A New Approach to Robust Partial Least Squares Regression Analysis

Abstract

Partial Least Squares Regression (PLSR) is a linear regression technique developed to relate many independent variables to one or several dependent variables. Robust methods are introduced to reduce or remove the effects of outlying data points. In the previous studies in robust PLSR field it has been mentioned that if the sample covariance matrix is properly robustified further robustification of the linear regression steps of the PLS1 algorithm (PLSR with univariate dependent variable) becomes unnecessary. Therefore, the purpose of this study is to propose a new approach to robust PLSR based on statistical procedures for covariance matrix robustification by selecting the well-known S-estimators. Both simulation results and an analysis on a real data set, which is used in robust PLSR literature frequently, showing the effectiveness, success in fitting to regular data points and predictive power of the new proposed robust PLSR method.

Mixed Models of Non-Proportional Hazard and Application in The Open Distance Education Students Retention Data

“…The measure of the goodness of fit model uses the bias and MSE value resulted from the model simulation (Polat and Gunay [45]).…”