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On a Test of Dimensionality in Redundancy Analysis

Published online by Cambridge University Press:  01 January 2025

Yoshio Takane  and
Heungsun Hwang
Yoshio Takane*
Affiliation:
McGill University
Heungsun Hwang
Affiliation:
HEC Montreal
*
Requests for reprints should be sent to Yoshio Takane, Department of Psychology, McGill Universty, 1205 Dr. Penfield Ave., Montreal, QC H3A 1B1 Canada. E-mail: [email protected]
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Abstract

Lazraq and Cléroux (Psychometrika, 2002, 411–419) proposed a test for identifying the number of significant components in redundancy analysis. This test, however, is ill-conceived. A major problem is that it regards each redundancy component as if it were a single observed predictor variable, which cannot be justified except for the rare situations in which there is only one predictor variable. Consequently, the proposed test leads to drastically biased results, particularly when the number of predictor variables is large, and it cannot be recommended for use. This is shown both theoretically and by Monte Carlo studies.

Keywords

Reduced rank regressionPCA of instrumental variablesparallel analysispermutation tests
Type
Original Paper
Information
Psychometrika , Volume 70 , Issue 2 , June 2005 , pp. 271 - 281
Copyright
Copyright © 2005 The Psychometric Society

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Footnotes

The work reported in this paper was supported by Grant A6394 to the first author from the Natural Sciences and Engineering Research Council of Canada.

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