information.criteria {plsdof}R Documentation

Information criteria

Description

This function computes the optimal model parameters using three different model selection criteria (aic, bic, gmdl) and based on two different Degrees of Freedom estimates for Partial Least Squares.

Usage

information.criteria(RSS, DoF, yhat,sigmahat, n, DoF.max)

Arguments

RSS matrix of residual sum of squares. The columns correspond to the number of latent components for PLS, and the rows correspond to the different kernel parameters. If the vanilla kernel is used, RSS consists of one row. For a Gaussian kernel, each row corresponds to a sigma value.
DoF Degrees of Freedom. The size of DoF is the same as the size of RSS.
yhat matrix of squared norm of yhat. The size of yhat is the same as the size of RSS.
sigmahat Estimated model error. The size of sigmahat is the same as the size of RSS.
n number of observations.
DoF.max Upper bound for the degrees of freedom.

Details

In an initial step, we first normalize the DoF to lie in the range 0 and DoF.max. For linear Partial Least Squares, a sensible upper bound DoF.max is given by DoF.max=min(nrow(X)-1,ncol(X)).

Value

DoF degrees of freedom
par.aic indices for the aic-optimal model
par.bic indices for the bic-optimal model
par.gmdl indices for the gmdl-optimal model
par.aic.naive indices for the aic-optimal model if the naive Degrees of Freedom are used
par.bic.naive indices for the bic-optimal model if the naive Degrees of Freedom are used
par.gmdl.naive indices for the gmdl-optimal model if the naive Degrees of Freedom are used

Author(s)

Nicole Kraemer, Mikio Braun

References

Akaikie, H. (1973) "Information Theory and an Extension of the Maximum Likelihood Principle". Second International Symposium on Information Theory, 267 - 281.

Hansen, M., Yu, B. (2001). "Model Selection and Minimum Descripion Length Principle". Journal of the American Statistical Association, 96, 746 - 774

Kraemer, N., Braun, M.L. (2007) "Kernelizing PLS, Degrees of Freedom, and Efficient Model Selection", Proceedings of the 24th International Conference on Machine Learning, Omni Press, 441 - 448

Schwartz, G. (1979) "Estimating the Dimension of a Model" Annals of Statistics 26(5), 1651 - 1686.

See Also

kernel.pls.ic

Examples

## This is an internal function called by kernel.pls.ic


[Package plsdof version 0.1-1 Index]