Component-Based Regularization of Multivariate Generalized Linear Mixed Models

We address the component-based regularization of a multivariate Generalized Linear Mixed Model (GLMM) in the framework of grouped data. A set Y of random responses is modelled with a multivariate GLMM, based on a set X of explanatory variables, a set A of additional explanatory variables, and random effects to introduce the within-group dependence of observations. Variables in X are assumed many and redundant so that regression demands regularization. This is not the case for A, which contains few and selected variables. Regularization is performed building an appropriate number of orthogonal components that both contribute to model Y and capture relevant structural information in X. To estimate the model, we propose to maximize a criterion specific to the supervised component-based generalized linear regression (SCGLR) within an adaptation of Schall’s algorithm. This extension of SCGLR is tested on both simulated and real grouped data, and compared to ridge and LASSO regularizations. Supplementary material for this article is available online.