plsRglm (version 1.5.1)

aic.dof: Akaike and Bayesian Information Criteria and Generalized minimum description length

Description

This function computes the Akaike and Bayesian Information Criteria and the Generalized minimum description length.

Usage

aic.dof(RSS, n, DoF, sigmahat)
bic.dof(RSS, n, DoF, sigmahat)
gmdl.dof(sigmahat, n, DoF, yhat)

Value

vector

numerical values of the requested AIC, BIC or GMDL.

Arguments

RSS

vector of residual sum of squares.

n

number of observations.

DoF

vector of Degrees of Freedom. The length of DoF is the same as the length of RSS.

sigmahat

Estimated model error. The length of sigmahat is the same as the length of RSS.

yhat

vector of squared norm of Yhat. The length of yhat is the same as the length of sigmahat.

Author

Frédéric Bertrand

https://fbertran.github.io/homepage/

Details

The gmdl criterion is defined as $$gmdl=\frac{n}{2}log(S)+\frac{DoF}{2}log(F)+\frac{1}{2}log(n)$$ with $$S=\hat\sigma^2$$

References

M. Hansen, B. Yu. (2001). Model Selection and Minimum Descripion Length Principle, Journal of the American Statistical Association, 96, 746-774.
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.L. Braun, Kernelizing PLS, Degrees of Freedom, and Efficient Model Selection, Proceedings of the 24th International Conference on Machine Learning, Omni Press, (2007) 441-448.

See Also

plsR.dof for degrees of freedom computation 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)
dof.object <- plsR.dof(modpls)
aic.dof(modpls$RSS,modpls$nr,dof.object$DoF,dof.object$sigmahat)
bic.dof(modpls$RSS,modpls$nr,dof.object$DoF,dof.object$sigmahat)
gmdl.dof(dof.object$sigmahat,modpls$nr,dof.object$DoF,dof.object$yhat)
naive.object <- plsR.dof(modpls,naive=TRUE)
aic.dof(modpls$RSS,modpls$nr,naive.object$DoF,naive.object$sigmahat)
bic.dof(modpls$RSS,modpls$nr,naive.object$DoF,naive.object$sigmahat)
gmdl.dof(naive.object$sigmahat,modpls$nr,naive.object$DoF,naive.object$yhat)