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The Simultaneous Maximization of Congruence for Two or More Matrices under Orthogonal Rotation

Published online by Cambridge University Press:  01 January 2025

Frank B. Brokken
Frank B. Brokken*
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Frank Brokken, Department of Education, University of Groningen, Westerhaven 16, k. 902, 9718 AW Groningen, the Netherlands.
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Abstract

While a rotation procedure currently exists to maximize simultaneously Tucker's coefficient of congruence between corresponding factors of two factor matrices under orthogonal rotation of one factor matrix, only approximate solutions are known for the generalized case where two or more matrices are rotated. A generalization and modification of the existing rotation procedure to simultaneously maximize the congruence is described. An example using four data matrices, comparing the generalized congruence maximization procedure with alternative rotation procedures, is presented. The results show a marked improvement of the obtained congruence using the generalized congruence maximization procedure compared to other procedures, without a significant loss of success with respect to the least squares criterion. A computer program written by the author to perform the rotations is briefly discussed.

Keywords

factor analysisfactor matching
Type
Original Paper
Information
Psychometrika , Volume 50 , Issue 1 , March 1985 , pp. 51 - 56
Copyright
Copyright © 1985 The Psychometric Society

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References

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