A simple general procedure for orthogonal rotation

Psychometrika

Volumn 66, Issue 2, 2001, Pages 289-306

  Jennrich, Robert I ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Factor analysis; Global convergence; Orthomax; Pairwise methods; Quartimax; Simultaneous diagonalization; Simultaneous rotation; Singular value decomposition; Varimax

Indexed keywords

EID: 0035534938     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02294840     Document Type: Article

References (25)

1. Buck, R.C. (1956). Advanced calculus. New York, NY: McGraw-Hill
2. Carroll, J.B. (1953). An analytical solution for approximating simple structure in factor analysis. Psychometrika, 18, 32-38.
3. Cliff, N. (1966). Orthogonal rotation to congruence. Psychometrika, 31, 33-42.
4. de Leeuw, J. (1994). Block-relaxation algorithms in statistics. In H.H. Bock, W. Lenski, & M.M. Richter (Eds.), Information systems and data analysis (pp. 308-324). Berlin: Springer.
5. de Leeuw, J., & Pruzansky, S. (1978). A new computational method to fit the weighted Euclidean distance model. Psychometrika, 43, 479-490.
6. Dempster, A.P., Laird, N.M., & Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B, 39, 1-38.
7. Golub, G.H., & van Loan, C.F. (1989). Matrix computations. London: The Johns Hopkins University Press.
8. Harman, H.H. (1960). Modern factor analysis. Chicago, IL: University of Chicago Press.
9. Heiser, W.J. (1995). Convergent computation by iterative majorization: Theory and applications in multidimensional data analysis. In W.J. Krzanowski (Ed.), Recent advances in descriptive multivariate analysis (pp. 157-189). Oxford: Oxford University Press.
10. Horst, P. (1965). Factor analysis of data matrices. New York, NY: Holt, Rinehart and Winston.
11. Jamshidian, M., & Jennrich, R.I. (1997). Acceleration of the EM algorithm by using quasi-Newton methods. Journal of the Royal Statistical Society, Series B, 59, 569-587.
12. Kaiser, H.F. (1958). The varimax criterion for analytic rotation in factor analysis. Psychometrika, 23, 187-200.
13. Kaplan, W. (1999). Maxima and minima with applications. New York, NY: Wiley.
14. Kiers, H.A.L. (1990). Majorization as a tool for optimizing a class of matrix functions. Psychometrika, 55, 417-428.
15. Kiers, H.A.L., & ten Berge, J.M.F. (1992). Minimization of a class of matrix trace functions by means of refined majorization. Psychometrika, 57, 371-382.
16. Kiers, H.A.L., ten Berge, J.M.F., Takane, Y., & de Leeuw, J. (1990). A generalization of Takane's algorithm for DEDICOM. Psychometrika, 55, 151-158.
17. Loomis, L.H. & Sternberg, S. (1968). Advanced calculus. Reading, PA: Addison-Wesley.
18. Luenberger, D.G. (1984). Linear and nonlinear programming. Reading, PA: Addison-Wesley.
19. Magnus, J.R., & Neudecker, H. ( 1999). Matrix differential calculus with applications to statistics and econometrics. New York, NY: Wiley.
20. Mulaik, S.A. (1972). The foundations of factor analysis. New York, NY: McGraw-Hill.
21. Neuhaus, J.O., & Wrigley, C. (1954). The quartimax method: An analytical approach to orthogonal simple structure. British Journal of Statistical Psychology, 7, 81-91.
22. Sherin, R.J. (1966). A matrix formulation of Kaiser's varimax criterion. Psychometrika, 34, 535-538.
23. Takane, Y. (1985). Diagonal estimation in DEDICOM. Proceedings of the 1985 Annual Meeting of the Behaviormetric Society, 13, 100-101.
24. ten Berge, J.M.F. (1984). A joint treatment of varimax rotation and the problem of diagonalizing symmetric matrices simultaneously in the least squares sense. Psychometrika, 49, 347-358.
25. ten Berge, J.M.F., Knol, D.L., & Kiers, H.A.L. (1988). A treatment of the orthomax rotation family in terms of diagonalization, and a re-examination of the singular value approach to varimax rotation. Computational Statistics Quarterly, 4, 207-217.