Provides a wrapper for the bootstrap function boot from the
boot R package.
Implements non-parametric bootstraps for PLS
Regression models by either (Y,X) or (Y,T) resampling.
Usage
bootpls(
object,
typeboot = "plsmodel",
R = 250,
statistic = NULL,
sim = "ordinary",
stype = "i",
stabvalue = 1e+06,
verbose = TRUE,
...
)Arguments
- object
An object of class
plsRmodelto bootstrap- typeboot
The type of bootstrap. Either (Y,X) boostrap (
typeboot="plsmodel") or (Y,T) bootstrap (typeboot="fmodel_np"). Defaults to (Y,X) resampling.- R
The number of bootstrap replicates. Usually this will be a single positive integer. For importance resampling, some resamples may use one set of weights and others use a different set of weights. In this case
Rwould be a vector of integers where each component gives the number of resamples from each of the rows of weights.- statistic
A function which when applied to data returns a vector containing the statistic(s) of interest.
statisticmust take at least two arguments. The first argument passed will always be the original data. The second will be a vector of indices, frequencies or weights which define the bootstrap sample. Further, if predictions are required, then a third argument is required which would be a vector of the random indices used to generate the bootstrap predictions. Any further arguments can be passed to statistic through the...argument.- sim
A character string indicating the type of simulation required. Possible values are
"ordinary"(the default),"balanced","permutation", or"antithetic".- stype
A character string indicating what the second argument of
statisticrepresents. Possible values of stype are"i"(indices - the default),"f"(frequencies), or"w"(weights).- stabvalue
A value to hard threshold bootstrap estimates computed from atypical resamplings. Especially useful for Generalized Linear Models.
- verbose
should info messages be displayed ?
- ...
Other named arguments for
statisticwhich are passed unchanged each time it is called. Any such arguments tostatisticshould follow the arguments whichstatisticis required to have for the simulation. Beware of partial matching to arguments ofbootlisted above.
Value
An object of class "boot". See the Value part of the help of
the function boot.
Details
More details on bootstrap techniques are available in the help of the
boot function.
References
A. Lazraq, R. Cleroux, and J.-P. Gauchi. (2003). Selecting both
latent and explanatory variables in the PLS1 regression model.
Chemometrics and Intelligent Laboratory Systems, 66(2):117-126.
P.
Bastien, V. Esposito-Vinzi, and M. Tenenhaus. (2005). PLS generalised linear
regression. Computational Statistics & Data Analysis, 48(1):17-46.
A. C. Davison and D. V. Hinkley. (1997). Bootstrap Methods and Their
Applications. Cambridge University Press, Cambridge.
Author
Frédéric Bertrand
frederic.bertrand@lecnam.net
https://fbertran.github.io/homepage/
Examples
data(Cornell)
XCornell<-Cornell[,1:7]
yCornell<-Cornell[,8]
# Lazraq-Cleroux PLS ordinary bootstrap
set.seed(250)
modpls <- plsR(yCornell,XCornell,3)
#> ____************************************************____
#> ____Component____ 1 ____
#> ____Component____ 2 ____
#> ____Component____ 3 ____
#> ____Predicting X without NA neither in X nor in Y____
#> ****________________________________________________****
#>
#(Y,X) resampling
Cornell.bootYX <- bootpls(modpls, R=250, verbose=FALSE)
#(Y,T) resampling
Cornell.bootYT <- bootpls(modpls, typeboot="fmodel_np", R=250, verbose=FALSE)
# Using the boxplots.bootpls function
boxplots.bootpls(Cornell.bootYX,indices=2:8)
# Confidence intervals plotting
confints.bootpls(Cornell.bootYX,indices=2:8)
#> Warning: extreme order statistics used as endpoints
#> Warning: extreme order statistics used as endpoints
#> Warning: extreme order statistics used as endpoints
#>
#> X1 -0.2305299 -0.03654653 -0.2146155 -0.01243502 -0.2657483 -0.063567788
#> X2 -0.3824730 -0.12056633 -0.4240731 -0.16474400 -0.2526435 0.006685662
#> X3 -0.2262325 -0.03807142 -0.2115428 -0.01464437 -0.2604663 -0.063567788
#> X4 -0.4336032 -0.19861671 -0.4793055 -0.22524165 -0.3610949 -0.107030999
#> X5 -0.2895056 0.13307318 -0.3083408 0.07915147 -0.1560125 0.231479782
#> X6 0.3197348 0.65767612 0.3256605 0.67125328 0.2415264 0.587119147
#> X7 -0.2387634 -0.03963758 -0.2590735 -0.03271142 -0.2540574 -0.027695351
#>
#> X1 -0.2867282 -0.07494113
#> X2 -0.2795110 -0.11744873
#> X3 -0.2795040 -0.07955903
#> X4 -0.4109452 -0.17018880
#> X5 -0.1803183 0.17569760
#> X6 0.3172633 0.64752609
#> X7 -0.2222602 0.03146667
#> attr(,"typeBCa")
#> [1] TRUE
plots.confints.bootpls(confints.bootpls(Cornell.bootYX,indices=2:8))
#> Warning: extreme order statistics used as endpoints
#> Warning: extreme order statistics used as endpoints
#> Warning: extreme order statistics used as endpoints
# Graph similar to the one of Bastien et al. in CSDA 2005
boxplot(as.vector(Cornell.bootYX$t[,-1])~factor(rep(1:7,rep(250,7))),
main="Bootstrap distributions of standardised bj (j = 1, ..., 7).")
points(c(1:7),Cornell.bootYX$t0[-1],col="red",pch=19)
# \donttest{
library(boot)
boot.ci(Cornell.bootYX, conf = c(0.90,0.95), type = c("norm","basic","perc","bca"), index=2)
#> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
#> Based on 250 bootstrap replicates
#>
#> CALL :
#> boot.ci(boot.out = Cornell.bootYX, conf = c(0.9, 0.95), type = c("norm",
#> "basic", "perc", "bca"), index = 2)
#>
#> Intervals :
#> Level Normal Basic
#> 90% (-0.2149, -0.0521 ) (-0.1971, -0.0401 )
#> 95% (-0.2305, -0.0365 ) (-0.2146, -0.0124 )
#>
#> Level Percentile BCa
#> 90% (-0.2380, -0.0811 ) (-0.2573, -0.0857 )
#> 95% (-0.2657, -0.0636 ) (-0.2867, -0.0749 )
