Subset selection for PLS.
Requested again by varbanov.ar
Here is more detail about the current process:
Current P&G approach to PLS variable selection using an internal web tool
VIP determines order of removal
Minimizing PRESS is used as stopping rule
Backward elimination after max PLS factors is specified (e.g., 5)
For each iteration and range of PLS factor (from 1 to max)
First, all predictors with VIP<0.8 are dropped
Then, the predictor with smallest VIP is dropped
Best PLS Model (smallest PRESS) from this iteration is compared to best model
from previous iterations
Stop variable selection if PRESS is no improvement to PRESS
A pass across remaining predictors for removal of redundant ones is made after
that to complete variable selection
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Optimal PLS Model (with smallest PRESS) has 1 PLS factor and 3 predictors
Web Tool provides Best Subset Models up to specified maximum size by user
Helpful alternatives when the Optimal Model has large number of predictors left
in model
Could consider smaller size models if PRESS does not increase much
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More detail from Silvio Miccio (silvio.silvio 
It would be great to have a kind of best subset algorithm for PLS, finding factors or groups of factors relevant for predicting Y. Practice has shown that dropping unimportant factors results in models with lower generalization error.
Doing subset selection only based on VIP is something I do not feel comfortable with. The threshold values for VIP are arbitrary (like the folklore value of 0.05 for p-values).
Thanks for the suggestion. Development is investigating this.
