Generalized Functional Extended Redundancy Analysis

Heungsun Hwang, Hye Won Suk, Yoshio Takane, Jang Han Lee, Jooseop Lim

Research output: Contribution to journalArticle

3 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)101-125
Number of pages25
JournalPsychometrika
Volume80
Issue number1
DOIs
StatePublished - Mar 1 2015

Keywords

  • data reduction
  • exponential family responses
  • functional data analysis
  • functional extended redundancy analysis
  • generalized linear models
  • penalized likelihood

ASJC Scopus subject areas

  • Psychology(all)
  • Applied Mathematics

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    Hwang, H., Suk, H. W., Takane, Y., Lee, J. H., & Lim, J. (2015). Generalized Functional Extended Redundancy Analysis. Psychometrika, 80(1), 101-125. https://doi.org/10.1007/s11336-013-9373-x