Iteratively Reweighted Partial Least Squares Estimation for Generalized Linear Regression

Abstract

I extend the concept of partial least squares (PLS) into the framework of generalized linear models. A spectroscopy example in a logistic regression framework illustrates the developments. These models form a sequence of rank 1 approximations useful for predicting the response variable when the explanatory information is severely ill-conditioned. Iteratively reweighted PLS algorithms are presented with various theoretical properties. Connections to principal-component and maximum likelihood estimation are made, as well as suggestions for rules to choose the proper rank of the final model.

KEY WORDS:

• Biased estimation
• Cross-validation
• Ill-conditioned information
• Latent variables
• Principal components