#> Calculations and Intervals on Original Scale
#> Some basic intervals may be unstable
#> Some percentile intervals may be unstable
#> Some BCa intervals may be unstable
plot(Cornell.bootYX,index=2)
jack.after.boot(Cornell.bootYX, index=2, useJ=TRUE, nt=3)
plot(Cornell.bootYX,index=2,jack=TRUE)
car::dataEllipse(Cornell.bootYX$t[,2], Cornell.bootYX$t[,3], cex=.3,
levels=c(.5, .95, .99), robust=TRUE)
rm(Cornell.bootYX)
# PLS balanced bootstrap
set.seed(225)
Cornell.bootYX <- bootpls(modpls, sim="balanced", R=250, verbose=FALSE)
boot.array(Cornell.bootYX, indices=TRUE)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,] 5 4 9 2 4 11 5 3 1 5 9 6
#> [2,] 1 10 4 1 8 3 7 2 11 8 5 11
#> [3,] 2 6 1 8 4 1 10 5 1 10 5 7
#> [4,] 7 9 2 12 5 7 6 9 7 7 6 8
#> [5,] 5 11 3 8 4 4 6 2 7 1 5 5
#> [6,] 2 6 4 10 9 11 7 8 5 12 12 4
#> [7,] 6 6 11 2 7 7 9 2 4 8 2 12
#> [8,] 5 9 9 11 10 10 7 2 3 10 2 6
#> [9,] 6 2 3 8 2 9 8 10 6 9 11 7
#> [10,] 5 8 4 4 2 12 4 1 10 12 8 12
#> [11,] 2 1 4 6 11 10 9 10 7 6 4 6
#> [12,] 1 1 1 1 10 2 9 1 12 7 10 1
#> [13,] 1 2 11 9 10 4 1 10 1 7 12 3
#> [14,] 11 3 1 7 5 12 6 6 9 8 1 7
#> [15,] 3 11 8 7 1 9 6 1 4 1 4 5
#> [16,] 10 12 12 8 9 6 3 5 1 2 8 12
#> [17,] 1 8 7 8 1 3 10 3 7 9 8 9
#> [18,] 5 1 1 1 5 4 4 11 8 7 3 9
#> [19,] 2 5 3 2 12 7 4 7 10 11 4 10
#> [20,] 2 4 2 11 10 10 10 5 7 7 4 12
#> [21,] 7 10 8 1 12 4 11 7 9 12 2 7
#> [22,] 5 5 11 6 8 6 12 9 7 9 4 5
#> [23,] 8 12 6 12 9 8 1 5 1 2 11 4
#> [24,] 2 2 3 6 10 1 9 11 11 8 2 2
#> [25,] 4 7 11 7 7 7 1 6 1 5 3 11
#> [26,] 4 11 8 8 1 2 6 9 10 11 6 10
#> [27,] 3 4 12 8 11 8 1 10 9 1 3 12
#> [28,] 6 8 6 6 4 7 10 9 3 7 10 8
#> [29,] 5 1 2 12 10 9 4 9 8 6 11 8
#> [30,] 11 12 4 8 8 10 3 10 8 2 2 7
#> [31,] 6 11 3 7 5 11 3 12 6 5 4 10
#> [32,] 8 7 8 4 1 7 3 7 1 11 4 6
#> [33,] 2 11 5 3 2 8 11 9 2 2 6 9
#> [34,] 6 1 6 4 8 6 6 3 8 2 3 5
#> [35,] 6 4 10 5 11 7 10 11 4 5 7 4
#> [36,] 4 8 1 10 4 4 6 7 6 7 2 10
#> [37,] 9 1 6 4 10 6 8 11 12 2 4 7
#> [38,] 11 9 6 7 6 3 3 11 7 6 3 11
#> [39,] 7 4 1 7 3 3 9 12 2 3 10 3
#> [40,] 6 2 5 1 9 8 10 12 2 3 5 1
#> [41,] 8 12 1 9 9 8 6 6 12 12 2 9
#> [42,] 1 3 7 11 10 10 11 11 9 1 2 11
#> [43,] 11 2 10 9 6 9 1 9 7 10 1 5
#> [44,] 11 2 12 7 11 1 12 6 9 10 6 5
#> [45,] 5 4 9 4 9 10 3 6 9 12 9 12
#> [46,] 8 2 1 11 6 8 10 11 11 12 9 4
#> [47,] 6 9 5 1 1 6 9 7 1 10 8 5
#> [48,] 6 5 3 3 12 10 11 12 11 4 11 11
#> [49,] 1 1 6 1 6 10 5 6 12 6 4 4
#> [50,] 2 2 1 12 11 2 12 7 5 5 3 9
#> [51,] 8 8 9 5 10 3 6 12 3 1 5 6
#> [52,] 4 12 9 9 5 10 9 6 8 8 5 11
#> [53,] 3 5 1 4 7 12 8 9 12 10 10 6
#> [54,] 3 5 11 3 11 12 7 11 10 4 9 2
#> [55,] 5 7 7 6 2 1 9 11 2 9 7 11
#> [56,] 8 4 2 7 8 1 6 6 11 3 8 2
#> [57,] 12 5 9 2 6 10 1 12 11 7 5 12
#> [58,] 1 12 6 12 7 5 2 6 9 1 6 12
#> [59,] 7 7 6 2 5 3 9 8 5 10 5 5
#> [60,] 7 5 2 5 4 7 2 8 4 8 6 2
#> [61,] 8 8 8 12 10 1 10 8 12 11 1 5
#> [62,] 1 9 9 4 3 4 7 1 1 11 7 6
#> [63,] 4 7 5 3 6 7 8 8 10 11 10 8
#> [64,] 2 10 11 6 6 9 11 6 11 3 8 8
#> [65,] 12 5 6 10 10 12 1 9 6 5 6 7
#> [66,] 11 9 2 12 5 2 9 11 5 2 6 7
#> [67,] 10 1 8 12 6 12 9 10 12 7 4 2
#> [68,] 7 5 8 3 6 12 12 8 3 6 12 1
#> [69,] 4 4 3 5 4 2 5 12 8 4 1 10
#> [70,] 10 11 11 8 8 6 1 9 7 8 11 11
#> [71,] 3 3 1 1 11 1 1 2 4 6 2 8
#> [72,] 12 12 8 8 8 12 2 10 3 11 5 11
#> [73,] 7 9 6 5 1 11 8 5 2 11 12 3
#> [74,] 6 9 1 10 9 3 1 3 1 4 5 4
#> [75,] 5 5 8 2 8 2 8 4 11 5 3 4
#> [76,] 8 2 4 9 8 12 10 6 3 4 11 9
#> [77,] 5 7 9 10 8 9 4 7 12 12 12 8
#> [78,] 6 9 9 3 7 3 4 12 4 7 3 11
#> [79,] 12 2 12 3 5 12 8 12 3 8 8 12
#> [80,] 12 4 7 6 8 5 7 3 8 9 11 3
#> [81,] 4 5 6 8 10 12 12 7 6 11 1 4
#> [82,] 8 3 10 11 5 5 4 12 10 2 8 4
#> [83,] 9 2 2 9 12 9 12 11 5 11 4 8
#> [84,] 4 7 9 9 1 2 12 7 9 3 11 12
#> [85,] 9 3 12 2 11 3 3 4 4 7 8 2
#> [86,] 6 2 2 7 12 3 8 10 2 5 10 10
#> [87,] 7 5 6 4 8 4 8 8 12 5 1 7
#> [88,] 5 4 11 4 2 4 4 9 3 1 8 12
#> [89,] 1 7 5 10 1 11 12 5 8 10 3 3
#> [90,] 9 2 6 8 4 8 1 1 9 6 2 3
#> [91,] 12 5 4 12 7 4 8 3 3 11 5 1
#> [92,] 5 12 10 4 3 11 9 11 3 12 9 1
#> [93,] 2 9 4 2 7 8 5 1 6 11 4 5
#> [94,] 10 1 2 7 7 2 9 2 5 12 6 11
#> [95,] 3 1 9 4 6 11 2 12 12 4 6 4
#> [96,] 8 9 3 1 1 11 9 3 12 12 11 5
#> [97,] 9 1 1 5 11 2 11 11 6 11 7 1
#> [98,] 8 11 4 1 3 5 9 1 10 8 8 2
#> [99,] 8 6 3 4 7 1 6 6 7 7 2 9
#> [100,] 10 9 10 2 11 7 1 5 9 5 4 6
#> [101,] 5 6 2 3 6 8 10 1 11 4 2 5
#> [102,] 7 6 1 9 1 1 10 8 9 12 11 11
#> [103,] 2 1 7 3 10 5 3 6 8 10 8 6
#> [104,] 1 9 5 4 4 11 10 2 5 2 2 2
#> [105,] 2 1 2 8 7 12 7 10 9 3 9 5
#> [106,] 1 1 12 8 3 6 8 6 3 3 9 10
#> [107,] 3 5 10 10 11 5 8 10 11 1 12 7
#> [108,] 4 12 7 10 1 10 11 1 10 12 3 8
#> [109,] 11 10 3 7 12 4 12 11 6 7 4 10
#> [110,] 11 4 5 2 12 8 7 7 12 8 3 2
#> [111,] 5 11 3 12 9 3 5 6 6 11 10 4
#> [112,] 11 6 6 5 4 1 6 11 11 12 10 9
#> [113,] 9 12 3 9 9 8 3 10 12 5 11 10
#> [114,] 12 8 6 3 2 4 1 1 12 7 7 12
#> [115,] 9 4 3 9 10 7 4 5 2 9 9 8
#> [116,] 4 7 3 4 6 5 4 6 10 5 3 12
#> [117,] 1 8 2 10 11 10 11 1 12 12 1 2
#> [118,] 6 7 3 7 7 8 9 11 12 9 12 5
#> [119,] 3 9 6 5 8 8 2 8 10 4 1 2
#> [120,] 5 9 11 2 10 10 2 10 12 4 11 6
#> [121,] 9 6 9 4 8 2 12 11 12 3 2 4
#> [122,] 9 11 7 11 2 4 12 4 2 4 9 9
#> [123,] 3 1 4 5 9 7 10 3 7 9 7 10
#> [124,] 5 6 9 3 3 4 11 11 8 1 6 6
#> [125,] 6 8 9 7 2 4 7 10 3 5 2 7
#> [126,] 3 7 2 2 11 7 12 6 10 10 7 1
#> [127,] 10 5 8 3 10 1 11 5 10 4 3 11
#> [128,] 9 6 3 4 2 2 10 2 1 2 11 1
#> [129,] 4 9 1 4 3 9 10 3 12 9 2 6
#> [130,] 11 10 9 10 3 6 8 11 12 6 3 5
#> [131,] 4 3 11 9 7 10 5 8 1 12 9 4
#> [132,] 11 1 9 6 10 10 6 5 2 2 11 4
#> [133,] 10 7 9 9 10 6 6 3 8 3 5 6
#> [134,] 3 8 6 10 12 3 4 11 7 10 4 11
#> [135,] 4 1 6 5 2 8 10 5 9 11 2 11
#> [136,] 11 4 11 2 11 8 10 7 7 9 2 12
#> [137,] 5 2 10 4 12 6 7 5 1 1 9 4
#> [138,] 7 7 1 8 3 4 3 2 6 5 7 1
#> [139,] 12 2 8 3 2 2 7 11 11 4 6 10
#> [140,] 3 3 7 6 8 9 4 6 8 4 7 1
