linear.pls.fit: Linear Partial Least Squares Fit

In plsdof: Degrees of Freedom and Statistical Inference for Partial Least Squares Regression

Linear Partial Least Squares Fit

Description

This function computes the Partial Least Squares solution and the first derivative of the regression coefficients. This implementation scales mostly in the number of variables

Usage

linear.pls.fit(
  X,
  y,
  m = ncol(X),
  compute.jacobian = FALSE,
  DoF.max = min(ncol(X) + 1, nrow(X) - 1)
)

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=ncol(X).
compute.jacobian	Should the first derivative of the regression coefficients be computed as well? Default is FALSE
DoF.max	upper bound on the Degrees of Freedom. Default is min(ncol(X)+1,nrow(X)-1).

Details

We first standardize X to zero mean and unit variance.

Value

coefficients	matrix of regression coefficients
intercept	vector of regression intercepts
DoF	Degrees of Freedom
sigmahat	vector of estimated model error
Yhat	matrix of fitted values
yhat	vector of squared length of fitted values
RSS	vector of residual sum of error

covarianceif compute.jacobian is TRUE, the function returns the array of covariance matrices for the PLS regression coefficients.

TT	matrix of normalized PLS components

Author(s)

Nicole Kraemer

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

See Also

kernel.pls.fit, pls.cv,pls.model, pls.ic

Examples

n<-50 # number of observations
p<-5 # number of variables
X<-matrix(rnorm(n*p),ncol=p)
y<-rnorm(n)

pls.object<-linear.pls.fit(X,y,m=5,compute.jacobian=TRUE)

plsdof documentation built on Dec. 1, 2022, 1:13 a.m.