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Article Dans Une Revue Journal of Computational and Graphical Statistics Année : 2019

Component-based regularisation of multivariate generalised linear mixed models

Résumé

We address the component-based regularisation of a multivariate Generalised Linear Mixed Model (GLMM) in the framework of grouped data. A set Y of random responses is modelled with a multivariate GLMM, based on a set X of explanatory variables, a set A of additional explanatory variables, and random effects to introduce the within-group dependence of observations. Variables in X are assumed many and redundant so that regression demands regularisation. This is not the case for A, which contains few and selected variables. Regularisation is performed building an appropriate number of orthogonal components that both contribute to model Y and capture relevant structural information in X. To estimate the model, we propose to maximise a criterion specific to the Supervised Component-based Generalised Linear Regression (SCGLR) within an adaptation of Schall's algorithm. This extension of SCGLR is tested on both simulated and real grouped data, and compared to ridge and LASSO regularisations. Supplementary material for this article is available online.
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Dates et versions

hal-02064508 , version 1 (09-08-2019)

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Jocelyn Chauvet, Catherine Trottier, Xavier Bry. Component-based regularisation of multivariate generalised linear mixed models. Journal of Computational and Graphical Statistics, In press, ⟨10.1080/10618600.2019.1598870⟩. ⟨hal-02064508⟩
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