R help - Oct 2008 - package pls

Hi,
    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?

Thank you,

Tuan Nguyen.

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).

-- 
Bj?rn-Helge Mevik