Component-based Generalized Linear Regression using a PLS-extended variant of the Fisher scoring algorithm

In the current estimation of a GLM model, the correlation structure of regressors is not used as the basis on which to lean strong predictive dimensions. Looking for linear combinations of regressors that merely maximize the likelihood of the GLM has two major consequences: 1) collinearity of regressors is a factor of estimation instability, and 2) as predictive dimensions may lean on noise, both predictive and explanatory powers of the model are jeopardized. For a single dependent variable, attempts have been made to adapt PLS Regression, which solves this problem in the classical Linear Model, to GLM estimation. In this paper, we first discuss the methods thus developed, and then propose an algorithm that combines PLS regression with GLM estimation in the multivariate context, under a conditional independence assumption. Our algorithm is tested on simulated data. ∗Corresponding author Tel : +33 (0)467 144 164, Fax : +33 (0)467 143 558 Email addresses: [email protected] (X. Bry), [email protected] (C. Trottier), [email protected] (T. Verron) Preprint submitted to Elsevier September 30, 2011 ha l-0 06 64 77 8, v er si on 1 31 J an 2 01 2