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Interpretation of Second-Order Factors

Published online by Cambridge University Press:  01 January 2025

Karl J. Holzinger
Karl J. Holzinger*
Affiliation:
University of Chicago
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Abstract

It is shown that a “second-order” factor pattern is equivalent to the transformation employed in rotating an orthogonal factor pattern to an oblique form. The correlation among the second-order factors may then be interpreted as due to the original first-order factors.

Type
Original Paper
Information
Psychometrika , Volume 10 , Issue 1 , March 1945 , pp. 21 - 25
Copyright
Copyright © 1945 Psychometric Society

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References

* The oblique solution consists of the structure Sjs, which gives the correlations between tests and factors, and the pattern Bjs, which represents the coefficients in the linear expressions between tests and oblique factors. The structure is obtained from the above transformation Tss and the pattern Ajs by the equation AjsTss = Sjs. The pattern Bjs is then obtained from the equation Bjs = Sjs ϕ ss-1, where θss is the matrix of the intercorrelations of the factors Ls.