eigenstrat: EIGENSTRAT for correcting for population stratification
In AssocTests: Genetic Association Studies
Description
Usage
Arguments
Details
Value
Author(s)
References
Examples
View source: R/EigenStrat_main.R
Description
Find the eigenvectors of the similarity matrix among the subjects
used for correcting for population stratification in the
population-based genetic association studies.
Usage
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eigenstrat(
genoFile,
outFile.Robj = "out.list",
outFile.txt = "out.txt",
rm.marker.index = NULL,
rm.subject.index = NULL,
miss.val = 9,
num.splits = 10,
topK = NULL,
signt.eigen.level = 0.01,
signal.outlier = FALSE,
iter.outlier = 5,
sigma.thresh = 6
)
Arguments
genoFile
a txt file containing the genotypes (0, 1, 2, or
9). The element of the file in Row i and Column j
represents the genotype at the ith marker of the jth
subject. 0, 1, and 2 denote the number of risk alleles, and 9
(default) is for the missing genotype.
outFile.Robj
the name of an R object for saving the list of
the results which is the same as the return value of this
function. The default is "out.list".
outFile.txt
a txt file for saving the eigenvectors
corresponding to the top significant eigenvalues.
rm.marker.index
a numeric vector for the indices of the
removed markers. The default is NULL.
rm.subject.index
a numeric vector for the indices of the
removed subjects. The default is NULL.
miss.val
the number representing the missing data in the
input data. The default is 9. The element 9 for the missing data
in the genoFile should be changed according to the value of
miss.val.
num.splits
the number of groups into which the markers are
split. The default is 10.
topK
the number of eigenvectors to return. If NULL, it is
calculated by the Tracy-Widom test. The default is NULL.
signt.eigen.level
a numeric value which is the significance
level of the Tracy-Widom test. It should be 0.05, 0.01, 0.005, or
0.001. The default is 0.01.
signal.outlier
logical. If TRUE, delete the outliers of the
subjects; otherwise, do not search for the outliers. The default
is FALSE.
iter.outlier
a numeric value that is the iteration time for
finding the outliers of the subjects. The default is 5.
sigma.thresh
a numeric value that is the lower limit for
eliminating the outliers. The default is 6.
Details
Suppose that a total of n cases and controls are randomly
enrolled in the source population and a panel of m
single-nucleotide polymorphisms are genotyped. The genotype at a
marker locus is coded as 0, 1, or 2, with the value corresponding
to the copy number of risk alleles. All the genotypes are given in
the form of a m*n matrix, in which the element in the
ith row and the jth column represents the genotype
of the jth subject at the ith marker. This function
calculates the top eigenvectors or the eigenvectors with
significant eigenvalues of the similarity matrix among the
subjects to infer the potential population structure. See also
tw.
Value
eigenstrat returns a list, which contains the following components:
num.markers the number of markers excluding the removed markers.
num.subjects the number of subjects excluding the outliers.
rm.marker.index the indices of the removed markers.
rm.subject.index the indices of the removed subjects.
TW.level the significance level of the Tracy-Widom test.
signal.outlier dealing with the outliers in the subjects or not.
iter.outlier the iteration time for finding the outliers.
sigma.thresh the lower limit for eliminating the outliers.
num.outliers the number of outliers.
outliers.index the indices of the outliers.
num.used.subjects the number of the used subjects.
used.subjects.index the indices of the used subjects.
similarity.matrix the similarity matrix among the subjects.
eigenvalues the eigenvalues of the similarity matrix.
eigenvectors the eigenvectors corresponding to the eigenvalues.
topK the number of significant eigenvalues.
TW.stat the observed values of the Tracy-Widom statistics.
topK.eigenvalues the top eigenvalues.
topK.eigenvectors the eigenvectors corresponding to the top eigenvalues.
runtime the running time of this function.
Author(s)
Lin Wang, Wei Zhang, and Qizhai Li.
References
Lin Wang, Wei Zhang, and Qizhai Li. AssocTests: An R Package
for Genetic Association Studies. Journal of Statistical Software.
2020; 94(5): 1-26.
AL Price, NJ Patterson, RM Plenge, ME Weinblatt, NA
Shadick, and D Reich. Principal Components Analysis Corrects for
Stratification in Genome-Wide Association Studies. Nature
Genetics. 2006; 38(8): 904-909.
N Patterson, AL Price, and D Reich. Population
Structure and Eigenanalysis. PloS Genetics. 2006; 2(12):
2074-2093.
CA Tracy and H Widom. Level-Spacing Distributions and
the Airy Kernel. Communications in Mathematical
Physics. 1994; 159(1): 151-174.
