ttest.ppls: T-Test for regression coefficients
In ppls: Penalized Partial Least Squares

Description Usage Arguments Details Value Author(s) References See Also Examples

This function computes test statistics and p-values for the regression coefficients of Penalized Partial Least Squares.

1	ttest.ppls(ppls.object,ncomp,index.lambda)

`ppls.object`	an object returned by `penalized.pls.cv`
`ncomp`	integer. The number of components that are used. The default value is the cross-validation optimal number of components.
`index.lambda`	integer. The index of the penalization intensity, given by the vector `lambda` that was provided to `penalized.pls.cv`. The default value is the cross-validation optimal index.

We note that neither the distribution of the regression coefficients nor the correct degrees of freedom are known. Hence, the assumptions of the T-Test might not be fulfilled. We remark that this testing procedure is not discussed in Kraemer, Boulesteix and Tutz (2008). In general, the p-values need to be corrected in order to account for the multiple testing problem.

`tvalues`	vector of test statistics
`pvalues`	vector of p-values

Nicole Kraemer

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

penalized.pls.cv,jack.ppls

data(cookie) # load data
X<-as.matrix(cookie[,1:700]) # extract NIR spectra
y<-as.vector(cookie[,701]) # extract one constituent

pls.object<-penalized.pls.cv(X,y,ncomp=10,kernel=TRUE) # PLS without penalization
my.ttest<-ttest.ppls(pls.object) # test for the cv-optimal model

plot(sort(my.ttest$pvalues),type="l",ylab="sorted pvalues") # plot sorted p-values