aic {plsdof}R Documentation

Akaike information criterion

Description

This function computes the optimal parameter set based on the Akaike information criterion.

Usage

aic(RSS, n, DoF, sigmahat)

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 kernel width.
n number of observations.
DoF Degrees of Freedom. The size of DoF is the same as the size of RSS.
sigmahat Estimated model error. The size of sigmahat is the same as the size of RSS.

Details

The aic criterion is defined as

{aic}= \frac{{RSS}}{n} + 2\frac{{DoF}}{n} \sigma^ 2\,.

For the aic criterion, we need an estimtate for the model error \sigma. We use min(sigmahat) as an estimate. Note that it is also possible to use this function for other regression methods than Partial Least Squares.

Value

The function returns a vector of length 2 that contains the row and column index of the aic-optimal model.

Author(s)

Nicole Kraemer, Mikio L. Braun

References

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

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

See Also

information.criteria, kernel.pls.ic, bic, gmdl

Examples

## this is an internal function called by information.criteria() and kernel.pls.ic()

[Package plsdof version 0.1-1 Index]