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 x(1),x(2)..... x(p). It often occurs that the pr edictors are collinear which results in a high instability of the model obt ained by means of multiple linear regression. Several alternative methods h ave been proposed in order to tackle this problem. Among these methods Ridg e Regression (RR), Principal Component Regression (PCR) and Partial Least S quares (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 deri ves latent variables to be used as predictors. Like PLS, the dependent vari able plays a central role in determining the latent variables. We introduce new properties of latent root regression which give new insight into the d etermination of a prediction model. The mean squared error for the latent r oot estimator is explicitly given. Thus, a model may be deter-mined by comb ining latent root estimators in such a way that the associated mean squared error is minimized. The method is illustrated using two real data sets. (C ) 2001 Elsevier Science B.V. All rights reserved.