Partial Least Squares and Other Biased Regression Methods:

Abstract

Biased regression methods like ridge regression (RR), Liu type regression, principal component regression (PCR), partial least squares regression (PLSR) are some of the well known regression techniques which have been developed to cope with multicollinearity problem in multiple regression analysis. These help in reducing the variance of the regression parameters when the explanatory variables are multicollinear because when data is suffering from severe multicollinearity ordinary least squares (OLS) regression method leads to unstable estimates for the regression coefficients. This paper introduces a modified PLS estimator called now onwards as ‘PLSLiu’ estimator. The present research work compares average MSE’s (AMSE) of PLSLiu with OLS, RR, PCR, Liu and PLSR estimators through simulation study. Further the work compares the MSE of both PLSR and PLSLiu estimators theoretically under the assumption of homoscedasticity. We observe that the performance of the suggested estimator is better than all the above estimators in terms of average MSE when number of explanatory variables is less than the number of units in the sample.