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Determining the Number of Components from the Matrix of Partial Correlations

Published online by Cambridge University Press:  01 January 2025

Wayne F. Velicer
Wayne F. Velicer*
Affiliation:
University of Rhode Island
*
Requests for reprints should be sent to Wayne F. Velicer, Department of Psychology, University of Rhode Island, Kingston, R. I. 02881.
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Abstract

A common problem for both principal component analysis and image component analysis is determining how many components to retain. A number of solutions have been proposed, none of which is totally satisfactory. An alternative solution which employs a matrix of partial correlations is considered. No components are extracted after the average squared partial correlation reaches a minimum. This approach gives an exact stopping point, has a direct operational interpretation, and can be applied to any type of component analysis. The method is most appropriate when component analysis is employed as an alternative to, or a first-stage solution for, factor analysis.

Keywords

common variancefactor analysisimage component analysis
Type
Original Paper
Information
Psychometrika , Volume 41 , Issue 3 , September 1976 , pp. 321 - 327
Copyright
Copyright © 1976 The Psychometric Society

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References

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