Partial Least Squares Regression for Binary Responses and Its Associated Biplot Representation

In this paper, we propose a generalization of Partial Least Squares Regression (PLS-R) for a matrix of several binary responses and a a set of numerical predictors. We call the method Partial Least Squares Binary Logistic Regression (PLS-BLR). That is equivalent to a PLS-2 model for binary responses. Biplot and even triplot graphical representations for visualizing PLS-BLR models are described, and an application to real data is presented. Software packages for the calculation of the main results are also provided. We conclude that the proposed method and its visualization using triplots are powerful tools for the interpretation of the relations among predictors and responses.

Automated summary

This paper proposes a generalization of Partial Least Squares Regression (PLS-R) for a matrix of several binary responses and a set of numerical predictors, referred to as Partial Least Squares Binary Logistic Regression (PLS-BLR). The paper also describes the use of Biplot and Triplot graphical representations for visualizing PLS-BLR models and provides an application to real data. The conclusion is that the proposed method and its visualization using Triplots are powerful tools for interpreting the relations between predictors and responses.