Supervised component generalized linear regression using a PLS-extension 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 a technique, Supervised Component Generalized Linear Regression (SCGLR), that combines PLS regression with GLM estimation in the multivariate context. SCGLR is tested on both simulated and real data.