Supervised forward selection

Adopting the unsupervised option initially, the first two variables to be selected are those with the lowest pairwise correlation. The next variable selected has the smallest multiple squared correlation with those first two variables. This process is continued until the preset maximum level of multicolinearity (determined by the squared multiple correlation coefficient) is reached. Whitley et al. refer to this procedure as unsupervised forward selection (UFS). UFS can also be performed with a minimum variance criterion where only variables with variance above this minimum will be selected. These two criteria can be used by scientists simultaneously. With supervised variable selection, only those variables having a sufficiently high correlation with the response are considered for what effectively is UFS on this reduced set of variables. We will term this latter process, supervised forward selection (SFS). To see how these options work and to examine the effect they have on the model produced, we performed PLS on the data with both UFS and SFS configured to run with a range of response variable correlations (Table 8). 

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