Iterative Reweighted Partial Least Squares Estimation for GLMs

We extend the concept of partial least squares (PLS) into the framework of generalized linear models. These models form a sequence of rank one approximations useful for predicting the response variable when the explanatory information is severely ill-conditioned or ill-posed. An Iter­ ative reweighted PLS algorithm is presented with various theoretical prop­ erties. Connections to principal component and maximum likelihood esti­ mation are made, as well as suggestions for rules to choose the proper rank of the final model.