wilcox.selection.split: Wilcoxon-based variable selection in cross-validation (CV)...
In WilcoxCV: Wilcoxon-based variable selection in cross-validation
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
The function wilcox.selection.split performs variable ordering based on the Wilcoxon rank sum test for all niter CV or MCCV iterations.
Usage
1
wilcox.selection.split(x,y,split,algo="new",pvalue=FALSE)
Arguments
x
a matrix or a data frame of size n x p giving the expression levels of the p variables (genes) for the n observations (arrays).
Variables correspond to columns, observations to rows.
y
a vector of length n giving the class membership for the n observations (arrays). y can be
either a factor or a numeric and must be coded as 0,1.
split
A niter x ntest matrix giving the indices of the ntest observations included
in each of the niter test sets, as generated by the functions generate.split or generate.cv. The i-th row of split gives the indices of the observations included in the test data set for the i-th random splitting iteration.
algo
either "new" or "naive". If type="new", the new fast method
described in Boulesteix (2007) is used. If type="naive", results are obtained by running the
function wilcox.test niter times.
pvalue
Logical. Should p-values be returned?
Details
The Wilcoxon rank sum statistic is defined as the sum of the X-ranks of
the observations with y=0. The Wilcoxon rank sum test is equivalent to the
Mann-Whitney test. It is implemented in the function wilcox.test.
In the context of cross-validation (CV) or Monte-Carlo cross-validation (MCCV), wilcox.selection.split computes the
Wilcoxon rank sum statistic for each iteration, for each variable. At each iteration, a subset
of the n observations is excluded from the data set and considered as test data set.
The indices of the observations considered as test set for each of the niter iterations
are given in the niter x ntest matrix split.
Value
A list with the following components:
ordering.split
A niter x p matrix giving the indices of the genes ordered by pvalue. For example,
the first column of ordering.split gives the index of the variable with lowest pvalue in each of the
niter random splitting iterations, the second column of ordering.split gives the index of the variable with the second lowest pvalue in each of the niter random splitting iterations. For the i-th iteration, the indices of the 50 best variables are given in the 50 first columns of row i.
pvalue.split
Returned only if pvalue=TRUE. A niter x p matrix of pvalues. The element in the
i-th row and j-th column is the pvalue of variable j in the i-th iteration.
Author(s)
Anne-Laure Boulesteix (http://www.ibe.med.uni-muenchen.de/organisation/mitarbeiter/020_professuren/boulesteix/index.html)
References
A. L. Boulesteix (2007). WilcoxCV: an R package for fast variable selection in cross-validation. Bioinformatics 23:1702-1704.
See Also
wilcox.test, generate.split, generate.cv, wilcox.split
Examples
1
2
3
4
5
6
7
8
9
10
11
12
# load WilcoxCV library
library(WilcoxCV)
# Generate data
x<-matrix(rnorm(1000),100,10)
y<-sample(c(0,1),100,replace=TRUE)
# Generate 50 MCCV splits with ratio 2:1 for a data set including 90 observations
my.split<-generate.split(niter=50,n=90,ntest=30)
