Title: Extension to mixed models of the supervised component-based generalised linear regression
Authors: Jocelyn Chauvet - University of Montpellier (France) [presenting]
Catherine Trottier - University of Montpellier (France)
Xavier Bry - University of Montpellier (France)
Frederic Mortier - Cirad (France)
Abstract: The component-based regularisation of a multivariate Generalized Linear Mixed Model (GLMM) is adressed. 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.