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A joint treatment of varimax rotation and the problem of diagonalizing symmetric matrices simultaneously in the least-squares sense

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Abstract

The present paper contains a lemma which implies that varimax rotation can be interpreted as a special case of diagonalizing symmetric matrices as discussed in multidimensional scaling. It is shown that the solution by De Leeuw and Pruzansky is essentially equivalent to the solution by Kaiser. Necessary and sufficient conditions for maxima and minima are derived from first and second order partial derivatives. A counter-example by Gebhardt is reformulated and examined in terms of these conditions. It is concluded that Kaiser's method or, equivalently, the method by De Leeuw and Pruzansky is the most attractive method currently available for the problem at hand.

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References

  • De Leeuw, J. & Pruzansky, S. (1978). A new computational method to fit the weighted euclidian distance model.Psychometrika, 43,4, 479–490.

    Article  Google Scholar 

  • Gebhardt, F. (1968). A counterexample to two-dimensional Varimax-rotation.Psychometrika, 33,1, 35–36.

    Article  PubMed  Google Scholar 

  • Horst, P. (1965).Factor analysis of data matrices. New-York: Holt, Rinehart & Winston.

    Google Scholar 

  • Kaiser, H. F. (1958). The varimax criterion for analytic rotation in factor analysis.Psychometrika, 23,3, 187–200.

    Article  Google Scholar 

  • Luenburger, D. G. (1973).Introduction to linear and nonlinear programming. Reading (Mass.): Addison-Wesley.

    Google Scholar 

  • Mulaik, S. A. (1972).The foundations of factor analysis. New-York: McGraw-Hill.

    Google Scholar 

  • Neudecker, H. (1981). On the matrix formulation of Kaiser's Varimax criterion.Psychometrika, 46,3, 343–345.

    Article  Google Scholar 

  • Nevels, K. (1983). An explicit solution for pairwise rotations in Kaiser's Varimax method. (manuscript submitted to Psychometrika).

  • Schönemann, P. H. (1966). Varisim: a new machine method for orthogonal rotation.Psychometrika, 31,2, 235–248.

    Article  PubMed  Google Scholar 

  • Sherin, R. J. (1966). A matrix formulation of Kaiser's varimax criterion.Psychometrika, 31,4, 535–538.

    Article  PubMed  Google Scholar 

  • Young, F. W., Takane, Y. & Lewyckyj, R. (1978). Three notes on Alscal.Psychometrika, 43,3, 433–435.

    Google Scholar 

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The author is obliged to Dirk Knol for computational assistance and to Dirk Knol, Klaas Nevels and Frits Zegers for critically reviewing an earlier draft of this paper.

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ten Berge, J.M.F. A joint treatment of varimax rotation and the problem of diagonalizing symmetric matrices simultaneously in the least-squares sense. Psychometrika 49, 347–358 (1984). https://doi.org/10.1007/BF02306025

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  • DOI: https://doi.org/10.1007/BF02306025

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