# Compute the Wilcoxon rank sum statistic for the 50 iterations.
wilcox.selection.split(x=x,y=y,split=my.split,algo="new",pvalue=TRUE)
Example output
$ordering.split
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 7 4 9 3 8 6 10 2 5 1
[2,] 9 4 5 10 3 6 1 7 2 8
[3,] 10 6 4 7 3 5 9 1 8 2
[4,] 4 7 6 5 3 10 2 1 8 9
[5,] 8 6 9 5 7 4 3 2 1 10
[6,] 10 9 4 2 7 3 5 6 8 1
[7,] 4 9 10 7 2 8 5 6 3 1
[8,] 4 5 3 9 2 10 6 7 8 1
[9,] 4 10 5 9 1 7 6 2 8 3
[10,] 9 4 7 1 10 2 5 8 3 6
[11,] 4 10 7 8 5 3 2 6 9 1
[12,] 10 9 6 4 1 3 7 8 5 2
[13,] 4 7 1 9 3 10 6 2 5 8
[14,] 10 9 3 2 5 4 8 1 7 6
[15,] 10 4 9 1 3 6 8 5 2 7
[16,] 7 10 4 3 6 1 5 8 9 2
[17,] 4 7 1 9 5 3 2 6 10 8
[18,] 3 10 4 6 8 9 5 2 7 1
[19,] 7 1 9 10 4 5 3 2 6 8
[20,] 4 10 3 2 5 1 7 9 8 6
[21,] 3 7 4 9 1 6 8 2 10 5
[22,] 4 7 8 10 9 5 2 1 6 3
[23,] 4 9 7 8 10 1 2 5 3 6
[24,] 4 9 3 2 7 6 1 8 10 5
[25,] 4 6 5 8 7 10 2 1 9 3
[26,] 4 9 7 6 2 3 8 5 1 10
[27,] 4 9 1 6 3 7 5 10 8 2
[28,] 7 4 3 1 5 10 9 8 6 2
[29,] 9 1 4 10 5 6 2 7 3 8
[30,] 4 9 3 10 7 5 8 1 6 2
[31,] 4 2 1 9 6 10 5 3 7 8
[32,] 9 4 5 6 1 7 3 8 10 2
[33,] 4 2 3 10 9 5 7 6 1 8
[34,] 9 4 8 6 3 7 10 2 5 1
[35,] 7 3 10 8 6 9 4 1 2 5
[36,] 4 3 10 9 5 6 7 2 8 1
[37,] 9 4 10 6 1 7 3 2 5 8
[38,] 4 3 9 8 5 1 7 10 6 2
[39,] 9 4 8 6 10 2 1 7 5 3
[40,] 1 9 5 4 7 6 3 8 10 2
[41,] 4 3 8 2 1 7 10 6 9 5
[42,] 10 3 4 1 7 5 8 9 6 2
[43,] 4 10 5 3 9 1 6 7 8 2
[44,] 9 7 3 10 5 4 1 6 8 2
[45,] 4 6 10 2 5 9 8 3 7 1
[46,] 4 6 9 5 3 7 2 1 8 10
[47,] 4 10 9 8 3 7 1 6 2 5
[48,] 9 1 4 5 10 8 3 7 2 6
[49,] 3 10 4 9 2 1 7 5 8 6
[50,] 4 3 9 2 7 1 8 6 5 10
$pvalue.split
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.80446009 0.5957469 0.36398919 0.15371625 0.6972371 0.54766450
[2,] 0.76122660 0.8648785 0.51944230 0.27398412 0.3308589 0.74277552
[3,] 0.75024527 0.9248583 0.49410787 0.13741817 0.5476645 0.10374808
[4,] 0.77676349 0.7675319 0.58301899 0.09003695 0.5665694 0.49542818
[5,] 0.99030210 0.7612266 0.69731006 0.57607874 0.5273539 0.36197337
[6,] 0.90553034 0.4987451 0.62655566 0.20839589 0.7129461 0.77577623
[7,] 0.89715209 0.4662738 0.71565075 0.02635651 0.6808664 0.68086640
[8,] 0.81981899 0.4081276 0.30820015 0.17552002 0.2969564 0.42881087
[9,] 0.57930491 0.7520415 0.95721271 0.06903439 0.2859395 0.70724291
[10,] 0.45617396 0.6207502 0.88152811 0.11416577 0.7340119 0.89094404
[11,] 0.99053107 0.7848841 0.60154227 0.07700998 0.4128553 0.93379213
[12,] 0.46541294 0.9470910 0.49542818 0.31370931 0.8991875 0.27486484
[13,] 0.24417254 0.8918442 0.61531491 0.13168151 0.9011986 0.77206317
[14,] 0.77577623 0.5529196 0.34847186 0.57698958 0.5529196 0.84010992
[15,] 0.54500715 0.9526820 0.62655566 0.13482446 0.8493992 0.80318740
[16,] 0.82915184 0.9235949 0.40136755 0.39467511 0.8478888 0.43583845
[17,] 0.20381392 0.6487096 0.64011079 0.04658448 0.3375263 0.65735546
[18,] 0.99518659 0.8611191 0.09234851 0.29664004 0.8046430 0.57476634
[19,] 0.26385474 0.7902160 0.73613839 0.45277536 0.4527754 0.79021601
[20,] 0.71092992 0.3743894 0.32590089 0.09362902 0.5603086 0.87380141
[21,] 0.55842886 0.8233707 0.17086356 0.21619336 0.9855605 0.72189129
