Partial Least Squares

This function computes the Partial Least Squares fit.

Usage

pls.model(
  X,
  y,
  m = ncol(X),
  Xtest = NULL,
  ytest = NULL,
  compute.DoF = FALSE,
  compute.jacobian = FALSE,
  use.kernel = FALSE,
  method.cor = "pearson"
)

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? This remains independent from compute.DoF; callers can request covariance estimates while still returning the naive 1:(m + 1) Degrees of Freedom sequence. Default is FALSE
use.kernel: Should the kernel representation be used to compute the solution. Default is FALSE.
method.cor: How should the correlation to the response be computed? Default is ”pearson”.

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.

predictionif Xtest is provided, the predicted y-values for Xtest. mseif Xtest and ytest are provided, the mean squared error on the test data. corif Xtest and ytest are provided, the correlation to the response on the test data.

Details

This function computes the Partial Least Squares fit and its Degrees of Freedom. Further, it returns the regression coefficients and various quantities that are needed for model selection in combination with information.criteria.

References

Kraemer, N., Sugiyama M. (2011). "The Degrees of Freedom of Partial Least Squares Regression". Journal of the American Statistical Association 106 (494) https://www.tandfonline.com/doi/abs/10.1198/jasa.2011.tm10107

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

Author

Nicole Kraemer, Mikio L. Braun

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)