information.criteria {plsdof} | R Documentation |
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.
information.criteria(RSS, DoF, yhat,sigmahat, n, DoF.max)
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. |
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))
.
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 |
Nicole Kraemer, Mikio Braun
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.
## This is an internal function called by kernel.pls.ic