[22,] 0.72724318 0.4891394 0.86387652 0.09201608 0.4599237 0.72724318
[23,] 0.72189129 0.7675319 0.85164867 0.24921618 0.7953203 0.85164867
[24,] 0.95268203 0.5216123 0.19580638 0.03567578 0.9905311 0.70411606
[25,] 0.50054899 0.4855078 0.62919174 0.17221022 0.2700969 0.24505179
[26,] 0.83472516 0.5313570 0.53135702 0.20845216 0.7520415 0.38737500
[27,] 0.17418016 0.8552983 0.57626236 0.12469203 0.6421248 0.44092732
[28,] 0.35560810 0.8268162 0.24821017 0.16585405 0.5844016 0.77981449
[29,] 0.13784688 0.7272432 0.91994717 0.17205786 0.4671347 0.48913936
[30,] 0.78488413 0.8773877 0.24965893 0.02646757 0.5689116 0.83084286
[31,] 0.20839589 0.1613929 0.52161228 0.08105991 0.5063078 0.30742872
[32,] 0.46184960 0.9055303 0.67786844 0.26972028 0.2801550 0.36081045
[33,] 0.71092992 0.2233341 0.29776858 0.15973739 0.5524128 0.58431881
[34,] 0.74864159 0.6015423 0.49124288 0.22608046 0.6692035 0.48380168
[35,] 0.58074845 0.6722719 0.25928386 0.50298485 0.7156507 0.37814643
[36,] 0.89681622 0.7681948 0.16417732 0.13128512 0.3829785 0.53207446
[37,] 0.62883397 0.8596323 0.82275721 0.09644929 0.9623874 0.60394406
[38,] 0.67211151 0.9952436 0.26495245 0.02039811 0.6634358 0.90982080
[39,] 0.57437553 0.4965964 0.87318194 0.23472789 0.7450691 0.44569024
[40,] 0.06425775 0.8825049 0.72724318 0.23941737 0.1954307 0.54258185
[41,] 0.59132649 0.4085280 0.30225941 0.07126387 0.9374894 0.65965411
[42,] 0.42273539 0.9436072 0.24793932 0.37025249 0.5167124 0.77721706
[43,] 0.56499467 0.9235949 0.42881087 0.04928913 0.2806111 0.58131698
[44,] 0.50054899 0.8254289 0.32530560 0.42786401 0.3617277 0.55507797
[45,] 0.91493944 0.2306643 0.63499179 0.01598899 0.2448108 0.09425603
[46,] 0.70956366 0.5270207 0.48913936 0.03690092 0.4671347 0.17205786
[47,] 0.73401186 0.8254289 0.50816119 0.12847833 0.8440445 0.75204154
[48,] 0.25388089 0.7272432 0.62365436 0.26894171 0.4817430 0.73613839
[49,] 0.61531491 0.5347727 0.15084230 0.28996030 0.6920392 0.73613839
[50,] 0.73360435 0.4732913 0.29029755 0.07397659 0.8362973 0.76122660
[,7] [,8] [,9] [,10]
[1,] 0.08101219 0.4866923 0.30504019 0.57950660
[2,] 0.76122660 0.9515391 0.09347117 0.36840957
[3,] 0.48669231 0.7862695 0.56347712 0.09181589
[4,] 0.34974899 0.7953203 0.92789684 0.59968798
[5,] 0.52735388 0.3130467 0.48841964 1.00000000
[6,] 0.55291962 0.8493992 0.14765240 0.11721949
[7,] 0.37182097 0.5888241 0.22167265 0.27966072
[8,] 0.54889601 0.6747845 0.34360000 0.41495512
[9,] 0.69839786 0.9192790 0.47808003 0.14414804
[10,] 0.43484397 0.8254289 0.02313167 0.53920656
[11,] 0.22608046 0.3304733 0.95268203 0.16861531
[12,] 0.59132649 0.7583333 0.11817441 0.07916864
[13,] 0.23941737 0.9387404 0.43171119 0.70078150
[14,] 0.80318740 0.7129461 0.29631523 0.29086056
[15,] 0.99053107 0.8308429 0.18378349 0.04241791
[16,] 0.32558725 0.8572903 0.89508605 0.38805062
[17,] 0.18328713 0.9617535 0.32558725 0.92359488
[18,] 0.94709101 0.5747663 0.79532026 0.16344891
[19,] 0.23010383 0.8825049 0.26385474 0.41122632
[20,] 0.71971317 0.7912255 0.77315518 0.17793877
[21,] 0.17852731 0.7675319 0.48029276 0.84219957
[22,] 0.34723136 0.3472314 0.43171119 0.41122632
