  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.
