plsdof (version 0.2-9)

information.criteria: Information criteria

Description

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

Usage

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

Arguments

RSS

vector of residual sum of squares.

DoF

vector of Degrees of Freedom. The length of DoF is the same as the length of RSS.

yhat

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.

sigmahat

Estimated model error. The length of sigmahat is the same as the length of RSS.

n

number of observations.

criterion

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.

See Also

pls.ic

Examples

# NOT RUN {
## This is an internal function called by pls.ic

# }