[23,] 0.36871670 0.4654129 0.31370931 0.68606987
[24,] 0.52161228 0.9621376 0.10652243 0.97159856
[25,] 0.38737500 0.3371718 0.61235833 0.40731956
[26,] 0.36803758 0.5711743 0.23550485 0.94771681
[27,] 0.60058698 0.7821756 0.17048116 0.75520705
[28,] 0.05635164 0.7153768 0.63547290 0.58440156
[29,] 0.85458994 0.9199472 0.09201608 0.42481805
[30,] 0.37982519 0.5851212 0.09194421 0.29631523
[31,] 0.71294607 0.8031874 0.21272007 0.30742872
[32,] 0.46184960 0.7848841 0.12578216 0.78488413
[33,] 0.56825871 0.9671535 0.53678688 0.51377235
[34,] 0.57698958 0.4196598 0.04122455 0.58512123
[35,] 0.09994413 0.3718210 0.41747400 0.36556156
[36,] 0.64566715 0.8689025 0.33960404 0.23375665
[37,] 0.76819479 0.9717859 0.03909752 0.55554334
[38,] 0.74300908 0.6548050 0.38086143 0.77933879
[39,] 0.72724318 0.3293402 0.13784688 0.44569024
[40,] 0.36572905 0.8084834 0.15768056 0.86387652
[41,] 0.59968798 0.3817106 0.78602668 0.62508755
[42,] 0.48669231 0.6039441 0.62048847 0.18279077
[43,] 0.59785654 0.8950860 0.44293198 0.13090915
[44,] 0.19171470 0.7520415 0.10364512 0.33120435
[45,] 0.76669906 0.3304733 0.30742872 0.11177003
[46,] 0.51169053 0.7630326 0.37202917 0.80848340
[47,] 0.51583368 0.3939561 0.36803758 0.18768919
[48,] 0.64047794 0.5743755 0.12573204 0.48174303
[49,] 0.61531491 0.7272432 0.38482977 0.17580091
[50,] 0.49608047 0.7519833 0.38814185 0.90325686
WilcoxCV documentation built on May 2, 2019, 4:16 a.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
The function wilcox.selection.split performs variable ordering based on the Wilcoxon rank sum test for all niter CV or MCCV iterations.
Usage
1 | wilcox.selection.split(x,y,split,algo="new",pvalue=FALSE)
|
Arguments
x |
a matrix or a data frame of size n x p giving the expression levels of the p variables (genes) for the n observations (arrays). Variables correspond to columns, observations to rows. |
y |
a vector of length n giving the class membership for the n observations (arrays). |
split |
A |
algo |
either |
pvalue |
Logical. Should p-values be returned? |
Details
The Wilcoxon rank sum statistic is defined as the sum of the X-ranks of
the observations with y=0. The Wilcoxon rank sum test is equivalent to the
Mann-Whitney test. It is implemented in the function wilcox.test.
In the context of cross-validation (CV) or Monte-Carlo cross-validation (MCCV), wilcox.selection.split computes the
Wilcoxon rank sum statistic for each iteration, for each variable. At each iteration, a subset
of the n observations is excluded from the data set and considered as test data set.
The indices of the observations considered as test set for each of the niter iterations
are given in the niter x ntest matrix split.
Value
A list with the following components:
ordering.split |
A |
pvalue.split |
Returned only if |
Author(s)
Anne-Laure Boulesteix (http://www.ibe.med.uni-muenchen.de/organisation/mitarbeiter/020_professuren/boulesteix/index.html)
References
A. L. Boulesteix (2007). WilcoxCV: an R package for fast variable selection in cross-validation. Bioinformatics 23:1702-1704.
