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A Case of Extreme Simplicity of the Core Matrix in Three-Mode Principal Components Analysis

Published online by Cambridge University Press:  01 January 2025

Takashi Murakami ,
Jos M. F. Ten Berge  and
Henk A. L. Kiers
Takashi Murakami*
Affiliation:
Nagoya University
Jos M. F. Ten Berge
Affiliation:
University of Groningen
Henk A. L. Kiers
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Takashi Murakami, Department of Educational Psychology, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-01, Japan.
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Abstract

In three-mode Principal Components Analysis, the P ×Q ×R core matrix G can be transformed to simple structure before it is interpreted. It is well-known that, when P = QR, G can be transformed to the identity matrix, which implies that all elements become equal to values specified a priori. In the present paper it is shown that, when P = QR − 1, G can be transformed to have nearly all elements equal to values specified a priori. A closed-form solution for this transformation is offered. Theoretical and practical implications of this simple structure transformation of G are discussed.

Keywords

three-mode principal components analysiscore matrix rotationssimple structure
Type
Original Paper
Information
Psychometrika , Volume 63 , Issue 3 , September 1998 , pp. 255 - 261
Copyright
Copyright © 1998 The Psychometric Society

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Footnotes

Constructive comments from anonymous reviewers are gratefully acknowledged.

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