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A Comparison of Four Methods of Constructing Factor Scores

Published online by Cambridge University Press:  01 January 2025

Roderick P. McDonald  and
E. J. Burr
Roderick P. McDonald
Affiliation:
University of New England, N.S.W., Australia
E. J. Burr
Affiliation:
University of New England, N.S.W., Australia
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Abstract

Four least-squares methods for constructing factor scores have been described in the literature. The formal properties of these scores are developed, and they are compared in terms of four generally desirable properties of constructed factor scores. In particular, it is shown that two of the methods yield scores that are conditionally unbiassed, and univocal in the sense of Guilford and Michael, though not orthogonal, while one of the other methods yields orthogonal scores.

It is shown that constructed factor scores cannot be simultaneously univocal and orthogonal, unless we choose the special basis in factor space given by Canonical Factor Analysis.

The general problem of choosing between the methods is discussed, on the basis of the theoretical relations obtained.

Type
Original Paper
Information
Psychometrika , Volume 32 , Issue 4 , December 1967 , pp. 381 - 401
Copyright
Copyright © 1967 The Psychometric Society

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Footnotes

*

EDITOR’S NOTE: The reader will quickly discover that this article develops several of the generalizations given in the second part of the preceding article, “On Factors and Factor Scores.” Independent development of the same generalizations is, of course, not a new phenomenon. Because the Presidential Address automatically is accepted for publication and given space in the December issue, it was decided that the only fair thing to do was to print this article in the same issue.

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