See Also
wilcox.test, generate.split, generate.cv, wilcox.split
Examples
1 2 3 4 5 6 7 8 9 10 11 12 | # load WilcoxCV library
library(WilcoxCV)
# Generate data
x<-matrix(rnorm(1000),100,10)
y<-sample(c(0,1),100,replace=TRUE)
# Generate 50 MCCV splits with ratio 2:1 for a data set including 90 observations
my.split<-generate.split(niter=50,n=90,ntest=30)
# Compute the Wilcoxon rank sum statistic for the 50 iterations.
wilcox.selection.split(x=x,y=y,split=my.split,algo="new",pvalue=TRUE)
|
Example output
$ordering.split
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 7 4 9 3 8 6 10 2 5 1
[2,] 9 4 5 10 3 6 1 7 2 8
[3,] 10 6 4 7 3 5 9 1 8 2
[4,] 4 7 6 5 3 10 2 1 8 9
[5,] 8 6 9 5 7 4 3 2 1 10
[6,] 10 9 4 2 7 3 5 6 8 1
[7,] 4 9 10 7 2 8 5 6 3 1
[8,] 4 5 3 9 2 10 6 7 8 1
[9,] 4 10 5 9 1 7 6 2 8 3
[10,] 9 4 7 1 10 2 5 8 3 6
[11,] 4 10 7 8 5 3 2 6 9 1
[12,] 10 9 6 4 1 3 7 8 5 2
[13,] 4 7 1 9 3 10 6 2 5 8
[14,] 10 9 3 2 5 4 8 1 7 6
[15,] 10 4 9 1 3 6 8 5 2 7
[16,] 7 10 4 3 6 1 5 8 9 2
[17,] 4 7 1 9 5 3 2 6 10 8
[18,] 3 10 4 6 8 9 5 2 7 1
[19,] 7 1 9 10 4 5 3 2 6 8
[20,] 4 10 3 2 5 1 7 9 8 6
[21,] 3 7 4 9 1 6 8 2 10 5
[22,] 4 7 8 10 9 5 2 1 6 3
[23,] 4 9 7 8 10 1 2 5 3 6
[24,] 4 9 3 2 7 6 1 8 10 5
[25,] 4 6 5 8 7 10 2 1 9 3
[26,] 4 9 7 6 2 3 8 5 1 10
[27,] 4 9 1 6 3 7 5 10 8 2
[28,] 7 4 3 1 5 10 9 8 6 2
[29,] 9 1 4 10 5 6 2 7 3 8
[30,] 4 9 3 10 7 5 8 1 6 2
[31,] 4 2 1 9 6 10 5 3 7 8
[32,] 9 4 5 6 1 7 3 8 10 2
[33,] 4 2 3 10 9 5 7 6 1 8
[34,] 9 4 8 6 3 7 10 2 5 1
[35,] 7 3 10 8 6 9 4 1 2 5
[36,] 4 3 10 9 5 6 7 2 8 1
[37,] 9 4 10 6 1 7 3 2 5 8
[38,] 4 3 9 8 5 1 7 10 6 2
[39,] 9 4 8 6 10 2 1 7 5 3
[40,] 1 9 5 4 7 6 3 8 10 2
[41,] 4 3 8 2 1 7 10 6 9 5
[42,] 10 3 4 1 7 5 8 9 6 2
[43,] 4 10 5 3 9 1 6 7 8 2
[44,] 9 7 3 10 5 4 1 6 8 2
[45,] 4 6 10 2 5 9 8 3 7 1
[46,] 4 6 9 5 3 7 2 1 8 10
[47,] 4 10 9 8 3 7 1 6 2 5
[48,] 9 1 4 5 10 8 3 7 2 6
[49,] 3 10 4 9 2 1 7 5 8 6
[50,] 4 3 9 2 7 1 8 6 5 10
$pvalue.split
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.80446009 0.5957469 0.36398919 0.15371625 0.6972371 0.54766450
[2,] 0.76122660 0.8648785 0.51944230 0.27398412 0.3308589 0.74277552
[3,] 0.75024527 0.9248583 0.49410787 0.13741817 0.5476645 0.10374808
[4,] 0.77676349 0.7675319 0.58301899 0.09003695 0.5665694 0.49542818
[5,] 0.99030210 0.7612266 0.69731006 0.57607874 0.5273539 0.36197337
[6,] 0.90553034 0.4987451 0.62655566 0.20839589 0.7129461 0.77577623
[7,] 0.89715209 0.4662738 0.71565075 0.02635651 0.6808664 0.68086640
[8,] 0.81981899 0.4081276 0.30820015 0.17552002 0.2969564 0.42881087
[9,] 0.57930491 0.7520415 0.95721271 0.06903439 0.2859395 0.70724291
[10,] 0.45617396 0.6207502 0.88152811 0.11416577 0.7340119 0.89094404
