  We address regularised versions of the Expectation-Maximisation (EM)
algorithm for Generalised Linear Mixed Models (GLMM) in the context of panel
data (measured on several individuals at different time points). A random
response y is modelled by a GLMM, using a set X of explanatory variables and
two random effects. The first effect introduces the dependence within
individuals on which data is repeatedly collected while the second embodies the
serially correlated time-specific effect shared by all the individuals.
Variables in X are assumed many and redundant, so that regression demands
regularisation. In this context, we first propose a L2-penalised EM algorithm
for low-dimensional data, and then a supervised component-based regularised EM
algorithm for the high-dimensional case.
