partial least square and VIP coefficient

[#1]

Hello,

I would like to know how the VIP are calculated in the VIP vs coefficient graphs. Where can I find some more details on that?

Lu

[#2 · Accepted solution]

Hi @Lu ,

  You can read more on the JMP help for PLS here. In addition, according to the JMP online book by Ian Cox and Marie Gaudard, Discovering Partial Least Squares with JMP, p. 22:

"The Variable Importance for the Projection (VIP) statistic, discussed in Wold (1995, p. 213) and In Wold et al. (2001, p. 123), is defined as a weighted sum of squares of the weights, W."..."Being based on weights, it measures a predictor's contribution to characterizing the factors used in the PLS model...".

  The VIP by default is 0.8, but can be changed in JMP and it is a cumulative measure of the influence of a variable on the model. An analogy would be "Portion" in the Boosted Tree and Bootstrap Forest platforms -- the portion of the model that is explained by a given factor X. Factors with both low VIP values and coefficients in the model can be deleted as their contribution is negligible.

  As a note: it is often better to use the VIP vs. Coefficients for Centered and Scaled Data because it considers the size of the effect as well as the VIP.  Again, the threshold value is 0.8, which may or may not be appropriate for your data. A higher or lower value might be more appropriate and should be considered when evaluating a model's performance to predict an outcome.

  I think you'll find the book by Cox & Gaudard helpful -- plus, you can find it for free as a PDF online in support.sas.com.

Hope this helps,

DS

[#3]

Thanks Diedrich

This is clear to me.

The default for VIP is 0.8 (does it mean that 80% of the variance is explained by this factor?)

You made the comparison with the "portion" for bootstrap forrest. Is the default also 0.8 for portion?

Lu

[#4]

Hi @Lu ,

  The default value for VIP of 0.8 is related to the weighted sum of squares of the weights. It is not a %. This would not make sense since the VIP factor can be larger than 1, which would imply >100% of the variance. It's a value to help the user judge whether a variable is important in the model or not.

  As for the portion in bootstrap forest or boosted trees, that is more of a %. If a variable has a portion of 0.32, then that particular factor comes into the decision tree analysis 32% of the time. It is not explaining 32% of the variance, that would be something more like what R^2 is measuring.

  As for the book, it might not be freely available anymore, but just do a search for the title and authors, and I'm sure you'll find it. At the very least, you could buy it from SAS or probably other known online shopping platforms.

DS

[#5 · Accepted solution]

Dear Diedrich
I can not find teh free PDF on PLS online in sas.com. Can you send me a link?

Regards,

Lu