@@ -219,46 +219,38 @@ colSums(res6$pvalstep)
219219
220220``` r
221221res6 $ InfCrit
222- # > AIC Q2cum_Y LimQ2_Y Q2_Y PRESS_Y RSS_Y
223- # > Nb_Comp_0 82.01205 NA NA NA NA 467.796667
224- # > Nb_Comp_1 53.15173 0.8966556 0.0975 0.89665563 48.344150 35.742486
225- # > Nb_Comp_2 41.08283 0.9175426 0.0975 0.20210989 28.518576 11.066606
226- # > Nb_Comp_3 32.06411 0.9399676 0.0975 0.27195907 8.056942 4.418081
227- # > Nb_Comp_4 33.76477 0.9197009 0.0975 -0.33759604 5.909608 4.309235
228- # > Nb_Comp_5 33.34373 0.9281373 0.0975 0.10506161 3.856500 3.521924
229- # > Nb_Comp_6 35.25533 0.9232562 0.0975 -0.06792167 3.761138 3.496074
230- # > R2_Y R2_residY RSS_residY PRESS_residY Q2_residY LimQ2
231- # > Nb_Comp_0 NA NA 11.00000000 NA NA NA
232- # > Nb_Comp_1 0.9235940 0.9235940 0.84046633 1.13678803 0.89665563 0.0975
233- # > Nb_Comp_2 0.9763431 0.9763431 0.26022559 0.67059977 0.20210989 0.0975
234- # > Nb_Comp_3 0.9905556 0.9905556 0.10388893 0.18945488 0.27195907 0.0975
235- # > Nb_Comp_4 0.9907882 0.9907882 0.10132947 0.13896142 -0.33759604 0.0975
236- # > Nb_Comp_5 0.9924713 0.9924713 0.08281624 0.09068364 0.10506161 0.0975
237- # > Nb_Comp_6 0.9925265 0.9925265 0.08220840 0.08844125 -0.06792167 0.0975
238- # > Q2cum_residY AIC.std DoF.dof sigmahat.dof AIC.dof
239- # > Nb_Comp_0 NA 37.010388 1.000000 6.5212706 46.0708838
240- # > Nb_Comp_1 0.8966556 8.150064 2.740749 1.8665281 4.5699686
241- # > Nb_Comp_2 0.9175426 -3.918831 5.085967 1.1825195 2.1075461
242- # > Nb_Comp_3 0.9399676 -12.937550 5.121086 0.7488308 0.8467795
243- # > Nb_Comp_4 0.9197009 -11.236891 5.103312 0.7387162 0.8232505
244- # > Nb_Comp_5 0.9281373 -11.657929 6.006316 0.7096382 0.7976101
245- # > Nb_Comp_6 0.9232562 -9.746328 7.000002 0.7633343 0.9711322
246- # > BIC.dof GMDL.dof DoF.naive sigmahat.naive AIC.naive BIC.naive
247- # > Nb_Comp_0 47.7893514 27.59461 1 6.5212706 46.0708838 47.7893514
248- # > Nb_Comp_1 4.9558156 21.34020 2 1.8905683 4.1699567 4.4588195
249- # > Nb_Comp_2 2.3949331 27.40202 3 1.1088836 1.5370286 1.6860917
250- # > Nb_Comp_3 0.9628191 24.40842 4 0.7431421 0.7363469 0.8256118
251- # > Nb_Comp_4 0.9357846 24.23105 5 0.7846050 0.8721072 0.9964867
252- # > Nb_Comp_5 0.9198348 28.21184 6 0.7661509 0.8804809 1.0227979
253- # > Nb_Comp_6 1.1359502 33.18348 7 0.8361907 1.1070902 1.3048716
254- # > GMDL.naive
255- # > Nb_Comp_0 27.59461
256- # > Nb_Comp_1 18.37545
257- # > Nb_Comp_2 17.71117
258- # > Nb_Comp_3 19.01033
259- # > Nb_Comp_4 24.16510
260- # > Nb_Comp_5 28.64206
261- # > Nb_Comp_6 33.63927
222+ # > AIC Q2cum_Y LimQ2_Y Q2_Y PRESS_Y RSS_Y R2_Y
223+ # > Nb_Comp_0 82.01205 NA NA NA NA 467.796667 NA
224+ # > Nb_Comp_1 53.15173 0.8966556 0.0975 0.89665563 48.344150 35.742486 0.9235940
