Partial Least Squares Regression Model Analysis with Wavelet Shrinkage

Abstract

Partial Least Squares Regression is a statistical method used for modeling the relationship between a set of independent variables and a set of dependent variables. It is beneficial when there are many independent variables, and there might be multicollinearity issues or when the number of observations is less than the number of predictor variables. The proposed method is to use wavelet shrinkage in processing noise data before estimating the parameters of the Partial Least Squares regression model, through the use of Daubechies, Symlets, and Coif lets Wavelet of different orders (3, 2, and 4) respectively, with estimating the University threshold level and applying it to a soft threshold rule to obtain de-noise data for independent and dependent variables. The comparison between the efficiency of the proposed and classical methods depends on the mean square error of the independent and dependent variables for each component and the overall total mean square error using simulation and real data. An algorithm in the MATLAB program was designed for this purpose. The research results revealed that the proposed methods are more efficient than the classical method.