Latent root regression analysis: an alternative method to PLS

Several applications are based on the assessment of a linear model linking a variable y to predictors x1, x2,…, xp. It often occurs that the predictors are collinear which results in a high instability of the model obtained by means of multiple linear regression. Several alternative methods have been proposed in order to tackle this problem. Among these methods Ridge Regression (RR), Principal Component Regression (PCR) and Partial Least Squares (PLS) are the most popular. We discuss another alternative method to Multiple Linear Regression (MLR) called Latent Root Regression (LRR). This method basically shares certain common characteristics with PLS as it derives latent variables to be used as predictors. Like PLS, the dependent variable plays a central role in determining the latent variables. We introduce new properties of latent root regression which give new insight into the determination of a prediction model. The mean squared error for the latent root estimator is explicitly given. Thus, a model may be determined by combining latent root estimators in such a way that the associated mean squared error is minimized. The method is illustrated using two real data sets.