[11,] 0.99053107 0.7848841 0.60154227 0.07700998 0.4128553 0.93379213
[12,] 0.46541294 0.9470910 0.49542818 0.31370931 0.8991875 0.27486484
[13,] 0.24417254 0.8918442 0.61531491 0.13168151 0.9011986 0.77206317
[14,] 0.77577623 0.5529196 0.34847186 0.57698958 0.5529196 0.84010992
[15,] 0.54500715 0.9526820 0.62655566 0.13482446 0.8493992 0.80318740
[16,] 0.82915184 0.9235949 0.40136755 0.39467511 0.8478888 0.43583845
[17,] 0.20381392 0.6487096 0.64011079 0.04658448 0.3375263 0.65735546
[18,] 0.99518659 0.8611191 0.09234851 0.29664004 0.8046430 0.57476634
[19,] 0.26385474 0.7902160 0.73613839 0.45277536 0.4527754 0.79021601
[20,] 0.71092992 0.3743894 0.32590089 0.09362902 0.5603086 0.87380141
[21,] 0.55842886 0.8233707 0.17086356 0.21619336 0.9855605 0.72189129
[22,] 0.72724318 0.4891394 0.86387652 0.09201608 0.4599237 0.72724318
[23,] 0.72189129 0.7675319 0.85164867 0.24921618 0.7953203 0.85164867
[24,] 0.95268203 0.5216123 0.19580638 0.03567578 0.9905311 0.70411606
[25,] 0.50054899 0.4855078 0.62919174 0.17221022 0.2700969 0.24505179
[26,] 0.83472516 0.5313570 0.53135702 0.20845216 0.7520415 0.38737500
[27,] 0.17418016 0.8552983 0.57626236 0.12469203 0.6421248 0.44092732
[28,] 0.35560810 0.8268162 0.24821017 0.16585405 0.5844016 0.77981449
[29,] 0.13784688 0.7272432 0.91994717 0.17205786 0.4671347 0.48913936
[30,] 0.78488413 0.8773877 0.24965893 0.02646757 0.5689116 0.83084286
[31,] 0.20839589 0.1613929 0.52161228 0.08105991 0.5063078 0.30742872
[32,] 0.46184960 0.9055303 0.67786844 0.26972028 0.2801550 0.36081045
[33,] 0.71092992 0.2233341 0.29776858 0.15973739 0.5524128 0.58431881
[34,] 0.74864159 0.6015423 0.49124288 0.22608046 0.6692035 0.48380168
[35,] 0.58074845 0.6722719 0.25928386 0.50298485 0.7156507 0.37814643
[36,] 0.89681622 0.7681948 0.16417732 0.13128512 0.3829785 0.53207446
[37,] 0.62883397 0.8596323 0.82275721 0.09644929 0.9623874 0.60394406
[38,] 0.67211151 0.9952436 0.26495245 0.02039811 0.6634358 0.90982080
[39,] 0.57437553 0.4965964 0.87318194 0.23472789 0.7450691 0.44569024
[40,] 0.06425775 0.8825049 0.72724318 0.23941737 0.1954307 0.54258185
[41,] 0.59132649 0.4085280 0.30225941 0.07126387 0.9374894 0.65965411
[42,] 0.42273539 0.9436072 0.24793932 0.37025249 0.5167124 0.77721706
[43,] 0.56499467 0.9235949 0.42881087 0.04928913 0.2806111 0.58131698
[44,] 0.50054899 0.8254289 0.32530560 0.42786401 0.3617277 0.55507797
[45,] 0.91493944 0.2306643 0.63499179 0.01598899 0.2448108 0.09425603
[46,] 0.70956366 0.5270207 0.48913936 0.03690092 0.4671347 0.17205786
[47,] 0.73401186 0.8254289 0.50816119 0.12847833 0.8440445 0.75204154
[48,] 0.25388089 0.7272432 0.62365436 0.26894171 0.4817430 0.73613839
