We address component-based regularization of a multivariate Generalized Linear Model (GLM). A set of random responses Y is assumed to depend, through a GLM, on a set X of explanatory variables, as well as on a set T of additional covariates. X is partitioned into R conceptually homogeneous blocks X1 , … , XR, viewed as explanatory themes. Variables in each X,. are assumed many and redundant. Thus, generalized linear regression demands regularization with respect to each X,.. By contrast, variables in T are assumed selected so as to demand no regularization. Regularization is performed searching each X,. for an appropriate number of orthogonal components that both contribute to model Y and capture relevant structural information in X,.. We propose a very general criterion to measure structural relevance (SR) of a component in a block, and show how to take SR into account within a Fisher-scoring-type algorithm in order to estimate the model. We show how to deal with mixed-type explanatory variables. The method, named THEME-SCGLR, is tested on simulated data, and then applied to rainforest data in order to model the abundance of tree-species.