[R] Partial Least Squares

[Thomas Lumley]

On Fri, 20 Aug 2004, Spencer Graves wrote:
>       Also, have you considered "sem" (structural equation modeling)?
>  From what I've heard, partial least squares started out as a solution
> without a clear problem statement, i.e., an algorithm claiming to solve
> a problem but without a clear statement of a probability model for which
> their algorithm produced the (approximate) maximum likelihood or
> Bayesian posterior mode.  Structural equation modeling, by contrast,
> provides the model and problem statement that partial least squares
> seems to try to solve.  I got this impression from reading the PLS
> article in the Encyclopedia of Statistical Sciences.
>

I don't think that's quite right.  If you look at how PLS is used and who
uses it, it is in situations where maximum likelihood estimation often is
not possible or not reliable because of the dimension of the predictor
variables.  It is a regularised version of SEM, which can be useful even
if the penalty term is not clearly specified.

	-thomas