plsdof (version 0.2-1)

bic: Bayesian information criterion

Description

This function computes the Bayesian Information Criterion and its argmin.

Usage

bic(RSS, n, DoF, sigmahat)

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.

Value

• score
  the vector of the bic values
• par
  index of the first local minimum of score

Details

The bic criterion is defined as $${bic}= \frac{{RSS}}{n} + log(n)\frac{{DoF}}{n} \sigma^ 2\,.$$ Note that it is also possible to use this function for other regression methods than Partial Least Squares.

References

Schwartz, G. (1979) "Estimating the Dimension of a Model" Annals of Statistics 26(5), 1651 - 1686. Kraemer, N., Sugiyama M. (2010). "The Degrees of Freedom of Partial Least Squares Regression". preprint http://arxiv.org/abs/1002.4112 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, pls.ic, aic, gmdl

Examples

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