Regularising Generalised Linear Mixed Models with an autoregressive random effect

TL;DR

This paper develops regularised EM algorithms for Generalised Linear Mixed Models with autoregressive random effects, improving modeling of panel data with many redundant variables.

Contribution

It introduces L2-penalised and supervised component-based regularised EM algorithms for GLMMs with autoregressive random effects.

Findings

Effective regularisation of GLMMs with serially correlated effects

Enhanced variable selection in high-dimensional panel data

Improved model fitting with regularised EM algorithms

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 one introduces the dependence within individuals on which data is repeatedly collected while the second one 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, and then a supervised component-based regularised EM algorithm as an alternative.