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On the Matrix Formulation of Kaiser's Varimax Criterion

Published online by Cambridge University Press:  01 January 2025

H. Neudecker
H. Neudecker*
Affiliation:
University of Amsterdam
*
Requests for reprints should be sent to Professor H. Neudecker, Department of Econometrics and Mathematical Economics, Jodenbreestraat 23, 1011 NH Amsterdam, The Netherlands.
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Abstract

The author provides a full-fledged matrix derivation of Sherin's matrix formulation of Kaiser's varimax criterion. He uses matrix differential calculus in conjunction with the Hadamard (or Schur) matrix product. Two results on Hadamard products are presented.

Keywords

Matrix differential calculusHadamard (or Schur) productVarimax
Type
Notes And Comments
Information
Psychometrika , Volume 46 , Issue 3 , September 1981 , pp. 343 - 345
Copyright
Copyright © 1981 The Psychometric Society

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References

Bentler, P. M. & Lee, S. Y. Matrix derivatives with chain rule and rules for simple, Hadamard and Kronecker products. Journal of Mathematical Psychology, 1978, 17, 225–262.CrossRefGoogle Scholar
Kaiser, H. F. The varimax criterion for analytic rotation in factor analysis. Psychometrika, 1958, 23, 187–200.CrossRefGoogle Scholar
Nel, D. G. On matrix differentiation in statistics. South African Statistical Journal, 1980, 14, 137–193.Google Scholar
Neudecker, H. Some theorems on matrix differentiation with special reference to Kronecker products. Journal of the American Statistical Association, 1969, 64, 953–963.CrossRefGoogle Scholar
Neudecker, H. A derivation of the Hessian of the (concentrated) likelihood function of the factor model employing the Schur product. British Journal of Mathematical and Stastistical Psychology, 1975, 28, 152–156.CrossRefGoogle Scholar
Rao, C. R. & Mitra, S. K. Generalized inverse of matrices and its applications, 1971, New York: John Wiley & Sons.Google Scholar
Sherin, R. J. A matrix formulation of Kaiser's varimax criterion. Psychometrika, 1966, 31, 535–538.CrossRefGoogle ScholarPubMed
Wong, C. S. Matrix derivatives and their applications in statistics. Journal of Mathematical Psychology, 1980, 22, 70–80.CrossRefGoogle Scholar