A new method of regression on latent variables. Application to spectral data

Several applications are based on the assessment of a linear model linking a set of variables Y to a set of predictors X. In the presence of strong colinearity among predictors, as in the case with spectral data, several alternative procedures to ordinary least squares (OLS) are proposed. We discuss a new alternative approach which we refer to as regression models through constrained principal components analysis (RM-CPCA). This method basically shares certain common characteristics with PLS regression as the dependent variables play a central role in determining the latent variables to be used as predictors. Unlike PLS, however, the approach discussed herein leads to straightforward models. This method also bears some similarity to latent root regression analysis (LRR) that was discussed by several authors. Moreover, a tuning parameter that ranges between 0 and 1 is introduced and the family of models thus formed includes several other methods as particular cases.