  We address component-based regularisation of a multivariate Generalized
Linear Mixed Model. A set of random responses Y is modelled by a GLMM, using a
set X of explanatory variables and a set T of additional covariates. Variables
in X are assumed many and redundant: generalized linear mixed regression
demands regularisation with respect to X. By contrast, variables in T are
assumed few and selected so as to demand 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. We
propose to optimize a SCGLR-specific criterion within a Schall's algorithm in
order to estimate the model. This extension of SCGLR is tested on simulated and
real data, and compared to Ridge-and Lasso-based regularisations.
