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Tests for Linear Trend in the Smallest Eigenvalues of the Correlation Matrix

Published online by Cambridge University Press:  01 January 2025

Peter M. Bentler  and
Ke-Hai Yuan
Peter M. Bentler*
Affiliation:
University of California, Los Angeles
Ke-Hai Yuan
Affiliation:
University of California, Los Angeles
*
Requests for reprints should be sent to Peter M. Bentler, Department of Psychology, UCLA, Box 951563, Los Angeles CA 90095-1563.
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Abstract

A test for linear trend among a set of eigenvalues of a correlation matrix is developed. As a technical implementation of Cattell's scree test, this is a generalization of Anderson's test for the equality of eigenvalues, and extends Bentler and Yuan's work on linear trends in eigenvalues of a covariance matrix. The power of minimum x2 and maximum likelihood ratio tests are compared. Examples show that the linear trend hypothesis is more realistic than the standard hypothesis of equality of eigenvalues, and that the hypothesis is compatible with standard decisions on the number of factors or components to retain in data analysis.

Keywords

principal componentseigenvalueslinear trend of eigenvaluesscree testasymptotic distributionminimum x2 estimate
Type
Original Paper
Information
Psychometrika , Volume 63 , Issue 2 , June 1998 , pp. 131 - 144
Copyright
Copyright © 1998 The Psychometric Society

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Footnotes

This work was supported by National Institute on Drug Abuse Grants DA01070 and DA00017. The assistance of Maia Berkane and several anonymous reviewers is gratefully acknowledged.

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