plsdof: linear.pls.fit – R documentation

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linear.pls.fit

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

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

Degrees of Freedom and Statistical Inference for Partial Least Squares Regression

v0.3-0

GPL (>= 2)

Authors

Nicole Kraemer, Mikio L. Braun

Initial release

2021-03-13