Supervised component generalized linear regression with multiple explanatory blocks: THEME-SCGLR

Bry Xavier, Trottier Catherine, Mortier Frédéric, Cornu Guillaume, Verron Thomas. 2016. Supervised component generalized linear regression with multiple explanatory blocks: THEME-SCGLR. In : The multiple facets of partial least squares and related methods: PLS, Paris, France, 2014. Abdi Hervé (ed.), Esposito Vinzi (ed.), Vincenzo (ed.), Russolillo Giorgio (ed.), Saporta Gilbert (ed.), Trinchera Laura (ed.). Cham : Springer International Publishing, 141-154. (Springer Proceedings in Mathematics and Statistics, 173) ISBN 978-3-319-40641-1 International Conference on Partial Least Squares and Related Methods (PLS2014). 8, Paris, France, 26 Mai 2014/28 Mai 2014.

Résumé : We address component-based regularization of a multivariate Generalized Linear Model (GLM). A set of random responses Y is assumed to depend, through a GLM, on a set X of explanatory variables, as well as on a set T of additional covariates. X is partitioned into R conceptually homogeneous blocks X1 , … , XR, viewed as explanatory themes. Variables in each X,. are assumed many and redundant. Thus, generalized linear regression demands regularization with respect to each X,.. By contrast, variables in T are assumed selected so as to demand no regularization. Regularization is performed searching each X,. for an appropriate number of orthogonal components that both contribute to model Y and capture relevant structural information in X,.. We propose a very general criterion to measure structural relevance (SR) of a component in a block, and show how to take SR into account within a Fisher-scoring-type algorithm in order to estimate the model. We show how to deal with mixed-type explanatory variables. The method, named THEME-SCGLR, is tested on simulated data, and then applied to rainforest data in order to model the abundance of tree-species.

Classification Agris : U10 - Informatique, mathématiques et statistiques
K01 - Foresterie - Considérations générales

Auteurs et affiliations

• Bry Xavier, UM2 (FRA)
• Trottier Catherine, UM2 (FRA)
• Mortier Frédéric, CIRAD-ES-UPR BSef (FRA)
• Cornu Guillaume, CIRAD-ES-UPR BSef (FRA) ORCID: 0000-0002-7523-5176
• Verron Thomas, SEITA (FRA)

Source : Cirad-Agritrop (https://agritrop.cirad.fr/583977/)

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