Examples
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eigenstratG.eg <- matrix(rbinom(3000, 2, 0.5), ncol = 30)
write.table(eigenstratG.eg, file = "eigenstratG.eg.txt", quote = FALSE,
sep = "", row.names = FALSE, col.names = FALSE)
eigenstrat(genoFile = "eigenstratG.eg.txt", outFile.Robj = "eigenstrat.result.list",
outFile.txt = "eigenstrat.result.txt", rm.marker.index = NULL,
rm.subject.index = NULL, miss.val = 9, num.splits = 10,
topK = NULL, signt.eigen.level = 0.01, signal.outlier = FALSE,
iter.outlier = 5, sigma.thresh = 6)
file.remove("eigenstratG.eg.txt", "eigenstrat.result.list", "eigenstrat.result.txt")
Example output
Loading required package: cluster
Loading required package: mvtnorm
Loading required package: combinat
Attaching package: ‘combinat’
The following object is masked from ‘package:utils’:
combn
Loading required package: fExtremes
Loading required package: timeDate
Loading required package: timeSeries
Loading required package: fBasics
Loading required package: fGarch
$num.markers
[1] 100
$num.subjects
[1] 30
$rm.marker.index
NULL
$rm.subject.index
NULL
$TW.level
[1] 0.01
$signal.outlier
[1] FALSE
$iter.outlier
[1] 5
$sigma.thresh
[1] 6
$num.outliers
NULL
$outliers.index
NULL
$num.used.subjects
[1] 30
$used.subjects.index
[1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
[26] 26 27 28 29 30
$similarity.matrix
[,1] [,2] [,3] [,4] [,5]
[1,] 0.504823019 -0.002065908 0.019716344 0.017508800 -0.0234256469
[2,] -0.002065908 0.412586495 0.099376365 -0.030928017 -0.0151805797
[3,] 0.019716344 0.099376365 0.435454075 -0.001681213 -0.0036751697
[4,] 0.017508800 -0.030928017 -0.001681213 0.478222477 0.0356755506
[5,] -0.023425647 -0.015180580 -0.003675170 0.035675551 0.5080335960
[6,] -0.066815778 -0.014831689 0.045039495 -0.003358736 0.0097408427
[7,] -0.026632986 -0.027218554 -0.035487456 -0.056671432 -0.0305276893
[8,] -0.008763545 -0.029820411 0.052253502 -0.058023810 0.0169058163
[9,] 0.022021391 -0.036684528 0.003397999 0.026334665 -0.0709783066
[10,] -0.042784836 -0.002412424 0.009613859 0.009292651 0.0143934186
[11,] -0.059843402 -0.010238596 -0.059249078 -0.038370832 -0.0216584848
[12,] 0.113093129 -0.080305260 -0.038139493 -0.009161599 -0.0509788261
[13,] 0.017808402 -0.053373534 -0.032172434 -0.040343938 -0.0357359304
[14,] 0.038678751 -0.032034676 -0.030302322 -0.002340386 0.0652665953
[15,] -0.036695494 0.003365073 0.014793146 -0.014337428 -0.0083887407
[16,] -0.014196467 0.067742857 -0.064371596 -0.032900700 -0.0491801549
[17,] -0.062225225 -0.031676494 -0.142514178 -0.066837198 -0.0853605091
[18,] -0.069168315 -0.118779083 -0.137058403 -0.028054484 -0.1221967780
[19,] -0.026119427 -0.017034170 -0.055331901 -0.138344811 -0.0396886184
[20,] -0.082771705 0.089593870 -0.060927776 -0.069476878 0.0657200786
[21,] 0.043654299 -0.046787529 -0.035934168 -0.056091098 -0.0002480018
[22,] -0.041840028 -0.043453304 0.050279034 -0.092508728 -0.0847862815
[23,] -0.021670032 -0.012699839 -0.041203777 -0.033862616 0.1362988064
[24,] 0.017667074 -0.073906804 -0.032537717 0.059584200 -0.0155739114
[25,] -0.048420802 -0.027878309 -0.026440215 -0.058571764 -0.0216256351
[26,] 0.022627900 0.002664484 0.043984958 0.013066337 0.0007928886
[27,] 0.002729591 -0.068081965 -0.006351246 -0.014228882 -0.0204527025
[28,] -0.109946516 0.013696196 -0.027754359 0.055696333 -0.0711087070
[29,] -0.070063528 0.053344137 0.033888743 0.095914955 -0.0218186030
