penalized.pls: Penalized Partial Least Squares

In ppls: Penalized Partial Least Squares

Description

computes the regression coefficients for Penalized Partial Least Squares.

Usage

penalized.pls(X, y, P, ncomp, kernel, scale ,blocks,select)

Arguments

X	matrix of input data
y	vector of response data
P	penalty matrix. Default value is P=NULL, i.e. no penalization is used
ncomp	number of components, default value is the rank of the centered matrix X, that is min(ncol(X),nrow(X)-1)
kernel	logical value. If kernel=TRUE, penalized PLS is computed based on the kernel algorithm. Default value is kernel=FALSE
scale	logical value. If scale=TRUE, the X variables are standardized to have unit variance. Default value is FALSE
blocks	vector of length ncol(X) that encodes a block structure of the data. Default value is 1:ncol(X). See below for more details.
select	logical variable. If logical=TRUE, block-wise variable selection is applied. Default value is FALSE. See below for more details.

Details

The regression coefficients can be computed in two different but equivalent ways. The first one is the extension of the classical NIPALS algorithm for PLS (which corresponds to kernel=FALSE), and the second one is based on a kernel representation. The latter method is in general faster if the number of observations is small compared to the number of variables. Note that P=NULL corresponds to Partial Least Squares without penalization. In addition, it is possible to select blocks of variables in each iteration step of penalized PLS. The block structure is encoded in the vector blocks of length ncol(X) that has the form 1,..,1,2,..,2,3,...,3,... . If select=TRUE, the algorithm select the weight vector with maximal penalized covariance under the constraint that only a single block in the weight vector is non-zero. This strategy is used for the combination of penalized PLS and B-splines transformations.

Value

intercept	vector of length ncomp. The ith entry corresponds to the intercept for penalized PLS with i components
coefficients	matrix of dimension ncol(X) x ncomp. The ith column corresponds to the regressions coefficients for penalized PLS with i components

Author(s)

Nicole Kraemer

References

N. Kraemer, A.-L. Boulsteix, and G. Tutz (2008). Penalized Partial Least Squares with Applications to B-Spline Transformations and Functional Data. Chemometrics and Intelligent Laboratory Systems 94, 60 - 69. http://dx.doi.org/10.1016/j.chemolab.2008.06.009

See Also

new.penalized.pls, penalized.pls.cv, ppls.splines.cv, Penalty.matrix

Examples

## example from the paper ##
# load BOD data
data(BOD)
X<-BOD[,1]
y<-BOD[,2]

Xtest=seq(min(X),max(X),length=200) # generate test data for plot
dummy<-X2s(X,Xtest,deg=3,nknot=20) # transformation of the data
Z=dummy$Z # transformed X data
Ztest=dummy$Ztest # transformed Xtest data
size=dummy$sizeZ # size of the transformed data
P<-Penalty.matrix(size,order=2)  # Penalty matrix
lambda<-200 # amount of penalization
number.comp<-3 # number of components

ppls<-penalized.pls(Z,y,P=lambda*P,ncomp=number.comp) # fit
new.ppls<-new.penalized.pls(ppls,Ztest)$ypred # prediction for test data
## plot fitted values for 2 components
plot(X,y,lwd=3,xlim=range(Xtest))
lines(Xtest,new.ppls[,2])

Example output

Loading required package: splines
Loading required package: MASS

ppls documentation built on May 1, 2019, 10:53 p.m.