225+ # > Nb_Comp_2 41.08283 0.9175426 0.0975 0.20210989 28.518576 11.066606 0.9763431
226+ # > Nb_Comp_3 32.06411 0.9399676 0.0975 0.27195907 8.056942 4.418081 0.9905556
227+ # > Nb_Comp_4 33.76477 0.9197009 0.0975 -0.33759604 5.909608 4.309235 0.9907882
228+ # > Nb_Comp_5 33.34373 0.9281373 0.0975 0.10506161 3.856500 3.521924 0.9924713
229+ # > Nb_Comp_6 35.25533 0.9232562 0.0975 -0.06792167 3.761138 3.496074 0.9925265
230+ # > R2_residY RSS_residY PRESS_residY Q2_residY LimQ2 Q2cum_residY
231+ # > Nb_Comp_0 NA 11.00000000 NA NA NA NA
232+ # > Nb_Comp_1 0.9235940 0.84046633 1.13678803 0.89665563 0.0975 0.8966556
233+ # > Nb_Comp_2 0.9763431 0.26022559 0.67059977 0.20210989 0.0975 0.9175426
234+ # > Nb_Comp_3 0.9905556 0.10388893 0.18945488 0.27195907 0.0975 0.9399676
235+ # > Nb_Comp_4 0.9907882 0.10132947 0.13896142 -0.33759604 0.0975 0.9197009
236+ # > Nb_Comp_5 0.9924713 0.08281624 0.09068364 0.10506161 0.0975 0.9281373
237+ # > Nb_Comp_6 0.9925265 0.08220840 0.08844125 -0.06792167 0.0975 0.9232562
238+ # > AIC.std DoF.dof sigmahat.dof AIC.dof BIC.dof GMDL.dof DoF.naive
239+ # > Nb_Comp_0 37.010388 1.000000 6.5212706 46.0708838 47.7893514 27.59461 1
240+ # > Nb_Comp_1 8.150064 2.740749 1.8665281 4.5699686 4.9558156 21.34020 2
241+ # > Nb_Comp_2 -3.918831 5.085967 1.1825195 2.1075461 2.3949331 27.40202 3
242+ # > Nb_Comp_3 -12.937550 5.121086 0.7488308 0.8467795 0.9628191 24.40842 4
243+ # > Nb_Comp_4 -11.236891 5.103312 0.7387162 0.8232505 0.9357846 24.23105 5
244+ # > Nb_Comp_5 -11.657929 6.006316 0.7096382 0.7976101 0.9198348 28.21184 6
245+ # > Nb_Comp_6 -9.746328 7.000002 0.7633343 0.9711322 1.1359502 33.18348 7
246+ # > sigmahat.naive AIC.naive BIC.naive GMDL.naive
247+ # > Nb_Comp_0 6.5212706 46.0708838 47.7893514 27.59461
248+ # > Nb_Comp_1 1.8905683 4.1699567 4.4588195 18.37545
249+ # > Nb_Comp_2 1.1088836 1.5370286 1.6860917 17.71117
250+ # > Nb_Comp_3 0.7431421 0.7363469 0.8256118 19.01033
251+ # > Nb_Comp_4 0.7846050 0.8721072 0.9964867 24.16510
252+ # > Nb_Comp_5 0.7661509 0.8804809 1.0227979 28.64206
253+ # > Nb_Comp_6 0.8361907 1.1070902 1.3048716 33.63927
262254```
263255
264256The number of significant predictors per components, which is a criteria of significance for [ Bastien et al. (2005)] ( http://www.sciencedirect.com/science/article/pii/S0167947304000271 ) , can be obtained via the following code:
@@ -368,15 +360,15 @@ res
368360# > X6 5.5177190
369361# > X7 -44.9000310
370362# > Information criteria and Fit statistics:
371- # > AIC RSS_Y R2_Y R2_residY RSS_residY AIC.std
372- # > Nb_Comp_0 82.01205 467.79667 NA NA 11.0000000 37.010388
373- # > Nb_Comp_1 53.15173 35.74249 0.923594 0.923594 0.8404663 8.150064