#> [141,] 4 2 3 12 9 10 10 10 5 6 12 10
#> [142,] 4 9 8 8 3 3 4 10 10 1 7 7
#> [143,] 12 3 10 9 2 8 8 6 10 7 9 10
#> [144,] 7 3 4 5 11 2 12 12 7 12 6 10
#> [145,] 1 3 6 9 12 12 10 12 8 11 7 4
#> [146,] 7 3 11 3 12 4 10 4 10 2 5 6
#> [147,] 12 3 8 3 5 11 2 6 7 5 3 10
#> [148,] 3 12 6 4 7 12 6 11 4 2 5 3
#> [149,] 8 5 12 2 10 2 7 4 2 8 11 2
#> [150,] 12 6 7 6 12 4 12 9 3 12 4 3
#> [151,] 11 5 5 4 7 10 2 12 9 10 6 2
#> [152,] 9 3 8 2 7 7 1 6 9 3 8 3
#> [153,] 4 2 7 1 5 3 6 6 7 8 11 4
#> [154,] 1 5 7 5 8 12 4 6 6 9 6 9
#> [155,] 4 8 4 1 8 2 6 4 6 10 9 6
#> [156,] 4 11 3 10 3 2 5 2 12 11 1 5
#> [157,] 12 7 1 11 2 6 3 8 3 8 11 7
#> [158,] 2 2 3 11 11 11 3 6 7 9 11 6
#> [159,] 8 11 2 10 1 11 12 11 3 4 2 5
#> [160,] 4 10 1 5 10 1 6 11 1 6 5 2
#> [161,] 11 9 3 11 6 10 2 11 6 7 9 8
#> [162,] 10 11 1 7 2 6 12 8 6 3 10 11
#> [163,] 11 10 7 1 2 3 4 9 8 6 7 7
#> [164,] 9 2 10 8 1 8 3 10 5 4 9 5
#> [165,] 5 1 4 6 10 7 5 6 2 3 2 2
#> [166,] 8 12 10 3 7 7 3 3 11 12 9 12
#> [167,] 4 9 4 11 8 9 4 6 8 4 3 10
#> [168,] 9 5 3 5 2 10 12 7 12 10 4 11
#> [169,] 2 3 2 10 5 8 7 5 12 7 2 10
#> [170,] 10 6 10 8 6 12 6 3 9 6 6 3
#> [171,] 6 5 6 7 7 12 1 9 4 4 12 3
#> [172,] 5 12 5 12 1 8 5 7 7 1 8 8
#> [173,] 9 7 2 2 1 9 8 5 3 5 5 2
#> [174,] 12 2 10 4 10 5 10 7 5 10 1 6
#> [175,] 1 5 1 11 11 12 10 1 3 12 5 1
#> [176,] 4 8 12 4 9 7 4 12 8 4 1 9
#> [177,] 1 10 2 4 11 4 9 4 2 5 9 8
#> [178,] 10 6 6 2 4 6 5 2 1 10 9 8
#> [179,] 9 8 7 7 8 3 1 5 11 9 11 5
#> [180,] 1 9 11 6 2 10 1 11 11 6 12 3
#> [181,] 9 9 10 6 9 6 6 7 2 12 3 5
#> [182,] 12 2 2 9 7 3 7 4 11 10 3 8
#> [183,] 8 2 9 8 12 1 8 9 10 2 10 5
#> [184,] 11 5 12 10 12 9 1 10 2 12 12 5
#> [185,] 10 1 11 4 8 9 5 6 1 8 10 1
#> [186,] 4 12 5 9 12 1 5 12 9 8 4 9
#> [187,] 3 9 9 9 6 5 7 5 8 4 6 10
#> [188,] 1 5 1 1 2 6 11 8 10 1 5 6
#> [189,] 4 6 5 6 4 12 9 8 2 1 12 9
#> [190,] 3 5 2 4 11 10 12 6 10 11 3 12
#> [191,] 7 9 5 4 8 12 3 4 12 3 8 12
#> [192,] 5 3 7 5 2 11 8 9 11 6 6 7
#> [193,] 3 10 10 8 9 5 10 3 6 9 7 4
#> [194,] 8 7 4 2 7 3 9 3 4 9 2 2
#> [195,] 7 12 8 5 4 10 7 1 10 7 1 7
#> [196,] 4 10 3 12 10 12 7 7 9 8 6 2
#> [197,] 9 2 1 7 11 5 2 10 6 5 12 8
#> [198,] 6 2 11 12 2 8 11 1 9 1 8 11
#> [199,] 4 3 1 3 12 2 11 7 6 4 5 7
#> [200,] 9 2 5 5 9 7 2 2 7 3 5 4
#> [201,] 2 1 10 10 8 5 1 2 6 11 9 4
#> [202,] 5 1 12 11 1 8 5 3 4 9 9 2
#> [203,] 6 12 2 6 8 4 3 12 2 12 1 3
#> [204,] 12 8 3 1 10 4 3 3 8 3 3 10
#> [205,] 1 6 12 5 10 2 7 6 3 9 2 2
#> [206,] 7 8 5 7 12 3 4 6 7 3 11 12
#> [207,] 1 10 12 3 12 3 12 4 3 10 9 6
#> [208,] 2 12 9 10 11 7 8 10 7 9 4 7
#> [209,] 6 11 4 7 9 11 11 1 8 11 8 7
#> [210,] 8 1 9 3 7 7 4 4 3 1 8 1
#> [211,] 5 3 1 9 12 6 10 4 5 12 3 11
#> [212,] 2 2 9 8 7 7 10 9 1 5 4 7
#> [213,] 10 1 4 5 1 9 8 6 9 8 3 11
#> [214,] 4 2 6 3 11 3 5 9 4 1 8 12
#> [215,] 4 10 5 4 9 3 8 12 5 1 6 4
#> [216,] 2 3 5 3 1 11 7 5 1 12 2 9
#> [217,] 3 12 11 7 12 9 6 11 10 6 4 8
#> [218,] 8 6 3 2 9 5 8 9 9 2 7 3
#> [219,] 1 7 6 11 3 4 1 11 12 10 2 9
#> [220,] 11 11 3 8 10 9 8 9 9 10 8 6
#> [221,] 7 8 1 7 4 8 10 5 7 2 3 4
#> [222,] 12 2 6 8 11 3 2 2 3 4 10 3
#> [223,] 10 1 4 11 4 12 10 2 9 11 10 3
#> [224,] 3 8 4 5 8 4 1 8 11 9 12 3
#> [225,] 1 12 7 5 12 5 1 8 2 11 7 11
#> [226,] 9 1 11 12 11 1 3 10 1 4 8 8
#> [227,] 1 11 5 4 1 10 5 12 3 10 5 12
#> [228,] 12 1 10 12 9 5 11 4 2 6 11 5
#> [229,] 10 6 2 1 12 11 8 11 11 9 2 5
#> [230,] 5 4 2 11 1 10 11 7 6 3 2 9
#> [231,] 1 1 8 2 6 7 1 12 12 10 4 3
#> [232,] 3 8 10 3 8 10 3 5 10 7 6 6
#> [233,] 7 5 6 2 2 2 12 6 3 4 2 1
#> [234,] 4 3 10 11 8 7 7 6 5 4 4 1
#> [235,] 6 4 2 6 3 11 6 5 4 5 11 7
#> [236,] 5 4 5 11 2 9 7 5 12 5 7 12
#> [237,] 9 4 3 12 3 12 6 1 10 3 11 1
#> [238,] 7 3 5 11 8 5 11 1 5 7 1 10
#> [239,] 1 7 6 3 7 2 7 1 5 2 4 5
#> [240,] 10 11 1 2 12 8 12 4 7 5 1 3
#> [241,] 8 5 9 11 11 1 6 3 4 11 2 2
#> [242,] 5 11 10 10 12 10 12 4 1 9 4 1
#> [243,] 12 3 7 5 5 10 3 6 8 12 1 10
#> [244,] 5 1 6 2 10 9 8 5 9 12 5 9
#> [245,] 10 4 3 6 12 11 11 12 1 12 2 6
#> [246,] 1 3 2 11 7 9 1 5 5 8 12 5
#> [247,] 10 4 8 9 12 7 10 10 1 9 8 2
#> [248,] 5 12 1 7 5 12 10 8 1 7 8 7
#> [249,] 9 7 3 8 8 5 9 7 10 7 1 11
#> [250,] 7 7 6 11 11 2 9 7 9 3 7 10
# Using the boxplots.bootpls function
boxplots.bootpls(Cornell.bootYX,indices=2:8)
# Confidence intervals plotting
confints.bootpls(Cornell.bootYX,indices=2:8)
#> Warning: extreme order statistics used as endpoints
#> Warning: extreme order statistics used as endpoints
#> Warning: extreme order statistics used as endpoints
#> Warning: extreme order statistics used as endpoints
#>
#> X1 -0.2192145 -0.03502591 -0.2119416 -0.02617619 -0.2520071 -0.066241725
#> X2 -0.3828012 -0.11801756 -0.4193349 -0.15286851 -0.2645190 0.001947385
#> X3 -0.2154695 -0.03582192 -0.2088689 -0.02820433 -0.2469063 -0.066241725
#> X4 -0.4379789 -0.21238307 -0.4660525 -0.22425891 -0.3620776 -0.120283989
#> X5 -0.2967356 0.13546366 -0.2921161 0.09312255 -0.1699835 0.215255066
#> X6 0.3276202 0.67729268 0.3397828 0.68421162 0.2285681 0.572996919
#> X7 -0.2394465 -0.03754892 -0.2166742 -0.03032279 -0.2564461 -0.070094620
#>
#> X1 -0.2459524 -0.04831319
#> X2 -0.2918411 -0.11466891
#> X3 -0.2394376 -0.04850420
#> X4 -0.4645601 -0.20487969
#> X5 -0.2196585 0.18011275
#> X6 0.3325666 0.69760910
#> X7 -0.2561586 -0.06959096
#> attr(,"typeBCa")
#> [1] TRUE
plots.confints.bootpls(confints.bootpls(Cornell.bootYX,indices=2:8))
#> Warning: extreme order statistics used as endpoints
#> Warning: extreme order statistics used as endpoints
#> Warning: extreme order statistics used as endpoints
#> Warning: extreme order statistics used as endpoints
# Graph similar to the one of Bastien et al. in CSDA 2005
boxplot(as.vector(Cornell.bootYX$t[,-1])~factor(rep(1:7,rep(250,7))),
main="Bootstrap distributions of standardised bj (j = 1, ..., 7).")
