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Functional Extended Redundancy Analysis

Published online by Cambridge University Press:  01 January 2025

Heungsun Hwang ,
Hye Won Suk ,
Jang-Han Lee ,
D. S. Moskowitz  and
Jooseop Lim
Heungsun Hwang*
Affiliation:
McGill University
Hye Won Suk
Affiliation:
McGill University
Jang-Han Lee
Affiliation:
Chung-Ang University
D. S. Moskowitz
Affiliation:
McGill University
Jooseop Lim
Affiliation:
Concordia University
*
Requests for reprints should be sent to Heungsun Hwang, Department of Psychology, McGill University, 1205 Dr. Penfield Avenue, Montreal, QC, H3A 1B1, Canada. E-mail: heungsun.hwang@mcgill.ca
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Abstract

We propose a functional version of extended redundancy analysis that examines directional relationships among several sets of multivariate variables. As in extended redundancy analysis, the proposed method posits that a weighed composite of each set of exogenous variables influences a set of endogenous variables. It further considers endogenous and/or exogenous variables functional, varying over time, space, or other continua. Computationally, the method reduces to minimizing a penalized least-squares criterion through the adoption of a basis function expansion approach to approximating functions. We develop an alternating regularized least-squares algorithm to minimize this criterion. We apply the proposed method to real datasets to illustrate the empirical feasibility of the proposed method.

Keywords

functional dataextended redundancy analysispenalized least squaresalternating regularized least-squares algorithm
Type
Original Paper
Information
Psychometrika , Volume 77 , Issue 3 , July 2012 , pp. 524 - 542
Copyright
Copyright © 2012 The Psychometric Society

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Footnotes

We thank the Associate Editor and three anonymous reviewers for their constructive comments on an earlier version of the paper, which greatly improved the quality of the paper. The work reported in the paper was supported by the National Research Foundation of Korea Grant (No. 2011-0027731) funded by the Korean government (MEST) to the third author, and by the Social Science and Humanities Research Council of Canada and Fonds de Recherche sur la Société et la Culture to the fifth author.

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