PLS regression - VIP treshold to exclude variables I have been developing PLS models in the software SIMCA. To optimize the model and decide which variables to exclude, I use the VIP (Variable Importance in Projection [1,2]) and in the software userguide it is stated that variables with VIP>1 are "good", variables with VIP < 0.5 are "bad" and should be excluded, and variables with VIP between 0.5 and 1 are a grey area and depend from case to case.
I have found support in literature for the statement that varibles with VIP close to or greater than 1 are considered good for the model, but I haven't find sources for the treshold of 0.5 to exclude variables. Can anyone confirm this?
 A: VIP is a measure of the combined importance of a given x variable in not only predicting y, but also describing the structure of the entire x block of variables. There does not appear to be an appropriate hard and fast rule (such as < 0.5) for determining a lower VIP cutoff for removing variables.
A commonly cited article (Chong and Jun, 2004) describes a method for selecting VIP thresholds with best performance, (based on sensitivity and specificity) depending on a range of factors, such as signal to noise ratio and how coefficients are distributed. They provide a formula, as well as some tabulated results (Table 5). In those tabulated results ~0.6 was about the lowest cutoff.
Perhaps an appropriate method is described by Andersen and Bro, 2010. They state, "It is not advisable to simply remove everything below one. Instead, a few of the variables with the very lowest VIP values should be removed. If the model improves, the method can be repeated on the reduced data set until no more improvements are found."
Chong I-G, Jun C-H (2005) Performance of some variable selection methods when multicollinearity is present. Chemometrics and Intelligent Laboratory Systems 78:103–112. doi: 10.1016/j.chemolab.2004.12.011
Andersen CM, Bro R (2010) Variable selection in regression—a tutorial. Journal of Chemometrics 24:728–737. doi: 10.1002/cem.1360
