Extension de la r\'egression lin\'eaire g\'en\'eralis\'ee sur composantes supervis\'ees (SCGLR) aux donn\'ees group\'ees

TL;DR

This paper extends the SCGLR method to handle grouped data in multivariate generalized linear mixed models, optimizing component-based regularization to improve model interpretability and performance.

Contribution

The paper introduces an extension of SCGLR for grouped data, integrating it with Schall's algorithm for better regularization in multivariate GLMMs.

Findings

Effective regularization with the extended SCGLR on simulated data

Improved model performance compared to Ridge and Lasso methods

Successful application to real grouped data

Abstract

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.