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Orthogonal Principal Planes

Published online by Cambridge University Press:  01 January 2025

Peter Filzmoser
Peter Filzmoser*
Affiliation:
Department of Statistics, Probability Theory and Actuarial Mathematics, Vienna University of Technology, Austria
*
Requests for reprints should be sent to Peter Filzmoser, Department of Statistics, Probability Theory and Actuarial Mathematics, Vienna University of Technology, Wiedner Hauptstr. 8-10, A-1040 Vienna, Austria. E-Mail: p.filzmoser@tuwien.ac.at
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Abstract

Factor analysis and principal component analysis result in computing a new coordinate system, which is usually rotated to obtain a better interpretation of the results. In the present paper, the idea of rotation to simple structure is extended to two dimensions. While the classical definition of simple structure is aimed at rotating (one-dimensional) factors, the extension to a simple structure for two dimensions is based on the rotation of planes. The resulting planes (principal planes) reveal a better view of the data than planes spanned by factors from classical rotation and hence allow a more reliable interpretation. The usefulness of the method as well as the effectiveness of a proposed algorithm are demonstrated by simulation experiments and an example.

Keywords

principal component analysisfactor analysisorthogonal rotationsimple structure
Type
Original Paper
Information
Psychometrika , Volume 65 , Issue 3 , September 2000 , pp. 363 - 376
Copyright
Copyright © 2000 The Psychometric Society

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Footnotes

The author is most grateful to the referees, the Associate Editor, and the Editor for helpful suggestions, which resulted in a completely improved version of an earlier manuscript. The author also wants to express his gratitude to Johann Millendorfer, the former head of STUDIA, who initiated the idea of this work.

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