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Centroid Orthogonal Transformations

Published online by Cambridge University Press:  01 January 2025

H. D. Landahl
H. D. Landahl*
Affiliation:
The University of Chicago
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Abstract

An initial transformation for facilitating the analysis of a factor problem is discussed. Such a transformation is used in the rotational procedure developed by L. L. Thurstone in an accompanying article.

Type
Original Paper
Information
Psychometrika , Volume 3 , Issue 4 , December 1938 , pp. 219 - 223
Copyright
Copyright © 1938 The Psychometric Society

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References

* The matrix thus set up is neither unique nor determined by an unique procedure, but is given in this form for convenience only.

† The condition may be stated with all subscript pairs interchanged.

* Thurstone, L. L., Primary Mental Abilities. 1938, Psychometric Monographs No. 1.

† The following may be generalized, approximately, for more than one vector.

‡ Most of the columns can be eliminated by inspection.

§ One might interchange the rows and obtain a still larger value for the expression given above, especially for the case of more than one known vector. Note that the orthogonality of a matrix is not affected by interchanging rows or by changing signs of rows; this fact is evident from the condition for orthogonality.