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")
| RSS | vector of residual sum of squares. |
|---|---|
| DoF | vector of Degrees of Freedom. The length of |
| yhat | vector of squared norm of yhat. The length of |
| sigmahat | Estimated model error. The length of |
| n | number of observations. |
| criterion | one of the options "aic", "bic" and "gmdl". |
degrees of freedom
vector of the model selection criterion
index of the first local minimum of
score
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.
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.
Nicole Kraemer, Mikio Braun
## This is an internal function called by pls.ic