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Generalized Functional Extended Redundancy Analysis

Author

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  • Heungsun Hwang
  • Hye Suk
  • Yoshio Takane
  • Jang-Han Lee
  • Jooseop Lim

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. Copyright The Psychometric Society 2015

Suggested Citation

  • Heungsun Hwang & Hye Suk & Yoshio Takane & Jang-Han Lee & Jooseop Lim, 2015. "Generalized Functional Extended Redundancy Analysis," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 101-125, March.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:1:p:101-125
    DOI: 10.1007/s11336-013-9373-x
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    References listed on IDEAS

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    1. Heungsun Hwang & Hye Suk & Jang-Han Lee & D. Moskowitz & Jooseop Lim, 2012. "Functional Extended Redundancy Analysis," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 524-542, July.
    2. Ferraty, F. & Van Keilegom, I. & Vieu, P., 2012. "Regression when both response and predictor are functions," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 10-28.
    3. Manteiga, Wenceslao Gonzalez & Vieu, Philippe, 2007. "Statistics for Functional Data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4788-4792, June.
    4. Michel Wedel & Wayne DeSarbo, 1995. "A mixture likelihood approach for generalized linear models," Journal of Classification, Springer;The Classification Society, vol. 12(1), pages 21-55, March.
    5. Mariano Valderrama, 2007. "An overview to modelling functional data," Computational Statistics, Springer, vol. 22(3), pages 331-334, September.
    6. Ferraty, F. & Van Keilegom, Ingrid & Vieu, P., 2012. "Regression when both response and predictor are functions," LIDAM Reprints ISBA 2012004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Heungsun Hwang & Marc Tomiuk, 2010. "Fuzzy clusterwise quasi-likelihood generalized linear models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 4(4), pages 255-270, December.
    8. Dauxois, J. & Pousse, A. & Romain, Y., 1982. "Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 136-154, March.
    9. S. le Cessie & J. C. van Houwelingen, 1992. "Ridge Estimators in Logistic Regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 191-201, March.
    10. Takane, Yoshio & Hwang, Heungsun, 2005. "An extended redundancy analysis and its applications to two practical examples," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 785-808, June.
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    Cited by:

    1. Minjung Kyung & Ju-Hyun Park & Ji Yeh Choi, 2022. "Bayesian Mixture Model of Extended Redundancy Analysis," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 946-966, September.
    2. Hye Won Suk & Heungsun Hwang, 2016. "Functional Generalized Structured Component Analysis," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 940-968, December.

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