[R] package pls

Bjørn-Helge Mevik b.h.mevik at usit.uio.no
Fri Oct 31 09:03:08 CET 2008

tsn4867 <tsn4867 at rice.edu> writes:

>    For the package "pls", I need to understand the algorithm for "simpls.fit"
> for Partial Least Squares. I'm not sure if simpls.fit tries to find the
> weight vectors (loadings) to maximize which of the two:  Cov(Xw, y) or
> maximize Cov^2(Xw,y)? Are these objective functions equivalent? (in some
> texts, they use the first and in other texts, they use the second
> obj. function.). I think the algorithm for simpls.fit is using Cov(Xw,y).
>     Also, can you give me some references where they state the equivalency of
> the two obj. functions?

The implementation in simpls.fit follows the algorithm in

     de Jong, S. (1993) SIMPLS: an alternative approach to partial
     least squares regression.  _Chemometrics and Intelligent
     Laboratory Systems_, *18*, 251-263.

(up to simplifications and performance changes).  I don't recall if the
criterion was cov or cov^2, but I believe they should be identical (up
to sign).

Bjørn-Helge Mevik

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