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arXiv · 1908.07908

Extension to mixed models of the Supervised Component-based Generalised Linear Regression

Jocelyn Chauvet·Catherine Trottier·Xavier Bry·Frederic Mortier
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Abstract

We address the component-based regularisation of a multivariate Generalized Linear Mixed Model (GLMM). A set of random responses Y is modelled by a GLMM, using a set X of explanatory variables, a set T of additional covariates, and random effects used to introduce the dependence between statistical units. Variables in X are assumed many and redundant, so that regression demands regularisation. By contrast, variables in T are assumed few and selected so as to require no regularisation. 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 data, and compared to Ridge- and Lasso-based regularisations.

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Jocelyn Chauvet, Catherine Trottier, Xavier Bry, Frederic Mortier. 2019-08-09. Extension to mixed models of the Supervised Component-based Generalised Linear Regression. https://arxiv.org/abs/1908.07908

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