Overview

This vignette is a short tutorial on the use of the core functions of the bootPLS package.

These functions can also be used to reproduce the simulations and the figures of the book chapter Magnanensi et al. (2016) and of the two articles https://doi.org/10.1007/978-3-319-40643-5_18, Magnanensi et al. (2017) https://doi.org/10.1007/s11222-016-9651-4 and Magnanensi et al. (2021), accepted.

Pine real dataset: pls and spls regressions

Load and display the pinewood worm dataset.

library(bootPLS)
library(plsRglm)
data(pine, package = "plsRglm")
Xpine<-pine[,1:10]
ypine<-log(pine[,11])
pairs(pine)

Michel Tenenhaus’ reported in his book, La régression PLS (1998) Technip, Paris, that most of the expert biologists claimed that this dataset features two latent variables, which is tantamount to the PLS model having two components.

PLS LOO and CV

Leave one out CV (K=nrow(pine)) one time (NK=1).

bbb <- plsRglm::cv.plsR(log(x11)~.,data=pine,nt=6,K=nrow(pine),NK=1,verbose=FALSE)
plsRglm::cvtable(summary(bbb))
#> ____************************************************____
#> ____Component____ 1 ____
#> ____Component____ 2 ____
#> ____Component____ 3 ____
#> ____Component____ 4 ____
#> ____Component____ 5 ____
#> ____Component____ 6 ____
#> ____Predicting X without NA neither in X nor in Y____
#> ****________________________________________________****
#>
#>
#> NK: 1
#>
#> CV Q2 criterion:
#> 0 1
#> 0 1
#>
#> CV Press criterion:
#> 1 2 3 4 5
#> 0 0 0 0 1

Set up 6-fold CV (K=6), 100 times (NK=2), and use random=TRUE to randomly create folds for repeated CV.

bbb2 <- plsRglm::cv.plsR(log(x11)~.,data=pine,nt=6,K=6,NK=100,verbose=FALSE)

Display the results of the cross-validation.

plsRglm::cvtable(summary(bbb2))
#> ____************************************************____
#> ____Component____ 1 ____
#> ____Component____ 2 ____
#> ____Component____ 3 ____
#> ____Component____ 4 ____
#> ____Component____ 5 ____
#> ____Component____ 6 ____
#> ____Predicting X without NA neither in X nor in Y____
#> ****________________________________________________****
#>
#>
#> NK: 1,  2,  3,  4,  5,  6,  7,  8,  9,  10
#> NK: 11,  12,  13,  14,  15,  16,  17,  18,  19,  20
#> NK: 21,  22,  23,  24,  25,  26,  27,  28,  29,  30
#> NK: 31,  32,  33,  34,  35,  36,  37,  38,  39,  40
#> NK: 41,  42,  43,  44,  45,  46,  47,  48,  49,  50
#> NK: 51,  52,  53,  54,  55,  56,  57,  58,  59,  60
#> NK: 61,  62,  63,  64,  65,  66,  67,  68,  69,  70
#> NK: 71,  72,  73,  74,  75,  76,  77,  78,  79,  80
#> NK: 81,  82,  83,  84,  85,  86,  87,  88,  89,  90
#> NK: 91,  92,  93,  94,  95,  96,  97,  98,  99,  100
#>
#> CV Q2 criterion:
#>   0   1
#>   0 100
#>
#> CV Press criterion:
#>  1  2  3  4  5  6
#> 13  0  1 28 13 45

The $$Q^2$$ criterion is recommended in that PLSR setting without missing data. A model with 1 component is selected by the cross-validation as displayed by the following figure. Hence the $$Q^2$$ criterion (1 component) does not agree with the experts (2 components).

