plsR.dof {plsRglm}

Computation of the Degrees of Freedom

Description

This function computes the Degrees of Freedom using the Krylov representation of PLS and other quantities that are used to get information criteria values. For the time present, it only works with complete datasets.

Usage

## S3 method for class 'dof'
plsR(modplsR, naive = FALSE)

Arguments

modplsR

A plsR model i.e. an object returned by one of the functions plsR, plsRmodel.default, plsRmodel.formula, PLS_lm or PLS_lm_formula.

naive

A boolean.

Details

If naive=FALSE returns values for estimated degrees of freedom and error dispersion. If naive=TRUE returns returns values for naive degrees of freedom and error dispersion. The original code from Nicole Kraemer and Mikio L. Braun was unable to handle models with only one component.

Value

DoF

Degrees of Freedom

sigmahat

Estimates of dispersion

Yhat

Predicted values

yhat

Square Euclidean norms of the predicted values

RSS

Residual Sums of Squares

Author(s)

Nicole Kraemer, Mikio L. Braun with improvements from Frédéric Bertrand
[e-mail]
https://fbertran.github.io/homepage/

References

N. Kraemer, M. Sugiyama. (2011). The Degrees of Freedom of Partial Least Squares Regression. Journal of the American Statistical Association, 106(494), 697-705.
N. Kraemer, M. Sugiyama, M.L. Braun. (2009). Lanczos Approximations for the Speedup of Kernel Partial Least Squares Regression, Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics (AISTATS), 272-279.

See Also

aic.dof and infcrit.dof for computing information criteria directly from a previously fitted plsR model.

Examples

data(Cornell)
XCornell<-Cornell[,1:7]
yCornell<-Cornell[,8]
modpls <- plsR(yCornell,XCornell,4)
plsR.dof(modpls) 
plsR.dof(modpls,naive=TRUE)