Robust Methods for Partial Least Squares Regression

Partial Least Squares Regression (PLSR) is a linear regression technique developed to deal with high-dimensional regressors and one or several response variables. In this paper we introduce robustified versions of the SIMPLS algorithm being the leading PLSR algorithm because of its speed and efficiency. Because SIMPLS is based on the empirical cross-covariance matrix between the response variables and the regressors and on linear least squares regression, the results are affected by abnormal observations in the data set. Two robust methods, RSIMCD and RSIMPLS, are constructed from a robust covariance matrix for high-dimensional data and robust linear regression. We introduce robust RMSECV and RMSEP values for model calibration and model validation. Diagnostic plots are constructed to visualize and classify the outliers. Several simulation results and the analysis of real data sets show the effectiveness and the robustness of the new approaches. Because RSIMPLS is roughly twice as fast as RSIMCD, it stands out as the overall best method.