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Assessing the Stability of Principal Components Using Regression

Published online by Cambridge University Press:  01 January 2025

Atanu R. Sinha  and
Bruce S. Buchanan
Atanu R. Sinha*
Affiliation:
John E. Anderson Graduate School of Management, University of California, Los Angeles
Bruce S. Buchanan
Affiliation:
Leonard N. Stern School of Business, New York University, New York
*
Send requests for reprints to Atanu R. Sinha, B418 Gold Hall, 110 Westwood Plaza, Los Angeles, CA 90095.
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Abstract

This paper presents an analysis, based on simulation, of the stability of principal components. Stability is measured by the expectation of the absolute inner product of the sample principal component with the corresponding population component. A multiple regression model to predict stability is devised, calibrated, and tested using simulated Normal data. Results show that the model can provide useful predictions of individual principal component stability when working with correlation matrices. Further, the predictive validity of the model is tested against data simulated from three non-Normal distributions. The model predicted very well even when the data departed from normality, thus giving robustness to the proposed measure. Used in conjunction with other existing rules this measure will help the user in determining interpretability of principal components.

Keywords

sampling stabilityPCAsimulationregression analysis
Type
Original Paper
Information
Psychometrika , Volume 60 , Issue 3 , September 1995 , pp. 355 - 369
Copyright
Copyright © 1995 The Psychometric Society

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Footnotes

The authors would like to thank the four anonymous reviewers and the two editors for their valuable comments. Atanu R. Sinha gratefully acknowledges the research support received from the Marketing Studies Center, AGSM, UCLA.

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