psychology, 56, 27-46. [883,884]
22. 1 Norm, " British Journal of Mathematical and Statistical Psychology, 58, 19-31. [880,883,884]
23. Whittle, P. (1952), "On Principal Components and Least Squares Methods in Factor Analysis, " Skandinavisk Aktuarietidskrift, 35, 223-239. [875]