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Supervised component generalized linear regression using a PLS-extension of the Fisher scoring algorithm

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  • Bry, X.
  • Trottier, C.
  • Verron, T.
  • Mortier, F.

Abstract

In the current estimation of a GLM model, the correlation structure of regressors is not used as the basis on which to lean strong predictive dimensions. Looking for linear combinations of regressors that merely maximize the likelihood of the GLM has two major consequences: (1) collinearity of regressors is a factor of estimation instability, and (2) as predictive dimensions may lean on noise, both predictive and explanatory powers of the model are jeopardized. For a single dependent variable, attempts have been made to adapt PLS regression, which solves this problem in the classical Linear Model, to GLM estimation. In this paper, we first discuss the methods thus developed, and then propose a technique, Supervised Component Generalized Linear Regression (SCGLR), that combines PLS regression with GLM estimation in the multivariate context. SCGLR is tested on both simulated and real data.

Suggested Citation

  • Bry, X. & Trottier, C. & Verron, T. & Mortier, F., 2013. "Supervised component generalized linear regression using a PLS-extension of the Fisher scoring algorithm," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 47-60.
    • Handle: RePEc:eee:jmvana:v:119:y:2013:i:c:p:47-60
    DOI: 10.1016/j.jmva.2013.03.013
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    References listed on IDEAS

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    1. Bastien, Philippe & Vinzi, Vincenzo Esposito & Tenenhaus, Michel, 2005. "PLS generalised linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 48(1), pages 17-46, January.
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    2. Meng, Ming & Mander, Sarah & Zhao, Xiaoli & Niu, Dongxiao, 2016. "Have market-oriented reforms improved the electricity generation efficiency of China's thermal power industry? An empirical analysis," Energy, Elsevier, vol. 114(C), pages 734-741.
    3. Jin Hee Bae & Minwoo Kim & J.S. Lim & Zong Woo Geem, 2021. "Feature Selection for Colon Cancer Detection Using K-Means Clustering and Modified Harmony Search Algorithm," Mathematics, MDPI, vol. 9(5), pages 1-14, March.

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