This function computes the optimal model parameters using three different model selection criteria (aic, bic, gmdl).

information.criteria(RSS, DoF, yhat = NULL, sigmahat, n, criterion = "bic")

## Arguments

RSS vector of residual sum of squares. vector of Degrees of Freedom. The length of DoF is the same as the length of RSS. vector of squared norm of yhat. The length of yhat is the same as the length of RSS. It is only needed for gmdl. Default value is NULL. Estimated model error. The length of sigmahat is the same as the length of RSS. number of observations. one of the options "aic", "bic" and "gmdl".

## Value

DoF

degrees of freedom

score

vector of the model selection criterion

par

index of the first local minimum of score

## Details

The Akaike information criterion (aic) is defined as $${aic}= \frac{{RSS}}{n} + 2\frac{{DoF}}{n} \sigma^ 2\,.$$ The Bayesian information criterion (bic) is defined as $${bic}= \frac{{RSS}}{n} + log(n)\frac{{DoF}}{n} \sigma^ 2\,.$$ The generalized minimum description length (gmdl) is defined as $$gmdl=\frac{n}{2}log(S)+\frac{DoF}{2}log(F)+\frac{1}{2}log(n)$$ with $$S=\hat \sigma ^2$$ Note that it is also possible to use the function information.criteria for other regression methods than Partial Least Squares.

## 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., Sugiyama M. (2011). "The Degrees of Freedom of Partial Least Squares Regression". Journal of the American Statistical Association 106 (494) https://www.tandfonline.com/doi/abs/10.1198/jasa.2011.tm10107

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.

pls.ic

## Author

Nicole Kraemer, Mikio Braun

## Examples


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