points(c(1:7),Cornell.bootYX$t0[-1],col="red",pch=19)
library(boot)
boot.ci(Cornell.bootYX, conf = c(0.90,0.95), type = c("norm","basic","perc","bca"),
index=2, verbose=FALSE)
#> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
#> Based on 250 bootstrap replicates
#>
#> CALL :
#> boot.ci(boot.out = Cornell.bootYX, conf = c(0.9, 0.95), type = c("norm",
#> "basic", "perc", "bca"), index = 2, verbose = FALSE)
#>
#> Intervals :
#> Level Normal Basic
#> 90% (-0.2044, -0.0498 ) (-0.1967, -0.0406 )
#> 95% (-0.2192, -0.0350 ) (-0.2119, -0.0262 )
#>
#> Level Percentile BCa
#> 90% (-0.2376, -0.0815 ) (-0.2216, -0.0718 )
#> 95% (-0.2520, -0.0662 ) (-0.2460, -0.0483 )
#> Calculations and Intervals on Original Scale
#> Some basic intervals may be unstable
#> Some percentile intervals may be unstable
#> Some BCa intervals may be unstable
plot(Cornell.bootYX,index=2)
jack.after.boot(Cornell.bootYX, index=2, useJ=TRUE, nt=3)
plot(Cornell.bootYX,index=2,jack=TRUE)
rm(Cornell.bootYX)
# PLS permutation bootstrap
set.seed(500)
Cornell.bootYX <- bootpls(modpls, sim="permutation", R=1000, verbose=FALSE)
boot.array(Cornell.bootYX, indices=TRUE)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,] 7 11 5 2 1 12 4 9 10 6 3 8
#> [2,] 10 6 12 9 8 2 11 4 7 1 5 3
#> [3,] 6 12 1 5 2 10 11 3 4 9 8 7
#> [4,] 5 7 9 4 11 2 6 8 12 1 10 3
#> [5,] 5 9 7 6 12 10 4 11 8 2 1 3
#> [6,] 8 12 7 10 1 4 3 2 5 6 9 11
#> [7,] 1 2 5 6 4 7 12 10 8 11 9 3
#> [8,] 9 1 12 7 2 11 8 3 5 6 10 4
#> [9,] 2 10 5 6 11 12 8 1 4 3 7 9
#> [10,] 10 1 9 7 12 3 4 11 5 8 2 6
#> [11,] 8 3 6 12 10 7 1 9 11 4 2 5
#> [12,] 9 2 4 1 3 10 6 12 11 7 5 8
#> [13,] 5 10 1 3 2 11 12 4 7 8 6 9
#> [14,] 7 4 3 2 9 12 10 11 8 5 1 6
#> [15,] 9 5 11 3 4 6 8 2 1 7 10 12
#> [16,] 3 9 1 12 4 5 6 7 11 2 8 10
#> [17,] 1 3 8 2 5 6 11 10 4 7 12 9
#> [18,] 5 12 2 10 4 11 9 3 1 6 7 8
#> [19,] 12 1 5 4 3 2 6 10 9 7 11 8
#> [20,] 12 11 6 8 2 5 1 3 7 9 4 10
#> [21,] 3 4 12 9 7 8 11 6 1 2 5 10
#> [22,] 4 2 1 5 6 10 7 11 3 8 9 12
#> [23,] 2 9 5 1 12 3 8 10 11 6 4 7
#> [24,] 9 5 7 4 12 2 6 1 10 11 3 8
#> [25,] 5 8 4 1 6 12 10 9 11 2 3 7
#> [26,] 5 7 8 12 3 2 4 10 6 9 11 1
#> [27,] 5 8 1 11 6 9 3 2 12 4 10 7
#> [28,] 3 8 12 4 11 10 2 5 7 6 1 9
#> [29,] 9 5 7 1 2 4 6 12 10 11 3 8
#> [30,] 7 3 11 6 2 1 8 12 9 5 10 4
#> [31,] 9 1 6 2 8 3 12 11 4 5 7 10
#> [32,] 3 8 7 9 4 6 2 10 1 5 12 11
#> [33,] 3 4 6 8 12 1 7 10 11 2 9 5
#> [34,] 9 10 12 8 3 4 6 5 2 1 11 7
#> [35,] 7 8 6 3 12 4 9 5 2 10 11 1
#> [36,] 5 9 6 11 7 4 12 8 3 1 2 10
#> [37,] 9 6 8 3 12 10 4 5 11 1 7 2
#> [38,] 7 9 12 10 5 6 2 3 1 8 11 4
#> [39,] 6 1 2 10 11 4 7 12 9 8 5 3
#> [40,] 6 1 5 9 3 7 10 11 4 2 8 12
#> [41,] 11 1 4 8 5 9 10 12 7 6 3 2
#> [42,] 2 3 1 12 8 4 9 6 11 5 7 10
#> [43,] 4 3 6 5 8 11 2 12 10 7 9 1
#> [44,] 4 7 11 3 10 5 2 1 6 8 9 12
#> [45,] 2 1 10 9 3 6 5 12 4 8 7 11
#> [46,] 12 8 10 7 3 11 4 1 9 6 5 2
#> [47,] 11 3 7 5 8 4 9 2 1 6 12 10
#> [48,] 11 5 1 3 2 8 7 4 12 6 10 9
#> [49,] 2 3 4 8 7 1 11 5 10 9 6 12
#> [50,] 12 10 5 2 6 3 1 7 11 8 9 4
#> [51,] 1 10 4 6 5 7 3 8 9 2 12 11
#> [52,] 6 9 7 2 11 8 12 3 4 1 10 5
#> [53,] 11 9 8 4 6 12 5 1 7 2 10 3
#> [54,] 12 9 8 3 4 1 11 6 7 2 10 5
#> [55,] 4 7 6 3 10 12 2 9 1 11 8 5
#> [56,] 10 8 4 5 9 7 12 6 11 2 1 3
#> [57,] 8 5 12 7 9 2 6 1 11 3 10 4
#> [58,] 9 1 6 5 12 11 7 3 10 4 8 2
#> [59,] 3 7 4 9 6 2 1 12 5 10 8 11
#> [60,] 12 7 11 4 8 9 10 6 5 2 1 3
#> [61,] 9 1 3 7 4 5 8 6 10 11 12 2
#> [62,] 8 5 2 11 10 1 7 4 6 3 9 12
#> [63,] 1 7 10 3 4 6 12 8 9 2 5 11
#> [64,] 6 11 8 7 3 4 5 1 2 9 10 12
#> [65,] 10 5 4 3 7 6 8 12 1 11 9 2
#> [66,] 11 7 6 12 3 2 9 10 4 8 1 5
#> [67,] 5 7 9 2 6 3 12 11 1 8 10 4
#> [68,] 11 3 8 6 10 4 7 2 1 9 12 5
#> [69,] 5 7 4 12 2 3 11 10 9 1 8 6
#> [70,] 1 4 3 12 10 6 5 11 2 8 9 7
#> [71,] 11 2 12 7 8 1 6 10 4 3 9 5
#> [72,] 4 5 9 8 7 10 12 2 3 11 6 1
#> [73,] 8 10 11 5 7 4 9 1 2 6 12 3
#> [74,] 9 3 5 2 8 4 1 6 12 10 11 7
#> [75,] 12 2 8 9 7 4 3 10 6 1 5 11
#> [76,] 4 6 3 1 10 2 8 12 5 9 7 11
#> [77,] 1 5 11 4 2 6 10 3 12 8 9 7
#> [78,] 2 3 8 10 7 12 1 6 5 9 11 4
#> [79,] 11 4 8 10 6 12 5 7 3 1 9 2
#> [80,] 4 8 3 6 9 1 11 7 2 12 5 10
#> [81,] 6 9 7 10 3 11 1 8 5 4 12 2
#> [82,] 4 9 11 1 12 5 7 8 3 10 2 6
#> [83,] 9 3 1 11 4 6 8 5 12 10 7 2
#> [84,] 1 2 11 5 9 4 6 8 10 7 3 12
#> [85,] 12 7 9 5 10 2 4 1 11 8 6 3
#> [86,] 7 12 3 5 2 11 1 4 6 8 10 9
#> [87,] 8 1 11 12 2 4 9 6 5 10 7 3
#> [88,] 10 2 5 12 6 1 3 11 4 9 7 8
#> [89,] 12 1 4 2 8 5 9 7 11 6 10 3
#> [90,] 1 12 11 9 6 5 4 2 8 10 7 3
#> [91,] 11 2 1 7 12 8 3 4 10 5 6 9
#> [92,] 5 1 8 2 4 6 12 10 9 3 7 11
#> [93,] 2 3 1 5 10 12 4 9 7 8 6 11
#> [94,] 6 1 2 5 12 10 11 8 4 7 9 3
#> [95,] 7 6 12 5 10 4 3 2 1 11 8 9
#> [96,] 2 3 9 10 7 1 5 6 4 12 8 11
#> [97,] 8 12 3 4 10 9 2 1 11 7 5 6
#> [98,] 8 6 2 1 7 10 11 5 9 3 12 4
#> [99,] 10 8 1 9 11 5 3 7 12 2 6 4
#> [100,] 4 7 1 10 6 11 3 12 2 5 8 9