plot(plsRglm::cvtable(summary(bbb2)),type="CVQ2")
#> ____************************************************____
#> ____Component____ 1 ____
#> ____Component____ 2 ____
#> ____Component____ 3 ____
#> ____Component____ 4 ____
#> ____Component____ 5 ____
#> ____Component____ 6 ____
#> ____Predicting X without NA neither in X nor in Y____
#> ****________________________________________________****
#>
#>
#> NK: 1,  2,  3,  4,  5,  6,  7,  8,  9,  10
#> NK: 11,  12,  13,  14,  15,  16,  17,  18,  19,  20
#> NK: 21,  22,  23,  24,  25,  26,  27,  28,  29,  30
#> NK: 31,  32,  33,  34,  35,  36,  37,  38,  39,  40
#> NK: 41,  42,  43,  44,  45,  46,  47,  48,  49,  50
#> NK: 51,  52,  53,  54,  55,  56,  57,  58,  59,  60
#> NK: 61,  62,  63,  64,  65,  66,  67,  68,  69,  70
#> NK: 71,  72,  73,  74,  75,  76,  77,  78,  79,  80
#> NK: 81,  82,  83,  84,  85,  86,  87,  88,  89,  90
#> NK: 91,  92,  93,  94,  95,  96,  97,  98,  99,  100
#>
#> CV Q2 criterion:
#>   0   1
#>   0 100
#>
#> CV Press criterion:
#>  1  2  3  4  5  6
#> 13  0  1 28 13 45

As for the CV Press criterion it is unable to point out a unique number of components.

plot(plsRglm::cvtable(summary(bbb2)),type="CVPress")
#> ____************************************************____
#> ____Component____ 1 ____
#> ____Component____ 2 ____
#> ____Component____ 3 ____
#> ____Component____ 4 ____
#> ____Component____ 5 ____
#> ____Component____ 6 ____
#> ____Predicting X without NA neither in X nor in Y____
#> ****________________________________________________****
#>
#>
#> NK: 1,  2,  3,  4,  5,  6,  7,  8,  9,  10
#> NK: 11,  12,  13,  14,  15,  16,  17,  18,  19,  20
#> NK: 21,  22,  23,  24,  25,  26,  27,  28,  29,  30
#> NK: 31,  32,  33,  34,  35,  36,  37,  38,  39,  40
#> NK: 41,  42,  43,  44,  45,  46,  47,  48,  49,  50
#> NK: 51,  52,  53,  54,  55,  56,  57,  58,  59,  60
#> NK: 61,  62,  63,  64,  65,  66,  67,  68,  69,  70
#> NK: 71,  72,  73,  74,  75,  76,  77,  78,  79,  80
#> NK: 81,  82,  83,  84,  85,  86,  87,  88,  89,  90
#> NK: 91,  92,  93,  94,  95,  96,  97,  98,  99,  100
#>
#> CV Q2 criterion:
#>   0   1
#>   0 100
#>
#> CV Press criterion:
#>  1  2  3  4  5  6
#> 13  0  1 28 13 45

PLS (Y,T) Bootstrap

The package features our bootstrap based algorithm to select the number of components in plsR regression. It is implemented with the nbcomp.bootplsR function.

set.seed(4619)
nbcomp.bootplsR(Y=ypine,X=Xpine,R =500)
#> [1] 1
#> ____************************************************____
#> ____Component____ 1 ____
#> ____Predicting X without NA neither in X nor in Y____
#> ****________________________________________________****
#>
#> [1] 2
#> ____************************************************____
#> ____Component____ 1 ____
#> ____Component____ 2 ____
#> ____Predicting X without NA neither in X nor in Y____
#> ****________________________________________________****
#>
#> [1] 3
#> ____************************************************____
#> ____Component____ 1 ____
#> ____Component____ 2 ____
#> ____Component____ 3 ____
#> ____Predicting X without NA neither in X nor in Y____
#> ****________________________________________________****
#>
#> [1] "Optimal number of components: K = 2"
#> [1] 2

The verbose=FALSE option suppresses messages output during the algorithm, which is useful to replicate the bootstrap technique. To set up parallel computing, you can use the parallel and the ncpus options.

