, Volume 63, Issue 3, pp 255–261 | Cite as

A case of extreme simplicity of the core matrix in three-mode principal components analysis

  • Takashi Murakami
  • Jos M. F. Ten Berge
  • Henk A. L. Kiers


In three-mode Principal Components Analysis, theP ×Q ×R core matrixG can be transformed to simple structure before it is interpreted. It is well-known that, whenP=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, whenP=QR − 1,G can be transformed to have nearly all elements equal to values spectified a priori. A cllsed-form solution for this transformation is offered. Theoretical and practical implications of this simple structure transformation ofG are discussed.

Key words

three-mode principal components analysis core matrix rotations simple structure 


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Copyright information

© The Psychometric Society 1998

Authors and Affiliations

  • Takashi Murakami
    • 1
  • Jos M. F. Ten Berge
    • 2
  • Henk A. L. Kiers
    • 2
  1. 1.Department of Educational PsychologyNagoya UniversityNagoyaJapan
  2. 2.University of GroningenThe Netherlands

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