Computation of the Degrees of Freedom

This function computes the Degrees of Freedom using the Krylov representation of PLS and other quantities that are used to get information criteria values. For the time present, it only works with complete datasets.

# S3 method for dof
plsR(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

DoF

Degrees of Freedom

sigmahat

Estimates of dispersion

Yhat

Predicted values

yhat

Square Euclidean norms of the predicted values

RSS

Residual Sums of Squares

Details

If naive=FALSE returns values for estimated degrees of freedom and error dispersion. If naive=TRUE returns returns values for naive degrees of freedom and error dispersion. The original code from Nicole Kraemer and Mikio L. Braun was unable to handle models with only one component.

References

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.

Author

Nicole Kraemer, Mikio L. Braun with improvements from Frédéric Bertrand
frederic.bertrand@utt.fr
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____
#> ****________________________________________________****
#> 
plsR.dof(modpls) 
#> $DoF
#> [1] 1.000000 2.740749 5.085967 5.121086 5.103312
#> 
#> $sigmahat
#> [1] 6.5212706 1.8665281 1.1825195 0.7488308 0.7387162
#> 
#> $Yhat
#>        Nt_0     Nt_1     Nt_2     Nt_3     Nt_4
#> 1  88.58333 95.03164 96.49529 97.55864 97.46485
#> 2  88.58333 96.36241 97.51798 97.59151 97.72308
#> 3  88.58333 95.91107 97.56157 97.44534 97.54025
#> 4  88.58333 94.98711 92.14504 91.80793 91.88728
#> 5  88.58333 88.36924 87.98130 85.99452 85.97024
#> 6  88.58333 93.65634 91.12235 91.77507 91.62905
#> 7  88.58333 81.65428 81.33705 81.49670 81.50559
#> 8  88.58333 82.31664 82.49582 82.57542 82.61982
#> 9  88.58333 82.02100 82.28564 82.52399 82.53440
#> 10 88.58333 82.56111 83.12821 83.26027 83.30569
#> 11 88.58333 82.05655 81.23614 81.92924 81.97612
#> 12 88.58333 88.07261 89.69361 89.04136 88.84362
#> 
#> $yhat
#> [1] 94164.08 94596.14 94620.81 94627.46 94627.57
#> 
#> $RSS
#> [1] 467.796667  35.742486  11.066606   4.418081   4.309235
#> 
plsR.dof(modpls,naive=TRUE) 
#> $DoF
#> [1] 1 2 3 4 5
#> 
#> $sigmahat
#> [1] 6.5212706 1.8905683 1.1088836 0.7431421 0.7846050
#> 
#> $Yhat
#>        Nt_0     Nt_1     Nt_2     Nt_3     Nt_4
#> 1  88.58333 95.03164 96.49529 97.55864 97.46485
#> 2  88.58333 96.36241 97.51798 97.59151 97.72308
#> 3  88.58333 95.91107 97.56157 97.44534 97.54025
#> 4  88.58333 94.98711 92.14504 91.80793 91.88728
#> 5  88.58333 88.36924 87.98130 85.99452 85.97024
#> 6  88.58333 93.65634 91.12235 91.77507 91.62905
#> 7  88.58333 81.65428 81.33705 81.49670 81.50559
#> 8  88.58333 82.31664 82.49582 82.57542 82.61982
#> 9  88.58333 82.02100 82.28564 82.52399 82.53440
#> 10 88.58333 82.56111 83.12821 83.26027 83.30569
#> 11 88.58333 82.05655 81.23614 81.92924 81.97612
#> 12 88.58333 88.07261 89.69361 89.04136 88.84362
#> 
#> $yhat
#> [1] 94164.08 94596.14 94620.81 94627.46 94627.57
#> 
#> $RSS
#> [1] 467.796667  35.742486  11.066606   4.418081   4.309235
#>