set.seed(4619)
res_boot_rep <- replicate(20,nbcomp.bootplsR(Y=ypine,X=Xpine,R =500,verbose =FALSE,parallel = "multicore",ncpus = 2))

It is easy to display the results with the barplot function.

barplot(table(res_boot_rep))

A model with two components should be selected using our bootstrap based algorithm to select the number of components. Hence the number of component selected with our algorithm agrees with what was stated by the experts.

sPLS (Y,T) Bootstrap

The package also features our bootstrap based algorithm to select, for a given $$\eta$$ value, the number of components in spls regression. It is implemented with the nbcomp.bootspls function.

nbcomp.bootspls(x=Xpine,y=ypine,eta=.5)
#> eta = 0.5
#> [1] 1
#> [1] 2
#> [1] 3
#> [1] 4
#>
#> Optimal parameters: eta = 0.5, K = 3

#> $mspemat #> #> eta= 0.5 , K= 3 0.9595453 #> #>$eta.opt
#> [1] 0.5
#>
#> $K.opt #> [1] 3 A doParallel and foreach based parallel computing version of the algorithm is implemented as the nbcomp.bootspls.para function. nbcomp.bootspls.para(x=Xpine,y=ypine,eta=.5) #> [1] "eta = 0.5" #> [1] 2 #> [1] 3 #> #> Optimal parameters: eta = 0.5, K = 2 #>$mspemat
#>
#> eta= 0.5 ; K= 2 1.131643
#>
#> $eta.opt #> [1] 0.5 #> #>$K.opt
#> [1] 2
nbcomp.bootspls.para(x=Xpine,y=ypine,eta=c(.2,.5))
#> [1] "eta = 0.2"
#> [1] 2
#> [1] 3
#> [1] "eta = 0.5"
#> [1] 2
#> [1] 3
#>
#> Optimal parameters: eta = 0.5, K = 2