#> [101,] 6 7 9 2 10 8 3 12 1 4 5 11
#> [102,] 9 12 6 7 3 4 11 1 5 2 8 10
#> [103,] 2 3 12 1 11 6 5 7 10 8 9 4
#> [104,] 6 8 7 1 11 4 2 12 3 5 10 9
#> [105,] 11 9 4 3 8 6 7 10 12 2 1 5
#> [106,] 5 6 11 2 12 8 10 9 7 4 3 1
#> [107,] 3 8 4 1 12 2 9 6 11 7 5 10
#> [108,] 2 8 1 10 12 4 9 11 5 7 6 3
#> [109,] 7 4 6 2 11 9 1 10 3 8 12 5
#> [110,] 2 11 1 12 7 4 8 3 10 9 6 5
#> [111,] 5 7 12 6 2 1 9 3 4 8 10 11
#> [112,] 10 12 4 9 3 8 1 6 11 5 2 7
#> [113,] 5 9 7 1 10 11 8 12 3 6 4 2
#> [114,] 4 2 3 6 10 11 7 8 1 12 5 9
#> [115,] 12 1 9 11 3 8 6 4 5 7 2 10
#> [116,] 9 6 4 3 11 5 2 1 12 8 10 7
#> [117,] 8 9 5 7 1 10 11 3 6 2 12 4
#> [118,] 3 12 9 2 10 1 5 8 7 4 11 6
#> [119,] 10 1 12 3 5 8 6 4 9 2 11 7
#> [120,] 1 11 10 2 12 3 7 5 4 8 9 6
#> [121,] 8 5 3 7 2 9 4 12 10 11 6 1
#> [122,] 7 9 10 5 12 6 3 11 8 4 1 2
#> [123,] 2 8 5 1 3 11 10 7 9 4 12 6
#> [124,] 8 9 2 11 5 7 6 4 3 1 10 12
#> [125,] 8 10 1 2 5 7 6 4 12 9 11 3
#> [126,] 3 5 6 7 2 1 10 12 9 11 4 8
#> [127,] 4 10 3 1 7 12 5 2 8 9 11 6
#> [128,] 7 3 10 2 5 8 4 12 9 1 11 6
#> [129,] 7 10 11 3 1 4 9 2 6 12 8 5
#> [130,] 12 6 1 2 3 7 11 5 8 10 9 4
#> [131,] 8 1 11 9 5 7 2 10 3 12 6 4
#> [132,] 9 5 11 8 3 6 10 2 1 12 7 4
#> [133,] 8 5 9 7 11 1 10 12 6 2 3 4
#> [134,] 11 6 9 10 3 8 5 7 2 1 4 12
#> [135,] 8 11 12 9 3 2 10 1 7 5 4 6
#> [136,] 9 2 10 4 12 8 6 1 5 3 7 11
#> [137,] 10 7 9 8 4 3 1 11 6 12 2 5
#> [138,] 12 2 7 10 5 11 8 6 1 4 3 9
#> [139,] 11 10 8 3 9 4 2 5 6 7 12 1
#> [140,] 11 9 4 5 3 6 1 8 12 2 7 10
#> [141,] 2 6 12 1 3 7 4 5 8 9 10 11
#> [142,] 12 1 3 8 10 11 5 4 9 7 2 6
#> [143,] 6 8 1 12 3 7 2 9 5 10 4 11
#> [144,] 11 1 8 12 5 2 3 9 6 10 7 4
#> [145,] 10 6 7 9 1 5 11 12 4 8 2 3
#> [146,] 6 5 8 9 1 4 3 11 7 10 2 12
#> [147,] 6 2 1 7 8 9 10 5 11 4 3 12
#> [148,] 10 12 9 3 5 2 8 6 4 11 7 1
#> [149,] 10 3 4 7 9 8 11 2 6 5 1 12
#> [150,] 1 9 2 4 10 12 11 8 6 7 5 3
#> [151,] 4 1 6 11 10 3 8 5 9 12 2 7
#> [152,] 8 3 2 7 6 4 10 5 1 12 11 9
#> [153,] 1 2 11 12 6 8 3 4 5 10 9 7
#> [154,] 1 9 6 5 3 4 10 11 8 2 7 12
#> [155,] 9 7 5 3 2 12 8 4 11 1 10 6
#> [156,] 11 8 3 2 10 6 5 12 7 4 1 9
#> [157,] 4 2 10 5 11 3 7 12 8 6 9 1
#> [158,] 2 12 4 6 11 1 10 9 8 5 3 7
#> [159,] 7 8 5 9 4 3 6 1 11 12 10 2
#> [160,] 2 1 8 11 5 9 7 4 12 10 6 3
#> [161,] 7 1 12 6 8 9 10 5 11 4 2 3
#> [162,] 10 11 6 7 2 5 1 3 12 4 9 8
#> [163,] 12 8 6 1 7 2 11 3 5 4 10 9
#> [164,] 6 2 12 8 1 5 10 3 7 4 9 11
#> [165,] 1 3 11 12 10 9 5 4 2 6 8 7
#> [166,] 12 5 1 2 8 4 9 3 7 10 6 11
#> [167,] 1 8 5 11 3 12 7 9 2 4 10 6
#> [168,] 10 11 3 4 12 5 2 7 9 6 1 8
#> [169,] 11 9 5 1 4 10 12 3 6 2 7 8
#> [170,] 8 10 12 4 3 2 1 7 11 9 5 6
#> [171,] 2 5 3 8 10 7 9 4 12 11 6 1
#> [172,] 8 6 5 11 9 10 1 2 7 12 3 4
#> [173,] 4 10 12 8 2 9 7 1 5 11 6 3
#> [174,] 11 10 6 5 3 2 4 7 12 9 1 8
#> [175,] 12 3 10 5 1 11 8 9 4 7 6 2
#> [176,] 9 6 7 8 11 3 5 10 2 12 4 1
#> [177,] 5 8 2 3 6 11 10 9 1 7 4 12
#> [178,] 5 12 8 3 9 4 1 10 11 6 2 7
#> [179,] 3 12 6 10 9 8 1 11 2 4 7 5
#> [180,] 4 12 1 3 8 10 11 5 7 2 9 6
#> [181,] 11 4 5 6 3 2 1 8 12 9 10 7
#> [182,] 7 12 3 1 6 2 5 11 8 10 9 4
#> [183,] 1 4 9 3 5 10 11 7 12 8 6 2
#> [184,] 12 9 3 5 11 6 8 4 1 7 10 2
#> [185,] 7 4 6 8 9 5 1 10 11 12 2 3
#> [186,] 2 9 8 12 1 11 5 3 10 4 7 6
#> [187,] 2 4 11 5 10 8 7 1 3 9 6 12
#> [188,] 4 2 9 7 1 8 11 3 5 12 6 10
#> [189,] 6 11 1 8 10 7 5 12 3 2 9 4
#> [190,] 12 7 10 11 8 3 4 6 5 9 1 2
#> [191,] 5 4 11 2 10 1 12 3 9 7 6 8
#> [192,] 1 8 2 7 10 5 6 11 4 3 9 12
#> [193,] 10 2 7 5 6 12 11 3 4 9 1 8
#> [194,] 4 8 5 10 11 6 3 12 7 1 9 2
#> [195,] 3 12 9 11 2 8 10 6 5 7 1 4
#> [196,] 8 4 12 2 3 9 10 7 5 6 1 11
#> [197,] 10 3 5 2 9 4 7 12 6 1 8 11
#> [198,] 1 6 2 10 9 8 7 4 5 11 3 12
#> [199,] 3 1 10 11 7 6 2 12 8 5 4 9
#> [200,] 11 4 3 5 9 10 12 1 6 7 8 2
#> [201,] 4 8 6 11 2 3 1 9 7 12 10 5
#> [202,] 7 11 2 5 12 3 10 6 1 4 9 8
#> [203,] 4 8 6 5 11 9 3 1 2 12 10 7
#> [204,] 5 10 7 3 9 2 4 8 11 1 12 6
#> [205,] 8 9 10 5 4 12 11 2 3 6 1 7
#> [206,] 3 10 9 5 6 8 4 1 11 2 12 7
#> [207,] 2 7 5 3 9 12 6 1 11 10 8 4
#> [208,] 1 4 12 2 9 7 8 6 3 5 10 11
#> [209,] 10 9 6 7 12 1 8 2 3 5 11 4
#> [210,] 1 9 8 12 11 2 7 6 4 10 3 5
#> [211,] 1 10 5 7 4 8 2 3 6 12 9 11
#> [212,] 3 1 4 7 12 2 11 10 6 5 8 9
#> [213,] 3 9 2 10 12 5 6 8 11 1 4 7
#> [214,] 4 2 3 12 10 11 1 9 8 6 7 5
#> [215,] 2 5 3 4 1 6 10 8 9 7 12 11
#> [216,] 1 2 4 10 9 6 3 5 7 12 11 8
#> [217,] 11 7 6 1 2 4 9 3 8 10 12 5
#> [218,] 5 2 3 11 6 1 8 12 10 7 4 9
#> [219,] 8 2 11 3 6 4 10 12 5 9 7 1
#> [220,] 12 1 10 2 11 4 7 8 6 9 5 3
#> [221,] 3 4 9 2 5 11 12 1 10 8 7 6
#> [222,] 9 5 6 4 2 7 8 11 10 3 12 1
#> [223,] 11 2 5 9 1 8 3 10 6 7 4 12
#> [224,] 4 7 9 5 10 12 2 8 1 11 3 6
#> [225,] 10 3 12 1 11 2 8 7 9 5 4 6
#> [226,] 7 3 9 1 10 6 5 2 8 4 11 12
#> [227,] 8 3 2 5 4 11 1 9 12 6 10 7
#> [228,] 8 3 5 9 4 11 2 12 1 6 10 7
#> [229,] 10 4 5 2 8 1 3 12 6 11 9 7
