Selecting both latent and explanatory variables in the PLS1 regression model

In this paper, two inferential procedures for selecting the significant predictors in the PLS1 regression model are introduced. The significant PLS components are first obtained and the two predictor selection methods, called PLS–Forward and PLS–Bootstrap, are applied to the PLS model obtained. They are also compared empirically to two other methods that exist in the literature with respect to the quality of fit of the model and to their predictive ability. Although none of the four methods is uniformly best, it is seen that PLS–Forward and PLS–Bootstrap perform well and can be very useful in practical situations in identifying the important explanatory variables.