#> $mspemat #> #> eta= 0.2 ; K= 2 1.076495 #> eta= 0.5 ; K= 2 1.067325 #> #>$eta.opt
#> [1] 0.5
#>
#> $K.opt #> result.2 #> 2 Bootstrap (Y,X) for the coefficients with number of components updated for each resampling Pinewood worm data reloaded. library(bootPLS) library(plsRglm) data(pine, package = "plsRglm") Xpine<-pine[,1:10] ypine<-log(pine[,11]) datasetpine <- cbind(ypine,Xpine) coefs.plsR.adapt.ncomp(datasetpine,sample(1:nrow(datasetpine))) #> [1] 2.000000000 8.064227044 -0.003019447 -0.054389603 -0.005212285 #> [6] -0.109946405 0.038799785 -0.078324545 -1.334080678 -0.045021804 #> [11] -0.390730689 0.054696227 Replicate the results to get the bootstrap distributions of the selected number of components and the coefficients. replicate(20,coefs.plsR.adapt.ncomp(datasetpine,sample(1:nrow(datasetpine)))) #> [,1] [,2] [,3] [,4] [,5] #> [1,] 2.000000000 2.000000000 2.000000000 2.000000000 2.000000000 #> [2,] 8.064227044 8.064227044 8.064227044 8.064227044 8.064227044 #> [3,] -0.003019447 -0.003019447 -0.003019447 -0.003019447 -0.003019447 #> [4,] -0.054389603 -0.054389603 -0.054389603 -0.054389603 -0.054389603 #> [5,] -0.005212285 -0.005212285 -0.005212285 -0.005212285 -0.005212285 #> [6,] -0.109946405 -0.109946405 -0.109946405 -0.109946405 -0.109946405 #> [7,] 0.038799785 0.038799785 0.038799785 0.038799785 0.038799785 #> [8,] -0.078324545 -0.078324545 -0.078324545 -0.078324545 -0.078324545 #> [9,] -1.334080678 -1.334080678 -1.334080678 -1.334080678 -1.334080678 #> [10,] -0.045021804 -0.045021804 -0.045021804 -0.045021804 -0.045021804 #> [11,] -0.390730689 -0.390730689 -0.390730689 -0.390730689 -0.390730689 #> [12,] 0.054696227 0.054696227 0.054696227 0.054696227 0.054696227 #> [,6] [,7] [,8] [,9] [,10] #> [1,] 2.000000000 2.000000000 2.000000000 2.000000000 2.000000000 #> [2,] 8.064227044 8.064227044 8.064227044 8.064227044 8.064227044 #> [3,] -0.003019447 -0.003019447 -0.003019447 -0.003019447 -0.003019447 #> [4,] -0.054389603 -0.054389603 -0.054389603 -0.054389603 -0.054389603 #> [5,] -0.005212285 -0.005212285 -0.005212285 -0.005212285 -0.005212285 #> [6,] -0.109946405 -0.109946405 -0.109946405 -0.109946405 -0.109946405 #> [7,] 0.038799785 0.038799785 0.038799785 0.038799785 0.038799785 #> [8,] -0.078324545 -0.078324545 -0.078324545 -0.078324545 -0.078324545 #> [9,] -1.334080678 -1.334080678 -1.334080678 -1.334080678 -1.334080678 #> [10,] -0.045021804 -0.045021804 -0.045021804 -0.045021804 -0.045021804 #> [11,] -0.390730689 -0.390730689 -0.390730689 -0.390730689 -0.390730689 #> [12,] 0.054696227 0.054696227 0.054696227 0.054696227 0.054696227 #> [,11] [,12] [,13] [,14] [,15] #> [1,] 2.000000000 2.000000000 2.000000000 2.000000000 2.000000000 #> [2,] 8.064227044 8.064227044 8.064227044 8.064227044 8.064227044 #> [3,] -0.003019447 -0.003019447 -0.003019447 -0.003019447 -0.003019447 #> [4,] -0.054389603 -0.054389603 -0.054389603 -0.054389603 -0.054389603 #> [5,] -0.005212285 -0.005212285 -0.005212285 -0.005212285 -0.005212285 #> [6,] -0.109946405 -0.109946405 -0.109946405 -0.109946405 -0.109946405 #> [7,] 0.038799785 0.038799785 0.038799785 0.038799785 0.038799785 #> [8,] -0.078324545 -0.078324545 -0.078324545 -0.078324545 -0.078324545 #> [9,] -1.334080678 -1.334080678 -1.334080678 -1.334080678 -1.334080678 #> [10,] -0.045021804 -0.045021804 -0.045021804 -0.045021804 -0.045021804 #> [11,] -0.390730689 -0.390730689 -0.390730689 -0.390730689 -0.390730689 #> [12,] 0.054696227 0.054696227 0.054696227 0.054696227 0.054696227 #> [,16] [,17] [,18] [,19] [,20] #> [1,] 2.000000000 2.000000000 2.000000000 2.000000000 2.000000000 #> [2,] 8.064227044 8.064227044 8.064227044 8.064227044 8.064227044 #> [3,] -0.003019447 -0.003019447 -0.003019447 -0.003019447 -0.003019447 #> [4,] -0.054389603 -0.054389603 -0.054389603 -0.054389603 -0.054389603 #> [5,] -0.005212285 -0.005212285 -0.005212285 -0.005212285 -0.005212285 #> [6,] -0.109946405 -0.109946405 -0.109946405 -0.109946405 -0.109946405 #> [7,] 0.038799785 0.038799785 0.038799785 0.038799785 0.038799785 #> [8,] -0.078324545 -0.078324545 -0.078324545 -0.078324545 -0.078324545 #> [9,] -1.334080678 -1.334080678 -1.334080678 -1.334080678 -1.334080678 #> [10,] -0.045021804 -0.045021804 -0.045021804 -0.045021804 -0.045021804 #> [11,] -0.390730689 -0.390730689 -0.390730689 -0.390730689 -0.390730689 #> [12,] 