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Simultaneous Optimization of Factor Assessibility and Representativeness: An Old Solution to a New Problem

Published online by Cambridge University Press:  01 January 2025

Vernon L. Greene
Vernon L. Greene*
Affiliation:
Indiana University
*
Requests for reprints should be sent to the Publications Secretary, Workshop in Political Theory and Policy Analysis, Morgan Hall 121, Indiana University, Bloomington, Indiana 47401.
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Abstract

P. M. Bentler has shown that Rao's canonical factor analysis is in effect a psychometric analysis, leading to factors that are maximally assessible from the data. He contrasts this with Kaiser and Caffrey's alpha factor analysis that leads to factors that maximally represent the true factors in the content domain. Noting the problems associated with factors that may be highly assessible, but not very representative, or vice versa, Bentler suggests the need for a technique that would, insofar as possible, be optimal with respect to both criteria. Such a technique is presented here, and is shown to resolve into a traditional scaling method, which in turn acquires a richer psychometric interpretation.

Keywords

alpha factor analysiscanonical factor analysisprincipal componentsreliabilityvalidity
Type
Notes and Comments
Information
Psychometrika , Volume 43 , Issue 2 , June 1978 , pp. 273 - 275
Copyright
Copyright © 1978 The Psychometric Society

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Footnotes

The author would like to gratefully acknowledge support for this research from the Workshop in Political Theory and Policy Analysis (Indiana University) and Esco Research Associates. The paper benefitted substantially from the criticisms and suggestions of an anonymous referee.

References

Bentler, P. M. Alpha-maximized factor analysis (alphamax): Its relation to alpha and canonical factor analysis. Psychometrika, 1968, 33, 335–345.CrossRefGoogle ScholarPubMed
Kaiser, H. F. & Caffrey, J. Alpha factor analysis. Psychometrika, 1965, 30, 1–14.CrossRefGoogle ScholarPubMed
Lord, F. M. Some relations between Guttman's principal components of scale analysis and other psychometric theory. Psychometrika, 1958, 23, 291–296.CrossRefGoogle Scholar