plsdof (version 0.2-1)

pls.model: Partial Least Squares

Description

This function computes the Partial Least Squares fit.

Usage

pls.model(X,y,m,Xtest=NULL,ytest=NULL,compute.DoF,compute.jacobian,use.kernel)

Arguments

X

matrix of predictor observations.

y

vector of response observations. The length of y is the same as the number of rows of X.

m

maximal number of Partial Least Squares components. Default is m=min(ncol(X),nrow(X)-1).

Xtest

optional matrix of test observations. Default is Xtest=NULL.

ytest

optional vector of test observations. Default is ytest=NULL.

compute.DoF

Logical variable. If compute.DoF=TRUE, the Degrees of Freedom of Partial Least Squares are computed. Default is compute.DoF=FALSE.

compute.jacobian

Should the first derivative of the regression coefficients be computed as well? Default is FALSE

use.kernel

Should the kernel representation be used to compute the solution. Default is FALSE.

Value

• coefficients
  matrix of regression coefficients
• intercept
  vector of intercepts
• DoF
  vector of Degrees of Freedom
• RSS
  vector of residual sum of error
• sigmahat
  vector of estimated model error
• Yhat
  matrix of fitted values
• yhat
  vector of squared length of fitted values
• covariance
  if compute.jacobian is TRUE, the function returns the array of covariance matrices for the PLS regression coefficients.
• prediction{if Xtest is provided, the predicted y-values for Xtest.} mse{if Xtest and ytest are provided, the mean squared error on the test data.}

Details

to do

References

Kraemer, N., Sugiyama M. (2010). "The Degrees of Freedom of Partial Least Squares Regression". preprint, http://arxiv.org/abs/1002.4112 Kraemer, N., Sugiyama, M., Braun, M.L. (2009) "Lanczos Approximations for the Speedup of Partial Least Squares Regression", Proceedings of the 12th International Conference on Artificial Intelligence and Stastistics, 272 - 279

See Also

pls.ic, pls.cv

Examples

n<-50 # number of observations
p<-15 # number of variables
X<-matrix(rnorm(n*p),ncol=p)
y<-rnorm(n)

ntest<-200 #
Xtest<-matrix(rnorm(ntest*p),ncol=p) # test data
ytest<-rnorm(ntest) # test data

# compute PLS + degrees of freedom + prediction on Xtest
first.object<-pls.model(X,y,compute.DoF=TRUE,Xtest=Xtest,ytest=NULL)

# compute PLS + test error
second.object=pls.model(X,y,m=10,Xtest=Xtest,ytest=ytest)