0.054696227 0.054696227 0.054696227 0.054696227 0.054696227 Parallel computing support with the ncpus and parallel="multicore" options. coefs.plsR.adapt.ncomp(datasetpine,sample(1:nrow(datasetpine)),ncpus=2,parallel="multicore") #> [1] 2.000000000 8.064227044 -0.003019447 -0.054389603 -0.005212285 #> [6] -0.109946405 0.038799785 -0.078324545 -1.334080678 -0.045021804 #> [11] -0.390730689 0.054696227 replicate(20,coefs.plsR.adapt.ncomp(datasetpine,sample(1:nrow(datasetpine)),ncpus=2,parallel="multicore")) #> [,1] [,2] [,3] [,4] [,5] #> [1,] 2.000000000 2.000000000 2.000000000 2.000000000 2.000000000 #> [2,] 8.064227044 8.064227044 8.064227044 8.064227044 8.064227044 #> [3,] -0.003019447 -0.003019447 -0.003019447 -0.003019447 -0.003019447 #> [4,] -0.054389603 -0.054389603 -0.054389603 -0.054389603 -0.054389603 #> [5,] -0.005212285 -0.005212285 -0.005212285 -0.005212285 -0.005212285 #> [6,] -0.109946405 -0.109946405 -0.109946405 -0.109946405 -0.109946405 #> [7,] 0.038799785 0.038799785 0.038799785 0.038799785 0.038799785 #> [8,] -0.078324545 -0.078324545 -0.078324545 -0.078324545 -0.078324545 #> [9,] -1.334080678 -1.334080678 -1.334080678 -1.334080678 -1.334080678 #> [10,] -0.045021804 -0.045021804 -0.045021804 -0.045021804 -0.045021804 #> [11,] -0.390730689 -0.390730689 -0.390730689 -0.390730689 -0.390730689 #> [12,] 0.054696227 0.054696227 0.054696227 0.054696227 0.054696227 #> [,6] [,7] [,8] [,9] [,10] #> [1,] 2.000000000 2.000000000 2.000000000 4.000000000 2.000000000 #> [2,] 8.064227044 8.064227044 8.064227044 10.934323181 8.064227044 #> [3,] -0.003019447 -0.003019447 -0.003019447 -0.004164703 -0.003019447 #> [4,] -0.054389603 -0.054389603 -0.054389603 -0.061586032 -0.054389603 #> [5,] -0.005212285 -0.005212285 -0.005212285 0.038677103 -0.005212285 #> [6,] -0.109946405 -0.109946405 -0.109946405 -0.568792403 -0.109946405 #> [7,] 0.038799785 0.038799785 0.038799785 0.135567126 0.038799785 #> [8,] -0.078324545 -0.078324545 -0.078324545 0.447111779 -0.078324545 #> [9,] -1.334080678 -1.334080678 -1.334080678 -0.885736030 -1.334080678 #> [10,] -0.045021804 -0.045021804 -0.045021804 -0.110684199 -0.045021804 #> [11,] -0.390730689 -0.390730689 -0.390730689 -1.141903333 -0.390730689 #> [12,] 0.054696227 0.054696227 0.054696227 -0.397050615 0.054696227 #> [,11] [,12] [,13] [,14] [,15] #> [1,] 2.000000000 2.000000000 2.000000000 2.000000000 2.000000000 #> [2,] 8.064227044 8.064227044 8.064227044 8.064227044 8.064227044 #> [3,] -0.003019447 -0.003019447 -0.003019447 -0.003019447 -0.003019447 #> [4,] -0.054389603 -0.054389603 -0.054389603 -0.054389603 -0.054389603 #> [5,] -0.005212285 -0.005212285 -0.005212285 -0.005212285 -0.005212285 #> [6,] -0.109946405 -0.109946405 -0.109946405 -0.109946405 -0.109946405 #> [7,] 0.038799785 0.038799785 0.038799785 0.038799785 0.038799785 #> [8,] -0.078324545 -0.078324545 -0.078324545 -0.078324545 -0.078324545 #> [9,] -1.334080678 -1.334080678 -1.334080678 -1.334080678 -1.334080678 #> [10,] -0.045021804 -0.045021804 -0.045021804 -0.045021804 -0.045021804 #> [11,] -0.390730689 -0.390730689 -0.390730689 -0.390730689 -0.390730689 #> [12,] 0.054696227 0.054696227 0.054696227 0.054696227 0.054696227 #> [,16] [,17] [,18] [,19] [,20] #> [1,] 2.000000000 2.000000000 2.000000000 2.000000000 4.000000000 #> [2,] 8.064227044 8.064227044 8.064227044 8.064227044 10.934323181 #> [3,] -0.003019447 -0.003019447 -0.003019447 -0.003019447 -0.004164703 #> [4,] -0.054389603 -0.054389603 -0.054389603 -0.054389603 -0.061586032 #> [5,] -0.005212285 -0.005212285 -0.005212285 -0.005212285 0.038677103 #> [6,] -0.109946405 -0.109946405 -0.109946405 -0.109946405 -0.568792403 #> [7,] 0.038799785 0.038799785 0.038799785 0.038799785 0.135567126 #> [8,] -0.078324545 -0.078324545 -0.078324545 -0.078324545 0.447111779 #> [9,] -1.334080678 -1.334080678 -1.334080678 -1.334080678 -0.885736030 #> [10,] -0.045021804 -0.045021804 -0.045021804 -0.045021804 -0.110684199 #> [11,] -0.390730689 -0.390730689 -0.390730689 -0.390730689 -1.141903333 #> [12,] 0.054696227 0.054696227 0.054696227 0.054696227 -0.397050615 Aze real dataset: binary logistic plsRglm and sgpls regressions PLSGLR (Y,T) Bootstrap Loading the data and creating the data frames. data(aze_compl) Xaze_compl<-aze_compl[,2:34] yaze_compl<-aze_compl$y
dataset <- cbind(y=yaze_compl,Xaze_compl)