#> [230,] 2 11 6 1 4 12 3 8 10 7 9 5
#> [231,] 2 9 4 8 1 3 6 12 5 7 10 11
#> [232,] 12 2 3 7 1 10 8 4 6 5 11 9
#> [233,] 5 11 6 4 7 12 10 1 8 9 2 3
#> [234,] 10 1 6 4 3 8 11 7 5 2 12 9
#> [235,] 6 3 7 8 12 2 5 4 1 10 9 11
#> [236,] 11 5 4 6 7 1 9 2 12 8 3 10
#> [237,] 6 5 4 2 7 12 8 1 11 9 3 10
#> [238,] 10 4 6 12 7 1 3 11 5 8 9 2
#> [239,] 12 2 7 3 8 9 6 5 4 11 10 1
#> [240,] 2 3 9 5 4 10 12 6 1 8 7 11
#> [241,] 7 1 4 8 11 6 5 9 12 3 10 2
#> [242,] 1 11 10 4 5 12 2 3 8 7 6 9
#> [243,] 3 6 7 2 1 9 12 5 11 10 8 4
#> [244,] 8 2 4 9 5 3 6 12 11 10 7 1
#> [245,] 9 10 1 5 8 4 12 6 3 2 7 11
#> [246,] 11 12 3 10 6 9 1 2 5 4 8 7
#> [247,] 9 1 6 8 11 7 2 5 12 10 4 3
#> [248,] 12 9 11 2 7 10 1 4 3 5 8 6
#> [249,] 5 6 8 12 1 3 10 9 11 7 4 2
#> [250,] 7 5 4 1 11 6 10 2 9 8 12 3
#> [251,] 11 12 6 8 7 3 9 1 2 4 5 10
#> [252,] 9 1 4 2 8 5 3 10 7 6 11 12
#> [253,] 11 1 3 7 10 8 9 6 12 4 2 5
#> [254,] 3 8 5 12 6 1 2 11 9 10 4 7
#> [255,] 3 8 10 11 9 4 2 6 12 7 1 5
#> [256,] 4 1 12 10 11 5 7 2 9 3 6 8
#> [257,] 6 9 1 2 7 8 11 3 4 5 12 10
#> [258,] 10 4 7 2 12 5 1 8 11 3 6 9
#> [259,] 12 1 9 10 8 3 7 4 6 2 11 5
#> [260,] 10 9 1 7 5 4 8 3 6 2 12 11
#> [261,] 2 3 12 9 5 1 4 7 10 6 8 11
#> [262,] 6 5 9 10 12 2 7 3 8 11 4 1
#> [263,] 8 12 10 11 1 2 5 6 4 3 7 9
#> [264,] 9 1 6 7 3 8 2 4 5 10 12 11
#> [265,] 8 4 10 12 5 11 3 6 2 7 1 9
#> [266,] 4 11 9 10 3 2 5 8 7 6 12 1
#> [267,] 3 12 8 10 9 2 6 1 4 5 11 7
#> [268,] 4 10 11 7 1 2 12 9 3 5 6 8
#> [269,] 10 3 1 6 11 2 12 9 8 4 7 5
#> [270,] 4 12 6 1 11 2 8 7 10 3 5 9
#> [271,] 2 6 1 12 9 10 11 3 8 4 7 5
#> [272,] 6 4 10 2 12 1 7 3 8 11 5 9
#> [273,] 4 11 5 1 12 6 9 8 2 3 7 10
#> [274,] 8 12 6 5 3 7 11 2 1 10 9 4
#> [275,] 1 8 7 12 9 4 6 2 10 5 3 11
#> [276,] 12 5 7 11 2 10 4 8 3 9 1 6
#> [277,] 4 5 1 9 7 2 11 10 12 3 6 8
#> [278,] 1 10 3 2 6 12 8 9 4 11 5 7
#> [279,] 10 1 9 5 3 11 6 12 2 8 7 4
#> [280,] 6 10 12 4 2 9 11 5 1 3 8 7
#> [281,] 9 4 3 12 5 1 8 6 2 7 10 11
#> [282,] 2 11 10 12 9 8 7 1 5 6 4 3
#> [283,] 8 3 6 1 4 5 2 9 11 10 7 12
#> [284,] 1 11 4 2 12 5 10 8 7 3 9 6
#> [285,] 12 1 10 6 2 8 4 3 7 11 9 5
#> [286,] 10 1 6 2 7 3 12 9 5 11 8 4
#> [287,] 5 1 11 4 12 8 9 2 6 7 10 3
#> [288,] 2 4 5 10 9 3 1 11 8 6 7 12
#> [289,] 2 10 3 6 5 7 1 9 11 8 12 4
#> [290,] 11 6 3 8 10 7 4 9 2 12 5 1
#> [291,] 10 11 3 7 1 4 2 12 5 6 8 9
#> [292,] 8 7 4 1 3 11 5 9 10 6 12 2
#> [293,] 6 10 3 11 9 2 8 7 1 4 12 5
#> [294,] 10 12 3 2 9 4 11 7 8 1 6 5
#> [295,] 2 3 1 12 6 10 7 11 9 8 5 4
#> [296,] 5 2 6 7 10 4 11 9 8 12 1 3
#> [297,] 4 6 3 11 9 8 7 1 12 2 5 10
#> [298,] 5 10 8 12 2 7 1 3 6 11 4 9
#> [299,] 9 7 2 6 10 11 1 3 5 8 4 12
#> [300,] 2 9 12 5 4 6 8 3 7 11 10 1
#> [301,] 4 5 9 10 2 12 1 8 6 11 3 7
#> [302,] 5 7 10 12 11 3 4 9 6 8 2 1
#> [303,] 8 12 10 4 5 9 6 1 7 3 2 11
#> [304,] 7 3 2 11 9 12 5 6 10 4 8 1
#> [305,] 1 12 6 8 4 5 11 9 3 7 2 10
#> [306,] 12 3 8 4 9 1 5 6 10 2 7 11
#> [307,] 10 1 7 6 3 4 9 2 12 8 5 11
#> [308,] 6 7 2 11 10 4 3 5 1 12 9 8
#> [309,] 1 8 12 7 9 5 6 3 4 10 2 11
#> [310,] 1 2 10 7 8 4 12 3 5 11 9 6
#> [311,] 6 12 11 5 8 3 1 4 7 2 9 10
#> [312,] 5 11 7 4 12 2 8 9 1 6 10 3
#> [313,] 6 10 11 12 9 7 4 5 3 1 2 8
#> [314,] 3 6 8 10 11 9 2 5 4 12 1 7
#> [315,] 8 6 11 10 3 7 4 9 2 5 12 1
#> [316,] 2 3 1 5 10 8 6 7 9 11 4 12
#> [317,] 11 7 6 12 2 5 1 8 9 3 10 4
#> [318,] 5 12 8 10 6 4 11 7 3 1 9 2
#> [319,] 6 5 9 4 2 10 8 7 3 1 12 11
#> [320,] 2 11 6 4 7 5 12 8 1 10 3 9
#> [321,] 2 6 10 8 3 5 9 11 1 4 12 7
#> [322,] 9 1 11 2 6 4 8 3 12 10 7 5
#> [323,] 2 6 3 1 5 8 11 12 4 10 7 9
#> [324,] 3 2 6 9 5 11 10 8 4 7 12 1
#> [325,] 3 6 1 11 7 8 5 4 12 9 10 2
#> [326,] 1 2 6 12 4 5 8 10 11 9 3 7
#> [327,] 12 10 4 3 2 7 5 6 11 9 8 1
#> [328,] 9 2 3 5 7 6 4 11 10 1 8 12
#> [329,] 2 8 1 7 3 9 5 12 10 4 6 11
#> [330,] 3 6 1 12 2 4 7 8 5 11 9 10
#> [331,] 9 2 11 10 6 1 4 12 7 3 8 5
#> [332,] 11 2 8 12 7 5 1 10 6 9 3 4
#> [333,] 10 2 6 3 12 8 5 4 1 11 7 9
#> [334,] 7 10 5 11 4 12 1 8 6 3 2 9
#> [335,] 6 12 3 1 8 4 11 10 2 5 9 7
#> [336,] 11 4 7 8 12 6 10 9 5 3 1 2
#> [337,] 10 12 6 5 11 7 4 8 2 3 9 1
#> [338,] 4 5 10 2 8 11 12 7 9 1 6 3
#> [339,] 4 1 5 8 7 9 6 12 2 10 3 11
#> [340,] 4 10 5 11 3 1 2 7 6 9 8 12
#> [341,] 5 10 12 1 11 6 9 4 2 7 3 8
#> [342,] 6 8 3 5 1 4 12 10 9 2 11 7
#> [343,] 7 8 9 4 6 2 11 1 12 5 10 3
#> [344,] 7 9 10 6 8 2 11 4 5 12 1 3
#> [345,] 6 7 3 9 2 12 10 11 1 5 4 8
#> [346,] 6 1 4 5 3 2 8 10 7 12 9 11
#> [347,] 4 6 2 7 8 9 10 12 1 11 3 5
#> [348,] 3 8 6 4 5 9 7 11 2 10 12 1
#> [349,] 5 2 4 12 9 7 3 8 1 11 10 6
#> [350,] 7 9 12 11 3 2 6 8 5 4 1 10
#> [351,] 9 4 10 1 6 8 5 3 7 2 12 11
#> [352,] 7 11 4 8 3 5 1 9 6 10 12 2
#> [353,] 12 5 3 10 1 11 9 7 2 4 8 6
#> [354,] 3 1 5 9 8 6 4 12 11 2 10 7
#> [355,] 8 4 5 3 11 12 7 2 1 10 9 6
#> [356,] 6 4 10 11 7 5 1 2 9 8 3 12
#> [357,] 2 10 11 6 8 5 1 9 12 7 4 3
#> [358,] 5 12 2 10 7 4 8 6 9 1 3 11
