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Orthogonal Inter-Battery Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Walter Kristof
Walter Kristof*
Affiliation:
Educational Testing Service
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Abstract

It is the purpose of this paper to present a method of analysis for obtaining (i) inter-battery factors and (ii) battery specific factors for two sets of tests when the complete correlation matrix including communalities is given. In particular, the procedure amounts to constructing an orthogonal transformation such that its application to an orthogonal factor solution of the combined sets of tests results in a factor matrix of a certain desired form. The factors isolated are orthogonal but may be subjected to any suitable final rotation, provided the above classification of factors into (i) and (ii) is preserved. The general coordinate-free solution of the problem is obtained with the help of methods pertaining to the theory of linear spaces. The actual numerical analysis determined by the coordinate-free solution turns out to be a generalization of the formalism of canonical correlation analysis for two sets of variables. A numerical example is provided.

Type
Original Paper
Information
Psychometrika , Volume 32 , Issue 2 , June 1967 , pp. 199 - 227
Copyright
Copyright © 1967 The Psychometric Society

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Footnotes

*

This investigation has been supported by the U.S. Office of Naval Research under Contract Nonr-2752(00).

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