Product: TIBCO Spotfire®
Computing Partial Least Squares (PLS) in S+ .
Customer needs information on developing a Partial Least Squares (PLS) algorithm in S+.
The Partial Linear Algorithm (Golub-Pereyra algorithm for partially linear least-squares models), is an alternate algorithm of nonlinear regression for partially linear regression models where some of the parameters appear linearly in the predictor. If this is not checked, the Gauss-Newton algorithm is used. Details about this algorithm can be found in the following book:
--> Chambers, J. M., and Hastie, T. J. (eds) (1992). Statistical Models in S, Chapter 10, "Nonlinear Models". Pacific Grove, CA.: Wadsworth & Brooks/Cole.
The Partial Linear Algorithm should be used when there are linear parameters in the model as well as nonlinear parameters. When this is used, the right side of the formula should evaluate to the derivative matrix for the linear parameters, conditional on the nonlinear parameters. This matrix can be given instead as a vector whose length is a multiple of the length of the left side. The dialog can be accessed by selecting 'Regression / Nonlinear / Options' from the Statistics menu option.
StatLib has a function called pls() which may be more helpful. Go to the following URL to access this user-contributed function: http://lib.stat.cmu.edu/S/pls