#> [359,] 7 9 6 3 10 4 1 8 5 12 2 11
#> [360,] 11 9 12 10 4 3 5 6 7 8 1 2
#> [361,] 11 9 8 12 5 4 1 2 10 3 7 6
#> [362,] 7 3 11 9 4 10 2 5 8 6 1 12
#> [363,] 11 6 10 1 4 2 9 3 5 7 8 12
#> [364,] 9 7 2 4 5 12 10 8 11 3 6 1
#> [365,] 2 9 11 5 8 3 6 4 1 12 7 10
#> [366,] 5 7 9 4 12 3 1 11 10 8 6 2
#> [367,] 7 6 1 11 4 8 9 5 12 2 10 3
#> [368,] 7 2 9 6 8 11 3 10 5 12 1 4
#> [369,] 7 1 8 2 12 4 6 11 5 10 3 9
#> [370,] 9 7 6 8 12 10 2 5 3 11 1 4
#> [371,] 4 6 2 7 10 11 12 3 9 5 1 8
#> [372,] 11 4 3 1 5 7 2 12 10 8 6 9
#> [373,] 2 7 1 11 10 12 8 6 5 4 3 9
#> [374,] 9 2 1 12 4 3 7 11 5 6 10 8
#> [375,] 7 8 5 9 2 10 12 3 11 1 4 6
#> [376,] 8 3 4 1 6 2 10 7 5 11 9 12
#> [377,] 10 3 4 6 11 2 8 7 1 5 12 9
#> [378,] 10 3 8 2 5 4 9 12 6 7 11 1
#> [379,] 8 4 12 2 5 3 6 1 9 7 10 11
#> [380,] 4 6 11 7 8 2 10 5 1 3 9 12
#> [381,] 6 11 2 5 3 12 4 8 10 7 1 9
#> [382,] 12 11 5 3 8 6 2 9 4 1 10 7
#> [383,] 5 8 9 11 3 12 6 1 7 2 10 4
#> [384,] 3 4 11 7 9 12 6 1 8 10 5 2
#> [385,] 10 11 3 7 2 4 6 5 8 1 9 12
#> [386,] 3 2 11 1 6 5 12 7 9 4 10 8
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#> [788,] 2 7 12 1 8 5 4 10 6 11 3 9
#> [789,] 3 6 7 4 9 11 2 8 1 10 5 12
#> [790,] 8 7 10 9 4 5 11 6 3 2 1 12
#> [791,] 7 8 1 4 10 2 3 12 5 6 9 11
#> [792,] 12 4 8 2 5 6 9 10 3 11 7 1
#> [793,] 10 6 8 3 12 11 7 4 2 5 9 1
#> [794,] 5 12 8 11 4 9 3 10 7 2 6 1
#> [795,] 2 11 6 4 12 3 8 9 7 1 10 5
#> [796,] 11 9 10 6 1 3 4 7 5 8 2 12
#> [797,] 3 9 2 11 7 5 12 4 10 1 6 8
#> [798,] 11 8 4 10 12 3 2 1 6 9 7 5
#> [799,] 8 10 2 11 1 3 12 9 5 4 6 7
#> [800,] 5 8 11 10 9 1 4 3 12 6 7 2
#> [801,] 12 10 7 2 9 5 3 8 1 11 6 4
#> [802,] 4 2 12 7 5 3 10 8 11 6 9 1
#> [803,] 10 8 12 4 7 9 11 3 2 1 5 6
#> [804,] 5 2 7 8 12 1 3 9 10 6 11 4
#> [805,] 11 2 1 6 10 9 4 5 7 3 12 8
#> [806,] 9 11 10 3 8 4 7 5 6 1 2 12
#> [807,] 4 12 5 3 8 6 10 9 1 7 11 2
#> [808,] 3 7 8 12 5 10 11 2 1 4 6 9
#> [809,] 7 10 12 9 1 3 11 2 4 8 6 5
#> [810,] 11 9 4 5 12 6 7 3 1 2 8 10
#> [811,] 3 1 12 2 8 11 10 9 5 6 4 7
#> [812,] 5 9 8 10 12 1 4 3 11 2 6 7
#> [813,] 10 11 2 9 1 7 8 12 6 4 5 3
#> [814,] 2 4 7 1 3 8 9 10 5 12 11 6
#> [815,] 2 12 9 1 4 5 6 3 10 11 8 7
#> [816,] 9 5 11 1 3 4 6 2 7 10 12 8
#> [817,] 8 10 12 7 5 3 9 2 4 6 1 11
#> [818,] 9 6 11 1 2 4 8 5 10 7 12 3
#> [819,] 3 9 2 4 5 11 10 12 6 7 8 1
#> [820,] 3 8 12 10 11 6 4 1 7 5 2 9
#> [821,] 3 10 11 4 1 8 6 5 7 2 12 9
#> [822,] 8 6 2 7 11 4 10 3 1 12 5 9
#> [823,] 3 5 6 10 8 2 11 12 7 4 9 1
#> [824,] 11 9 7 6 2 5 12 3 10 4 8 1
#> [825,] 8 6 5 9 11 1 12 7 10 4 2 3
#> [826,] 11 2 12 3 1 10 5 8 9 7 6 4
#> [827,] 8 3 11 12 6 10 2 4 5 7 9 1
#> [828,] 1 9 12 11 5 8 6 10 4 2 3 7
#> [829,] 6 1 7 12 8 10 3 2 4 5 11 9
#> [830,] 8 2 9 3 6 5 4 11 7 10 1 12
#> [831,] 11 12 9 4 6 8 3 7 1 10 2 5
#> [832,] 7 12 6 5 1 4 3 8 9 11 2 10
#> [833,] 7 1 5 9 3 2 10 12 11 6 8 4
#> [834,] 12 5 4 3 8 6 10 1 2 9 11 7
#> [835,] 4 1 3 9 6 5 7 12 10 11 8 2
#> [836,] 9 11 1 5 7 8 10 6 3 12 2 4
#> [837,] 8 11 7 12 10 2 5 6 4 1 3 9
#> [838,] 8 11 2 7 5 3 9 1 12 10 6 4
#> [839,] 9 2 12 3 6 8 4 10 5 11 7 1
#> [840,] 2 1 8 11 5 3 7 6 9 12 4 10
#> [841,] 6 10 4 3 11 1 2 5 8 7 12 9
#> [842,] 12 11 2 6 9 1 3 10 4 5 8 7
#> [843,] 8 11 4 3 1 2 5 12 9 10 7 6
#> [844,] 7 6 5 3 8 4 1 11 2 9 10 12
#> [845,] 10 9 8 12 2 1 4 7 5 6 11 3
#> [846,] 10 7 12 3 5 9 8 6 1 4 2 11
#> [847,] 3 10 4 11 5 8 1 12 6 2 7 9
#> [848,] 1 2 7 5 8 12 3 6 4 10 9 11
#> [849,] 10 6 9 7 5 2 1 3 4 8 12 11
#> [850,] 1 6 12 5 3 10 11 2 9 8 4 7
#> [851,] 9 8 5 7 3 12 2 6 4 1 11 10
#> [852,] 8 12 9 10 3 5 4 6 11 7 1 2
#> [853,] 2 7 8 3 9 12 10 6 5 4 1 11
#> [854,] 9 10 5 6 2 11 3 8 7 1 4 12
#> [855,] 2 11 12 3 5 10 4 7 8 6 1 9
#> [856,] 11 5 6 9 3 2 4 12 8 1 7 10
#> [857,] 3 1 11 10 7 12 5 9 8 6 4 2
#> [858,] 10 8 5 2 1 12 4 7 9 3 11 6
#> [859,] 3 8 4 9 10 11 7 2 1 12 5 6
#> [860,] 3 9 10 7 5 11 8 4 6 12 2 1
#> [861,] 5 1 10 7 3 6 8 2 11 4 12 9
#> [862,] 3 9 6 12 11 8 2 10 7 4 1 5
#> [863,] 11 4 7 3 1 12 9 8 10 2 5 6
#> [864,] 9 12 3 4 1 5 10 8 7 2 6 11
#> [865,] 2 1 4 5 10 7 3 11 8 12 6 9
#> [866,] 11 3 8 2 10 9 7 4 1 6 5 12
#> [867,] 2 7 4 8 9 10 3 6 5 1 12 11
#> [868,] 11 6 2 9 12 1 7 10 5 3 4 8
#> [869,] 1 9 6 10 8 11 7 2 5 4 12 3
#> [870,] 11 10 5 2 3 9 6 4 7 8 12 1
#> [871,] 8 12 9 5 1 7 11 10 4 2 6 3
#> [872,] 6 10 1 9 12 3 8 5 2 7 4 11
#> [873,] 11 2 6 3 12 4 5 7 8 1 10 9
#> [874,] 4 9 11 8 5 6 2 1 7 3 12 10
#> [875,] 2 11 7 4 8 12 1 9 5 10 3 6
#> [876,] 1 12 10 8 5 4 6 9 11 7 3 2
#> [877,] 8 12 5 4 7 9 1 2 6 10 3 11
#> [878,] 9 7 6 11 12 5 10 4 2 1 8 3
#> [879,] 10 4 12 7 6 8 5 3 11 2 1 9
#> [880,] 5 4 9 8 11 6 1 2 12 3 7 10
#> [881,] 9 4 2 6 12 7 11 5 8 10 3 1
#> [882,] 1 9 10 3 7 5 6 4 11 2 12 8
#> [883,] 10 2 8 3 6 7 1 11 12 9 4 5
#> [884,] 7 9 10 3 6 4 2 8 11 12 1 5
#> [885,] 3 8 10 9 4 5 12 1 6 7 2 11
#> [886,] 7 11 1 2 9 12 6 5 4 10 8 3
