Modeling and Multivariate Methods - SAS

Chapter 21
Fitting Partial Least Squares Models
Using the Partial Least Squares Platform
The Partial Least Squares (PLS) platform fits linear models based on factors, namely, linear combinations of
the explanatory variables (Xs). These factors are obtained in a way that attempts to maximize the covariance
between the Xs and the response or responses (Ys). PLS exploits the correlations between the Xs and the Ys
to reveal underlying latent structures.
In contrast to ordinary least squares, PLS can be used when the predictors outnumber the observations. PLS
is used widely in modeling high-dimensional data in areas such as spectroscopy, chemometrics, genomics,
psychology, education, economics, political science, and environmental science.
Partial least squares performs well in situations such as the following, where the use of ordinary least squares
does not produce satisfactory results: More X variables than observations; highly correlated X variables; a
large number of X variables; several Y variables and many X variables.
Figure 21.1 A Portion of a Partial Least Squares Report