doi:10.1016/S0167-9473(02)00071-3
Copyright © 2002 Elsevier Science B.V. All rights reserved.
A new algorithm for latent root regression analysis
Evelyne Vigneau
,
and El Mostafa Qannari
ENITIAA/INRA, Unité de Sensométrie et de Chimiométrie, La Géraudière, B.P. 82225, 44322, Nantes Cedex 3, France
Available online 28 March 2002.
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Abstract
New properties of latent root regression are shown aiding insight into the determination of a prediction model. Moreover, a procedure for the determination of a prediction model is discussed. It has similarities to partial least squares and differ from the latter method only in the way components used as predictors are formed. This procedure is extended to the case where the problem at hand concerns the prediction of more than one variable. The method is illustrated using real data sets.
Author Keywords: Latent root regression; Prediction; Biased estimation; Partial least squares
Fig. 1. Root mean squares of the residuals (RMSE) evaluated on the validation set according to the number of components included in the sequential LRR model or in the PLS model. RMSE for OLS method is also given.
Fig. 2. Graph of the evolution of the eigenvalues λ0(.) in the course of sequential LRR algorithm.
Fig. 3. Root mean squares of the residuals (RMSE) evaluated on the validation set according to the number of components included in the sequential LRR model, for each of the dependent variables and for the Y matrix.
Fig. 4. Difference between the first eigenvalue of A′A and the first eigenvalue of Y′Y (criterion Δ) according to the number of components included in the sequential LRR model.