  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.
