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Generalized Functional Extended Redundancy Analysis

Published online by Cambridge University Press:  01 January 2025

Heungsun Hwang ,
Hye Won Suk ,
Yoshio Takane ,
Jang-Han Lee  and
Jooseop Lim
Heungsun Hwang*
Affiliation:
McGill University
Hye Won Suk
Affiliation:
Arizona State University
Yoshio Takane
Affiliation:
McGill University
Jang-Han Lee
Affiliation:
Chung-Ang 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, Quebec, H3A 1B1, Canada. E-mail: heungsun.hwang@mcgill.ca
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Abstract

Functional extended redundancy analysis (FERA) was recently developed to integrate data reduction into functional linear models. This technique extracts a component from each of multiple sets of predictor data in such a way that the component accounts for the maximum variance of response data. Moreover, it permits predictor and/or response data to be functional. FERA can be of use in describing overall characteristics of each set of predictor data and in summarizing the relationships between predictor and response data. In this paper, we extend FERA into the framework of generalized linear models (GLM), so that it can deal with response data generated from a variety of distributions. Specifically, the proposed method reduces each set of predictor functions to a component and uses the component for explaining exponential-family responses. As in GLM, we specify the random, systematic, and link function parts of the proposed method. We develop an iterative algorithm to maximize a penalized log-likelihood criterion that is derived in combination with a basis function expansion approach. We conduct two simulation studies to investigate the performance of the proposed method based on synthetic data. In addition, we apply the proposed method to two examples to demonstrate its empirical usefulness.

Keywords

functional data analysisfunctional extended redundancy analysisgeneralized linear modelsdata reductionexponential family responsespenalized likelihood

Information

Type
Original Paper
Information
Psychometrika , Volume 80 , Issue 1 , March 2015 , pp. 101 - 125
Copyright
Copyright © 2013 The Psychometric Society

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