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