374- # > DoF.dof sigmahat.dof AIC.dof BIC.dof GMDL.dof DoF.naive
375- # > Nb_Comp_0 1.000000 6.521271 46.070884 47.789351 27.59461 1
376- # > Nb_Comp_1 2.740749 1.866528 4.569969 4.955816 21.34020 2
377- # > sigmahat.naive AIC.naive BIC.naive GMDL.naive
378- # > Nb_Comp_0 6.521271 46.070884 47.78935 27.59461
379- # > Nb_Comp_1 1.890568 4.169957 4.45882 18.37545
363+ # > AIC RSS_Y R2_Y R2_residY RSS_residY AIC.std DoF.dof
364+ # > Nb_Comp_0 82.01205 467.79667 NA NA 11.0000000 37.010388 1.000000
365+ # > Nb_Comp_1 53.15173 35.74249 0.923594 0.923594 0.8404663 8.150064 2.740749
366+ # > sigmahat.dof AIC.dof BIC.dof GMDL.dof DoF.naive sigmahat.naive AIC .naive
367+ # > Nb_Comp_0 6.521271 46.070884 47.789351 27.59461 1 6.521271 46.070884
368+ # > Nb_Comp_1 1.866528 4.569969 4.955816 21.34020 2 1.890568 4.169957
369+ # > BIC.naive GMDL.naive
370+ # > Nb_Comp_0 47.78935 27.59461
371+ # > Nb_Comp_1 4.45882 18.37545
380372```
381373
382374It is also possible to obtain the matrix W∗ with the following command line:
@@ -941,20 +933,20 @@ Stratified balanced bootstrap: CIs for each of the predictors distribution.
941933
942934``` r
943935confints.bootpls(bordeaux.bootYX1strata )
944- # >
945- # > 1|2 -5.2285517 1.8448908 -3.0266055 2.1579125 -6.6883385 -1.5038206
946- # > 2|3 -1.4216229 4.9525537 -2.3021666 3.1831363 1.4147309 6.9000338
947- # > Temperature -0.7320271 3.1003955 -1.6883027 2.0324540 1.0278307 4.7485873
948- # > Sunshine -0.8132215 3.5499277 -0.7684357 2.2776395 1.1162563 4.1623315
949- # > Heat -0.7762493 2.4414119 -1.4124977 1.6043794 0.5748209 3.5916981
950- # > Rain -1.8637554 0.3290778 -1.4058759 0.4748013 -2.2942690 -0.4135918
951- # >
952- # > 1|2 -4.5562748 - 1.3483662
953- # > 2|3 1.2896677 4.7862147
954- # > Temperature 0.9261003 3.2057586
955- # > Sunshine 1.0299078 3.0499807
956- # > Heat 0.5437488 2.7944714
957- # > Rain -1.9548575 - 0.3625478
936+ # >
937+ # > 1|2 -5.2285517 1.8448908 -3.0266055 2.1579125 -6.6883385 -1.5038206 -4.5562748
938+ # > 2|3 -1.4216229 4.9525537 -2.3021666 3.1831363 1.4147309 6.9000338 1.2896677
939+ # > Temperature -0.7320271 3.1003955 -1.6883027 2.0324540 1.0278307 4.7485873 0.9261003
940+ # > Sunshine -0.8132215 3.5499277 -0.7684357 2.2776395 1.1162563 4.1623315 1.0299078
941+ # > Heat -0.7762493 2.4414119 -1.4124977 1.6043794 0.5748209 3.5916981 0.5437488
942+ # > Rain -1.8637554 0.3290778 -1.4058759 0.4748013 -2.2942690 -0.4135918 -1.9548575
943+ # >
944+ # > 1|2 -1.3483662
945+ # > 2|3 4.7862147
946+ # > Temperature 3.2057586
947+ # > Sunshine 3.0499807
948+ # > Heat 2.7944714
949+ # > Rain -0.3625478
958950# > attr(,"typeBCa")
959951# > [1] TRUE
960952```
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