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“Parallel Proportional Profiles” and other Principles for Determining the Choice of Factors by Rotation

Published online by Cambridge University Press:  01 January 2025

Raymond B. Cattell
Raymond B. Cattell*
Affiliation:
Duke University
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Abstract

The choosing of a set of factors likely to correspond to the real psychological unitary traits in a situation usually reduces to finding a satisfactory rotation in a Thurstone centroid analysis. Seven principles, three of which are new, are described whereby rotation may be determined and/or judged. It is argued that the most fundamental is the principle of “parallel proportional profiles” or “simultaneous simple structure.” A mathematical proof of the uniqueness of determination by this means is attempted and equations are suggested for discovering the unique position.

Type
Original Paper
Information
Psychometrika , Volume 9 , Issue 4 , December 1944 , pp. 267 - 283
Copyright
Copyright © 1944 The Psychometric Society

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Footnotes

*

Reyburn and Taylor (13) and others have sometimes spoken of an intermediate degree of reality. “If common factors are not causal they must at least be objective . . . [which requires] a certain form and degree of invariance” [namely, of factor loading of a test from battery to battery]. We should consider such factors to be in a transitory limbo, destined soon to emerge to one status or the other.

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