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A Note on the Identification of Restricted Factor Loading Matrices

Published online by Cambridge University Press:  01 January 2025

Paul A. Bekker
Paul A. Bekker*
Affiliation:
Department of Economics, Tilburg University
*
Requests for reprints should be sent to Paul A. Bekker, Tilburg University, Department of Econometrics, PO Box 90153, 5000 LE Tilburg, THE NETHERLANDS.
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Abstract

It is shown that problems of rotational equivalence of restricted factor loading matrices in orthogonal factor analysis are equivalent to problems of identification in simultaneous equations systems with covariance restrictions. A necessary (under a regularity assumption) and sufficient condition for local uniqueness is given and a counterexample is provided to a theorem by J. Algina concerning necessary and sufficient conditions for global uniqueness.

Keywords

identificationorthogonal rotationconfirmatory factor analysis
Type
Notes And Comments
Information
Psychometrika , Volume 51 , Issue 4 , December 1986 , pp. 607 - 611
Copyright
Copyright © 1986 The Psychometric Society

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Footnotes

The problem in this note should not be confused with the related problem of underidentification of factor loading matrices due to underidentification of unique variances. A clear discussion of that distinction was given by K. A. Bollen and K. G. Jöreskog (1985, Uniqueness does not imply identification, Sociological Methods and Research, 14, 155–163).

The author would like to thank Arie Kapteyn for his comments and suggestions. Financial support by the Netherlands Organization for the Advancement of Pure Research (ZWO) is gratefully acknowledged.

References

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