Fitting a logistic PLS regression model with 10 components. You have to use the family option when fitting the plsRglm.

modplsglm <- plsRglm(y~.,data=dataset,10,modele="pls-glm-family",family="binomial")
#> ____************************************************____
#>
#> Family: binomial
#> Link function: logit
#>
#> ____Component____ 1 ____
#> ____Component____ 2 ____
#> ____Component____ 3 ____
#> ____Component____ 4 ____
#> ____Component____ 5 ____
#> ____Component____ 6 ____
#> ____Component____ 7 ____
#> ____Component____ 8 ____
#> ____Component____ 9 ____
#> ____Component____ 10 ____
#> ____Predicting X without NA neither in X or Y____
#> ****________________________________________________****

Perform the bootstrap based algorithm with the nbcomp.bootplsRglm function. By default 250 resamplings are carried out.

set.seed(4619)
aze_compl.bootYT <- suppressWarnings(nbcomp.bootplsRglm(modplsglm))

Plotting the bootstrap distributions of the coefficients of the components.

plsRglm::boxplots.bootpls(aze_compl.bootYT)

Computing the bootstrap based confidence intervals of the coefficients of the components.

plsRglm::confints.bootpls(aze_compl.bootYT)
#> Warning in norm.inter(t, adj.alpha): extreme order statistics used as endpoints

#> Warning in norm.inter(t, adj.alpha): extreme order statistics used as endpoints