[30,] -0.006879060 0.033022196 0.023334983 0.054798581 -0.0602383162
[,6] [,7] [,8] [,9] [,10]
[1,] -0.066815778 -0.026632986 -0.0087635446 0.022021391 -0.042784836
[2,] -0.014831689 -0.027218554 -0.0298204110 -0.036684528 -0.002412424
[3,] 0.045039495 -0.035487456 0.0522535017 0.003397999 0.009613859
[4,] -0.003358736 -0.056671432 -0.0580238101 0.026334665 0.009292651
[5,] 0.009740843 -0.030527689 0.0169058163 -0.070978307 0.014393419
[6,] 0.448431389 0.048814001 0.0474228188 -0.060570417 -0.066232519
[7,] 0.048814001 0.453903209 -0.0448537419 -0.002712878 -0.048449226
[8,] 0.047422819 -0.044853742 0.4797587923 -0.065700064 -0.009139813
[9,] -0.060570417 -0.002712878 -0.0657000644 0.496668869 -0.026233145
[10,] -0.066232519 -0.048449226 -0.0091398134 -0.026233145 0.524024931
[11,] -0.034360623 -0.065362631 -0.0066046443 -0.076721608 -0.079800805
[12,] -0.045288911 -0.004542875 0.0018622741 -0.054898551 -0.069553132
[13,] -0.056178396 0.032632612 -0.0186640743 0.032816688 0.007036464
[14,] 0.022286521 0.052514456 -0.0509239054 0.012660066 -0.042942126
[15,] -0.062242837 -0.081032007 0.0067323337 -0.042571126 0.013452650
[16,] 0.094116785 0.010716276 -0.0811530550 -0.090376333 -0.084227388
[17,] -0.013453776 0.052765280 -0.0061432520 -0.075267516 -0.011026785
[18,] -0.042797230 0.088235398 0.0354482418 -0.024066459 -0.028497432
[19,] -0.013148117 -0.032202733 0.0454802042 0.008245440 -0.057009815
[20,] -0.045692356 0.002279193 -0.0601217646 0.066753756 0.058907872
[21,] 0.020867150 -0.001792797 -0.0341970371 0.028195863 -0.027771978
[22,] 0.053730371 -0.046746067 -0.0300731633 0.043589081 -0.031485059
[23,] -0.026309423 -0.120102809 -0.0002240495 -0.039054142 -0.052575263
[24,] -0.007373267 -0.109432550 -0.0612157806 -0.026856649 0.088808797
[25,] -0.013651922 0.016322992 -0.0152624826 -0.014625371 -0.048481772
[26,] -0.082710687 0.008527775 -0.0352237165 -0.035076475 -0.037797421
[27,] -0.021443239 -0.033258645 -0.0139609811 0.079339200 -0.036284516
[28,] -0.051874188 -0.024122043 0.0039739171 -0.063976005 0.021964853
[29,] -0.082667195 -0.003186706 -0.0050250780 -0.011714463 0.032824875
[30,] 0.020551930 0.027624634 -0.0547435302 -0.001938980 0.022385085
[,11] [,12] [,13] [,14] [,15]
[1,] -0.059843402 0.1130931286 0.017808402 0.038678751 -0.036695494
[2,] -0.010238596 -0.0803052603 -0.053373534 -0.032034676 0.003365073
[3,] -0.059249078 -0.0381394932 -0.032172434 -0.030302322 0.014793146
[4,] -0.038370832 -0.0091615986 -0.040343938 -0.002340386 -0.014337428
[5,] -0.021658485 -0.0509788261 -0.035735930 0.065266595 -0.008388741
[6,] -0.034360623 -0.0452889112 -0.056178396 0.022286521 -0.062242837
[7,] -0.065362631 -0.0045428745 0.032632612 0.052514456 -0.081032007
[8,] -0.006604644 0.0018622741 -0.018664074 -0.050923905 0.006732334
[9,] -0.076721608 -0.0548985509 0.032816688 0.012660066 -0.042571126
[10,] -0.079800805 -0.0695531325 0.007036464 -0.042942126 0.013452650
[11,] 0.490527357 -0.0265183761 0.020555301 -0.050339978 0.016986796
[12,] -0.026518376 0.5401764223 -0.039715620 -0.029212923 -0.012044908
[13,] 0.020555301 -0.0397156196 0.503294346 0.006652993 -0.015493307
[14,] -0.050339978 -0.0292129225 0.006652993 0.474527884 -0.137034186
[15,] 0.016986796 -0.0120449082 -0.015493307 -0.137034186 0.455990956
[16,] 0.068854006 -0.0230079120 -0.044423142 0.015941229 -0.078910164
[17,] 0.093199320 0.0915409863 0.010685585 -0.074304333 -0.015147032
[18,] 0.055308924 -0.0162775178 0.041380480 -0.008161483 -0.011083954
