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The PLS Procedure |

The PLS procedure fits models using any one of a number of linear
predictive methods, including *partial least squares* (PLS).
Ordinary least squares regression, as implemented in SAS/STAT
procedures such as PROC GLM and PROC REG, has the single goal of
minimizing
sample response prediction error, seeking linear functions of the
predictors that explain as much variation in each response as
possible. The techniques implemented in the PLS procedure have the
additional goal of accounting for variation in the predictors,
under the assumption that
directions in the predictor space that are well sampled should provide
better prediction for *new* observations when the predictors are
highly correlated. All of the techniques implemented in the PLS
procedure work by extracting successive linear combinations of the
predictors, called *factors* (also called *components* or *
latent vectors*), which optimally address one or both of these two
goals -explaining response variation and explaining
predictor variation. In particular, the method of partial least
squares balances the two objectives, seeking for factors that explain
both response and predictor variation.

Note that the name "partial least squares" also applies to a more
general statistical method that is *not* implemented in this
procedure.
The partial least squares method was originally developed in the
1960s by the econometrician Herman Wold (1966) for
modeling "paths" of causal relation between any number of
"blocks" of variables. However, the PLS procedure fits only
*predictive* partial least squares models, with one "block" of
predictors and one "block" of responses. If you are interested in
fitting more general path models, you should consider using the CALIS
procedure.

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