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Rotational Equivalence of Factor Loading Matrices with Specified Values

Published online by Cambridge University Press:  01 January 2025

Robert I. Jennrich
Robert I. Jennrich*
Affiliation:
University of California at Los Angeles
*
Requests for reprints should be sent to Robert I. Jennrich, Department of Mathematics, University of California, Los Angeles, CA 90024.
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Abstract

Under mild assumptions, when appropriate elements of a factor loading matrix are specified to be zero, all orthogonally equivalent matrices differ at most by column sign changes. Here a variety of results are given for the more complex case when the specified values are not necessarily zero. A method is given for constructing reflections to preserve specified rows and columns. When the appropriate k(k − 1)/2 elements have been specified, sufficient conditions are stated for the existence of 2k orthogonally equivalent matrices.

Keywords

orthogonal rotationspecified valuesreflectionsconfirmatory factor analysis
Type
Original Paper
Information
Psychometrika , Volume 43 , Issue 3 , September 1978 , pp. 421 - 426
Copyright
Copyright © 1978 The Psychometric Society

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Footnotes

This research was supported in part by the National Institute of Health Grant RR-3.

References

Dunn, J. E. A note on a sufficiency condition for uniqueness of a restricted factor matrix. Psychometrika, 1973, 38, 141–143.CrossRefGoogle Scholar
Jöreskog, K. G. A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 1969, 34, 183–202.CrossRefGoogle Scholar