Information criteria

This function computes information criteria for existing plsR model using Degrees of Freedom estimation.

Usage

infcrit.dof(modplsR, naive = FALSE)

Arguments

modplsR

A plsR model i.e. an object returned by one of the functions plsR, plsRmodel.default, plsRmodel.formula, PLS_lm or PLS_lm_formula.

naive

A boolean.

Value

matrix

AIC, BIC and gmdl values or NULL.

Details

If naive=FALSE returns AIC, BIC and gmdl values for estimated and naive degrees of freedom. If naive=TRUE returns NULL.

References

M. Hansen, B. Yu. (2001). Model Selection and Minimum Descripion Length Principle, Journal of the American Statistical Association, 96, 746-774.
N. Kraemer, M. Sugiyama. (2011). The Degrees of Freedom of Partial Least Squares Regression. Journal of the American Statistical Association, 106(494), 697-705.
N. Kraemer, M. Sugiyama, M.L. Braun. (2009). Lanczos Approximations for the Speedup of Kernel Partial Least Squares Regression, Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics (AISTATS), 272-279.

See also

plsR.dof for degrees of freedom computation and infcrit.dof for computing information criteria directly from a previously fitted plsR model.

Author

Frédéric Bertrand
frederic.bertrand@lecnam.net
https://fbertran.github.io/homepage/

Examples

data(Cornell)
XCornell<-Cornell[,1:7]
yCornell<-Cornell[,8]
modpls <- plsR(yCornell,XCornell,4)
#> ____************************************************____
#> ____Component____ 1 ____
#> ____Component____ 2 ____
#> ____Component____ 3 ____
#> ____Component____ 4 ____
#> ____Predicting X without NA neither in X nor in Y____
#> ****________________________________________________****
#> 
infcrit.dof(modpls)
#>            DoF.dof sigmahat.dof    AIC.dof    BIC.dof GMDL.dof DoF.naive
#> Nb_Comp_0 1.000000    6.5212706 46.0708838 47.7893514 27.59461         1
#> Nb_Comp_1 2.740749    1.8665281  4.5699686  4.9558156 21.34020         2
#> Nb_Comp_2 5.085967    1.1825195  2.1075461  2.3949331 27.40202         3
#> Nb_Comp_3 5.121086    0.7488308  0.8467795  0.9628191 24.40842         4
#> Nb_Comp_4 5.103312    0.7387162  0.8232505  0.9357846 24.23105         5
#>           sigmahat.naive  AIC.naive  BIC.naive GMDL.naive
#> Nb_Comp_0      6.5212706 46.0708838 47.7893514   27.59461
#> Nb_Comp_1      1.8905683  4.1699567  4.4588195   18.37545
#> Nb_Comp_2      1.1088836  1.5370286  1.6860917   17.71117
#> Nb_Comp_3      0.7431421  0.7363469  0.8256118   19.01033
#> Nb_Comp_4      0.7846050  0.8721072  0.9964867   24.16510