[49,] 0.61531491 0.5347727 0.15084230 0.28996030 0.6920392 0.73613839
[50,] 0.73360435 0.4732913 0.29029755 0.07397659 0.8362973 0.76122660
[,7] [,8] [,9] [,10]
[1,] 0.08101219 0.4866923 0.30504019 0.57950660
[2,] 0.76122660 0.9515391 0.09347117 0.36840957
[3,] 0.48669231 0.7862695 0.56347712 0.09181589
[4,] 0.34974899 0.7953203 0.92789684 0.59968798
[5,] 0.52735388 0.3130467 0.48841964 1.00000000
[6,] 0.55291962 0.8493992 0.14765240 0.11721949
[7,] 0.37182097 0.5888241 0.22167265 0.27966072
[8,] 0.54889601 0.6747845 0.34360000 0.41495512
[9,] 0.69839786 0.9192790 0.47808003 0.14414804
[10,] 0.43484397 0.8254289 0.02313167 0.53920656
[11,] 0.22608046 0.3304733 0.95268203 0.16861531
[12,] 0.59132649 0.7583333 0.11817441 0.07916864
[13,] 0.23941737 0.9387404 0.43171119 0.70078150
[14,] 0.80318740 0.7129461 0.29631523 0.29086056
[15,] 0.99053107 0.8308429 0.18378349 0.04241791
[16,] 0.32558725 0.8572903 0.89508605 0.38805062
[17,] 0.18328713 0.9617535 0.32558725 0.92359488
[18,] 0.94709101 0.5747663 0.79532026 0.16344891
[19,] 0.23010383 0.8825049 0.26385474 0.41122632
[20,] 0.71971317 0.7912255 0.77315518 0.17793877
[21,] 0.17852731 0.7675319 0.48029276 0.84219957
[22,] 0.34723136 0.3472314 0.43171119 0.41122632
[23,] 0.36871670 0.4654129 0.31370931 0.68606987
[24,] 0.52161228 0.9621376 0.10652243 0.97159856
[25,] 0.38737500 0.3371718 0.61235833 0.40731956
[26,] 0.36803758 0.5711743 0.23550485 0.94771681
[27,] 0.60058698 0.7821756 0.17048116 0.75520705
[28,] 0.05635164 0.7153768 0.63547290 0.58440156
[29,] 0.85458994 0.9199472 0.09201608 0.42481805
[30,] 0.37982519 0.5851212 0.09194421 0.29631523
[31,] 0.71294607 0.8031874 0.21272007 0.30742872
[32,] 0.46184960 0.7848841 0.12578216 0.78488413
[33,] 0.56825871 0.9671535 0.53678688 0.51377235
[34,] 0.57698958 0.4196598 0.04122455 0.58512123
[35,] 0.09994413 0.3718210 0.41747400 0.36556156
[36,] 0.64566715 0.8689025 0.33960404 0.23375665
[37,] 0.76819479 0.9717859 0.03909752 0.55554334
[38,] 0.74300908 0.6548050 0.38086143 0.77933879
[39,] 0.72724318 0.3293402 0.13784688 0.44569024
[40,] 0.36572905 0.8084834 0.15768056 0.86387652
[41,] 0.59968798 0.3817106 0.78602668 0.62508755
[42,] 0.48669231 0.6039441 0.62048847 0.18279077
[43,] 0.59785654 0.8950860 0.44293198 0.13090915
[44,] 0.19171470 0.7520415 0.10364512 0.33120435
[45,] 0.76669906 0.3304733 0.30742872 0.11177003
[46,] 0.51169053 0.7630326 0.37202917 0.80848340
[47,] 0.51583368 0.3939561 0.36803758 0.18768919
[48,] 0.64047794 0.5743755 0.12573204 0.48174303
[49,] 0.61531491 0.7272432 0.38482977 0.17580091
[50,] 0.49608047 0.7519833 0.38814185 0.90325686
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