Component-based regularization of a multivariate GLM with a thematic partitioning of the explanatory variables. (February 2020)

• Record Type: Journal Article
• Authors: Bry, Xavier; Trottier, Catherine; Mortier, Frédéric; Cornu, Guillaume
• Is Part Of: Statistical modelling. Volume 20:Number 1(2020)
• Page Start: 96
• Page End: 119
• Publication Date: 2020-02
• Subjects: components -- multivariate generalized linear model -- regularization -- SCGLR -- dimension reduction; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X18810114
• Languages: English
• ISSNs: 1471-082X

Abstract

We address component-based regularization of a multivariate generalized linear model (GLM). A vector of random responsesY is assumed to depend, through a GLM, on a setX of explanatory variables, as well as on a setA of additional covariates.X is partitioned intoR conceptually homogenous variable groupsX 1, …, X R, viewed as explanatory themes. Variables in eachX r are assumed many and redundant. Thus, generalized linear regression demands dimension reduction and regularization with respect to eachX r . By contrast, variables inA are assumed few and selected so as to demand no regularization. Regularization is performed searching eachX r for an appropriate number of orthogonal components that both contribute to modelY and capture relevant structural information inX r . To estimate a single-theme model, we first propose an enhanced version of Supervised Component Generalized Linear Regression (SCGLR), based on a flexible measure of structural relevance of components, and able to deal with mixed-type explanatory variables. Then, to estimate the multiple-theme model, we develop an algorithm encapsulating this enhanced SCGLR: THEME-SCGLR. The method is tested on simulated data and then applied to rainforest data in order to model the abundance of tree species.