#> [887,] 2 12 11 3 4 9 10 7 1 5 8 6
#> [888,] 3 7 1 4 6 10 11 5 12 8 9 2
#> [889,] 3 11 10 5 7 9 12 8 2 4 6 1
#> [890,] 2 11 9 12 4 10 1 3 6 5 7 8
#> [891,] 9 12 5 11 7 2 6 10 8 4 1 3
#> [892,] 9 5 11 12 6 10 2 7 4 8 1 3
#> [893,] 12 2 8 7 9 10 6 4 11 5 1 3
#> [894,] 10 6 11 2 4 8 3 1 7 9 5 12
#> [895,] 3 4 8 9 11 1 10 12 2 6 7 5
#> [896,] 9 6 11 10 12 8 4 3 1 2 7 5
#> [897,] 7 4 9 1 2 11 10 12 5 8 6 3
#> [898,] 4 6 2 7 9 1 12 8 3 5 11 10
#> [899,] 9 2 7 12 6 5 11 10 3 4 8 1
#> [900,] 7 9 8 3 12 1 4 10 5 2 11 6
#> [901,] 2 9 3 11 5 1 7 6 12 4 8 10
#> [902,] 5 1 6 2 8 4 3 7 11 10 9 12
#> [903,] 5 8 12 2 11 6 1 3 4 7 9 10
#> [904,] 12 8 7 10 3 4 5 11 9 2 6 1
#> [905,] 10 9 8 6 7 2 12 11 3 1 5 4
#> [906,] 5 2 11 1 4 3 12 6 10 7 9 8
#> [907,] 8 5 10 2 12 3 11 9 1 6 4 7
#> [908,] 4 9 12 3 6 11 8 7 5 2 1 10
#> [909,] 9 1 4 2 11 7 12 8 5 3 6 10
#> [910,] 8 1 12 9 5 3 11 6 10 2 4 7
#> [911,] 1 11 7 9 3 10 12 2 8 6 5 4
#> [912,] 6 2 4 9 8 10 7 1 3 5 11 12
#> [913,] 7 5 8 4 10 9 2 12 3 6 1 11
#> [914,] 6 12 1 8 9 3 4 11 2 5 7 10
#> [915,] 1 11 8 12 9 7 2 6 5 4 3 10
#> [916,] 6 8 3 9 2 1 4 10 12 11 7 5
#> [917,] 7 8 1 10 11 6 12 9 4 5 2 3
#> [918,] 4 3 5 11 12 7 9 6 2 10 1 8
#> [919,] 7 1 12 3 10 8 11 9 6 2 4 5
#> [920,] 4 10 6 7 3 8 1 2 11 5 12 9
#> [921,] 5 7 10 8 1 6 2 3 11 12 9 4
#> [922,] 9 6 10 7 4 3 8 2 5 11 1 12
#> [923,] 8 9 10 1 3 6 12 2 4 5 11 7
#> [924,] 9 8 7 6 4 12 5 2 3 11 10 1
#> [925,] 9 11 8 7 6 3 12 1 2 5 10 4
#> [926,] 1 6 3 10 9 8 11 5 12 4 2 7
#> [927,] 4 6 10 7 1 11 5 8 2 9 12 3
#> [928,] 5 7 3 8 11 9 10 6 12 4 2 1
#> [929,] 1 3 10 6 4 12 2 8 9 5 11 7
#> [930,] 10 8 1 9 4 11 7 6 2 12 5 3
#> [931,] 5 10 1 3 7 2 4 11 6 9 12 8
#> [932,] 9 7 4 6 3 10 2 8 5 11 1 12
#> [933,] 10 2 4 3 8 9 6 7 1 11 12 5
#> [934,] 11 1 4 10 5 2 8 6 9 12 7 3
#> [935,] 1 6 9 5 2 12 4 8 11 7 3 10
#> [936,] 7 3 8 5 9 12 1 2 4 10 11 6
#> [937,] 12 3 2 5 6 10 4 7 11 8 1 9
#> [938,] 6 2 9 1 4 3 11 5 8 10 7 12
#> [939,] 5 10 4 9 8 7 3 11 6 1 12 2
#> [940,] 8 5 6 3 11 2 4 9 1 7 12 10
#> [941,] 8 12 1 7 3 2 6 4 10 5 11 9
#> [942,] 5 4 10 1 2 3 8 11 6 7 12 9
#> [943,] 8 10 4 2 1 7 11 6 5 3 12 9
#> [944,] 4 11 6 5 10 9 7 3 2 12 8 1
#> [945,] 11 9 1 4 10 12 6 5 8 3 2 7
#> [946,] 3 5 11 8 9 2 4 1 6 12 7 10
#> [947,] 4 3 5 9 1 7 2 6 8 10 12 11
#> [948,] 8 9 2 3 11 6 1 5 4 7 12 10
#> [949,] 3 12 5 10 6 8 2 11 9 4 7 1
#> [950,] 2 5 8 6 12 4 7 9 11 1 10 3
#> [951,] 2 11 3 12 6 1 10 4 5 7 9 8
#> [952,] 7 4 1 9 6 3 8 12 10 5 11 2
#> [953,] 7 10 12 9 6 2 11 5 1 3 8 4
#> [954,] 6 7 10 8 4 3 11 1 12 9 5 2
#> [955,] 12 1 11 9 4 6 5 7 8 2 10 3
#> [956,] 4 8 6 3 5 1 10 9 11 2 12 7
#> [957,] 5 2 7 6 8 3 1 10 12 4 9 11
#> [958,] 4 3 5 7 12 11 1 8 6 10 9 2
#> [959,] 10 6 9 11 4 5 7 1 3 2 8 12
#> [960,] 12 4 6 11 3 8 7 5 10 2 1 9
#> [961,] 10 1 5 2 4 9 8 11 3 6 12 7
#> [962,] 7 5 6 1 4 2 12 11 9 3 10 8
#> [963,] 12 7 4 9 10 1 2 11 8 3 5 6
#> [964,] 7 9 11 4 2 12 1 5 10 6 3 8
#> [965,] 10 7 2 12 5 3 6 11 9 4 1 8
#> [966,] 3 11 10 9 5 8 4 6 2 1 7 12
#> [967,] 3 4 8 5 10 9 6 11 12 1 2 7
#> [968,] 8 9 3 12 6 1 10 5 4 2 7 11
#> [969,] 6 9 8 1 5 2 12 10 4 11 3 7
#> [970,] 1 9 2 4 7 5 12 3 6 11 8 10
#> [971,] 8 6 4 9 12 7 2 1 5 3 11 10
#> [972,] 5 7 9 6 11 12 3 10 4 2 8 1
#> [973,] 3 7 6 12 9 5 8 10 2 1 4 11
#> [974,] 2 10 4 8 11 5 12 1 9 3 7 6
#> [975,] 12 3 11 10 9 7 4 5 8 2 1 6
#> [976,] 8 9 4 12 2 3 6 10 1 5 7 11
#> [977,] 9 1 5 2 8 12 3 10 11 6 4 7
#> [978,] 4 2 5 1 9 10 12 11 6 7 3 8
#> [979,] 9 11 2 1 6 4 12 5 7 10 8 3
#> [980,] 8 3 10 7 11 9 6 2 12 1 5 4
#> [981,] 6 10 1 3 4 12 11 7 2 8 9 5
#> [982,] 4 10 7 5 9 1 6 8 12 11 2 3
#> [983,] 10 1 2 5 9 6 7 3 8 12 11 4
#> [984,] 10 12 8 5 6 11 1 9 7 4 3 2
#> [985,] 10 4 12 6 11 5 9 8 3 1 7 2
#> [986,] 7 3 12 4 11 9 10 8 5 1 6 2
#> [987,] 8 1 6 7 9 12 5 10 3 11 4 2
#> [988,] 2 5 11 8 3 12 4 7 1 6 10 9
#> [989,] 12 11 5 3 1 2 8 9 7 6 10 4
#> [990,] 4 1 3 2 11 10 5 7 12 8 6 9
#> [991,] 12 4 5 6 1 2 11 10 9 3 8 7
#> [992,] 3 1 6 9 7 12 10 5 4 11 8 2
#> [993,] 6 4 11 2 3 5 7 8 9 12 1 10
#> [994,] 8 2 9 4 6 12 5 3 10 1 11 7
#> [995,] 4 8 7 3 12 11 10 9 1 6 2 5
#> [996,] 5 8 2 3 7 10 12 11 4 6 9 1
#> [997,] 3 12 9 10 8 4 7 2 1 11 5 6
#> [998,] 11 12 1 10 9 5 7 4 8 3 2 6
#> [999,] 10 8 4 3 2 12 9 5 7 1 11 6
#> [1000,] 4 10 9 8 2 11 6 5 3 7 1 12
# Graph of bootstrap distributions
boxplot(as.vector(Cornell.bootYX$t[,-1])~factor(rep(1:7,rep(1000,7))),
main="Bootstrap distributions of standardised bj (j = 1, ..., 7).")
points(c(1:7),Cornell.bootYX$t0[-1],col="red",pch=19)
# Using the boxplots.bootpls function
boxplots.bootpls(Cornell.bootYX,indices=2:8)
library(boot)
plot(Cornell.bootYX,index=2)
qqnorm(Cornell.bootYX$t[,2],ylim=c(-1,1))
abline(h=Cornell.bootYX$t0[2],lty=2)
(sum(abs(Cornell.bootYX$t[,2])>=abs(Cornell.bootYX$t0[2]))+1)/(length(Cornell.bootYX$t[,2])+1)
#> [1] 0.5584416
rm(Cornell.bootYX)
# }