Application of Latent Roots Regression to Multicollinear Data

Abstract

Several applications are based on the assessment of a linear model including 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 using least squares estimation. Several alternative methods have been proposed in order to tackle this problem. Among these methods Ridge Regression, Principal Component Regression .We discuss a third method called Latent Root Regression. This method depends on the Eigen values and Eigen vectors of the matrix A'A ,where A is the matrix of y and x1, x2,..,xp . We introduce some properties of latent root regression which give new insight into the determination of a prediction model. 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 three real data sets. Namely: Economical , Medical and Environmental data . According to applications, our new estimators depending on the Latent Root Regression have better performances in the sense of MSE in most of the situations.