#> Warning in norm.inter(t, adj.alpha): extreme order statistics used as endpoints
#>
#>  [1,] -0.1909709 2.3581748 -0.4489036 1.9697388  1.11236461 3.531007
#>  [2,] -0.1514302 0.8243332 -0.3376837 0.7471037  0.20267973 1.287467
#>  [3,] -0.4319055 1.7434199 -0.6285256 1.5594694  0.22338048 2.411375
#>  [4,] -0.3748813 1.0973698 -0.5490521 0.9657205  0.05733105 1.572104
#>  [5,] -0.3963722 0.8830876 -0.5130832 0.8905919 -0.22108731 1.182588
#>  [6,] -0.6441165 1.2480090 -0.9267788 1.1913771 -0.47946992 1.638686
#>  [7,] -0.6863159 1.0264625 -0.8829492 1.0706084 -0.60361567 1.349942
#>  [8,] -1.1970167 1.4738770 -1.2043483 1.7957092 -1.37023450 1.629823
#>  [9,] -0.8340372 0.9057530 -1.0433636 0.9124285 -0.72858196 1.227210
#> [10,] -1.0786394 1.2056122 -1.1600493 1.2398892 -1.11385399 1.286084
#>
#>  [1,]  0.71686088 2.1861124
#>  [2,]  0.07412900 0.8286440
#>  [3,] -0.03355241 1.6424348
#>  [4,] -0.45493576 1.1619803
#>  [5,] -0.38904916 0.9004701
#>  [6,] -0.53350462 1.4582694
#>  [7,] -0.75368847 1.0112706
#>  [8,] -1.54876392 1.3140140
#>  [9,] -0.74456869 1.1516065
#> [10,] -1.02902293 1.3514701
#> attr(,"typeBCa")
#> [1] TRUE

Computing the bootstrap based confidence intervals of the coefficients of the components.

suppressWarnings(plsRglm::plots.confints.bootpls(plsRglm::confints.bootpls(aze_compl.bootYT)))

sparse PLSGLR (Y,T) Bootstrap

The package also features our bootstrap based algorithm to select, for a given $$\eta$$ value, the number of components in sgpls regression. It is implemented in the nbcomp.bootsgpls.

set.seed(4619)
data(prostate, package="spls")
nbcomp.bootsgpls((prostate$x)[,1:30], prostate$y, R=250, eta=0.2, typeBCa = FALSE)
#> [1] "eta = 0.2"
#> [1] "K = 1"
#> [1] "K = 2"
#> [1] "K = 3"
#> [1] "K = 4"
#> [1] "K = 5"
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#>
#> Optimal parameters: eta = 0.2, K = 4

#> $err.mat #> #> eta= 0.2 ; K= 4 0.2554545 #> #>$eta.opt
#> [1] 0.2
#>
#> $K.opt #> [1] 4 #> #>$cands
#>           [,1] [,2] [,3] [,4]
#> [1,] 0.2554545   30  0.2    4

A doParallel and foreach based parallel computing version of the algorithm is implemented as the nbcomp.bootspls.para function.

nbcomp.bootsgpls.para((prostate$x)[,1:30], prostate$y, R=250, eta=c(.2,.5), maxnt=10, typeBCa = FALSE)
#> [1] "eta = 0.2"
#> [1] "K = 1"
#> [1] "K = 2"
#> [1] "K = 3"
#> [1] "K = 4"
#> [1] "K = 5"
#> [1] "eta = 0.5"
#> [1] "K = 1"
#> [1] "K = 2"
#> [1] "K = 3"
#> [1] "K = 4"
#> [1] "K = 5"
#> Warning: glm.fit: algorithm did not converge
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#>
#> Optimal parameters: eta = 0.5, K = 4

#> $err.mat #> #> eta= 0.2 ; K= 4 0.2727273 #> eta= 0.5 ; K= 4 0.2636364 #> #>$eta.opt
#> [1] 0.5
#>
#> $K.opt #> [1] 4 #> #>$cands
#>           [,1] [,2] [,3] [,4]
#> [1,] 0.2636364 27.4  0.5    4
rm(list=c("Xpine","ypine","bbb","bbb2","aze_compl","Xaze_compl","yaze_compl","aze_compl.bootYT","dataset","modplsglm","pine","datasetpine","prostate","res_boot_rep"))