Séminaire des Doctorant·e·s :

Le 19 avril 2023 à 17:30 - Salle 109

Présentée par Gibaud Julien - Université Montpellier

Generalized linear model based on latent factors and supervised components

In this talk, we propose to model the residual variance-covariance matrix of the responses in a context of component-based multivariate model. A response matrix is assumed to depend, through a Generalized Linear Model, on a set of explanatory variables. Explanatory variables are partitioned into several conceptually homogenous variable groups, viewed as explanatory themes. Variables in themes are supposed many and redundant. Thus, generalized linear regression demands dimension reduction and regularization with respect to each theme. Regularization is performed searching each theme for an appropriate number of orthogonal components that both contribute to predict the response matrix and capture relevant structural information in themes. A set of few latent factors completes the model so as to model the covariance matrix of the responses conditional on the components. To estimate the multiple-theme model, we present an algorithm combining thematic component-based model estimation and factor model estimation. This new methodology is tested on simulated data and then applied to an agricultural ecology dataset.