R\'egularisation dans les Mod\`eles Lin\'eaires G\'en\'eralis\'es Mixtes avec effet al\'eatoire autor\'egressif

TL;DR

This paper develops regularised EM algorithms for Generalised Linear Mixed Models to handle high-dimensional, panel data with multiple random effects, improving variable selection and model fitting.

Contribution

It introduces L2-penalised and supervised component-based regularised EM algorithms tailored for high-dimensional GLMMs with complex random effects.

Findings

Effective regularisation for high-dimensional panel data

Improved variable selection in GLMMs

Enhanced model fitting with random effects

Abstract

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.