pls.dof: Computation of the Degrees of Freedom

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

Computation of the Degrees of Freedom

Description

This function computes the Degrees of Freedom using the Krylov representation of PLS.

Usage

pls.dof(pls.object, n, y, K, m, DoF.max)

Arguments

pls.object	object returned by linear.pls.fit or by kernel.pls.fit
n	number of observations
y	vector of response observations.
K	kernel matrix X X^t.
m	number of components
DoF.max	upper bound on the Degrees of Freedom.

Details

This computation of the Degrees of Freedom is based on the equivalence of PLS regression and the projection of the response vector y onto the Krylov space spanned by

Ky,K^2 y,...,K^m y.

Details can be found in Kraemer and Sugiyama (2011).

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
TT	matrix of normalized PLS components

Author(s)

Nicole Kraemer, Mikio L. Braun

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 Kernel Partial Least Squares Regression." Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics (AISTATS), p. 272-279

See Also

pls.model, pls.ic

Examples

# this is an internal function

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