[19,] 0.045510792 0.0670018982 -0.028257696 -0.015544949 -0.031942334
[20,] 0.001783388 -0.0685001847 -0.042695655 0.059286070 -0.046017270
[21,] -0.076003968 -0.0342879894 -0.027518508 -0.027566589 0.059443090
[22,] 0.010517969 0.0007839686 -0.033216554 -0.082171787 -0.015521524
[23,] -0.039707144 0.0208350033 -0.083286631 -0.072699748 0.023817939
[24,] 0.060654440 0.0524484500 -0.022741829 -0.043696660 0.023326978
[25,] 0.035356891 -0.0154301580 -0.089261953 0.001474022 0.008146694
[26,] -0.084507008 -0.0246896258 0.012422638 -0.017528398 0.060554831
[27,] -0.013478857 -0.0458818025 -0.006774995 0.021315889 -0.021770095
[28,] 0.015880038 -0.0267500522 -0.039892156 -0.018345282 0.007556836
[29,] -0.076505040 -0.0966679637 -0.008684902 -0.016957757 -0.001052312
[30,] -0.095864150 -0.0758884513 0.033145746 -0.018496988 -0.062882603
[,16] [,17] [,18] [,19] [,20]
[1,] -0.0141964675 -0.0622252252 -0.0691683149 -0.026119427 -0.082771705
[2,] 0.0677428565 -0.0316764938 -0.1187790832 -0.017034170 0.089593870
[3,] -0.0643715963 -0.1425141782 -0.1370584027 -0.055331901 -0.060927776
[4,] -0.0329006996 -0.0668371982 -0.0280544844 -0.138344811 -0.069476878
[5,] -0.0491801549 -0.0853605091 -0.1221967780 -0.039688618 0.065720079
[6,] 0.0941167853 -0.0134537761 -0.0427972297 -0.013148117 -0.045692356
[7,] 0.0107162761 0.0527652802 0.0882353979 -0.032202733 0.002279193
[8,] -0.0811530550 -0.0061432520 0.0354482418 0.045480204 -0.060121765
[9,] -0.0903763329 -0.0752675160 -0.0240664589 0.008245440 0.066753756
[10,] -0.0842273885 -0.0110267847 -0.0284974322 -0.057009815 0.058907872
[11,] 0.0688540061 0.0931993204 0.0553089240 0.045510792 0.001783388
[12,] -0.0230079120 0.0915409863 -0.0162775178 0.067001898 -0.068500185
[13,] -0.0444231421 0.0106855849 0.0413804802 -0.028257696 -0.042695655
[14,] 0.0159412290 -0.0743043330 -0.0081614833 -0.015544949 0.059286070
[15,] -0.0789101640 -0.0151470317 -0.0110839544 -0.031942334 -0.046017270
[16,] 0.5823670493 0.0372928558 0.0004992043 0.020347005 -0.023763547
[17,] 0.0372928558 0.5690167773 -0.0682012530 -0.007131014 0.039497178
[18,] 0.0004992043 -0.0682012530 0.5631755789 0.007450219 -0.078427527
[19,] 0.0203470055 -0.0071310138 0.0074502192 0.474959738 0.065853303
[20,] -0.0237635465 0.0394971780 -0.0784275267 0.065853303 0.526096317
[21,] -0.0693806953 -0.0157527962 -0.0231700596 -0.022320415 -0.067310151
[22,] -0.0349822950 -0.0230991065 0.0733213615 -0.088207753 -0.001237124
[23,] -0.0042269645 -0.0134778603 -0.0290025414 0.012700002 -0.021679670
[24,] 0.0353523621 -0.0007168739 0.0309943168 -0.068027313 -0.062461968
[25,] -0.0707332869 0.0415734214 0.0268405081 -0.013326041 -0.047940644
[26,] -0.0800097273 -0.0772820356 0.0177333782 -0.062426656 -0.018267844
[27,] 0.0006960394 0.0251568877 -0.1140944587 0.037512812 -0.047420230
[28,] -0.0290762907 -0.0369973422 0.0155370072 -0.073801270 -0.088193801
[29,] -0.0705339035 -0.0477947203 0.0071953624 0.027748285 0.004433983
[30,] 0.0115279531 -0.0863189921 -0.0440830016 -0.022944666 -0.047298915
[,21] [,22] [,23] [,24] [,25]
[1,] 0.0436542994 -0.0418400282 -0.0216700320 0.0176670743 -0.048420802
[2,] -0.0467875292 -0.0434533036 -0.0126998388 -0.0739068044 -0.027878309
[3,] -0.0359341677 0.0502790345 -0.0412037771 -0.0325377170 -0.026440215
[4,] -0.0560910977 -0.0925087281 -0.0338626162 0.0595841996 -0.058571764
[5,] -0.0002480018 -0.0847862815 0.1362988064 -0.0155739114 -0.021625635
[6,] 0.0208671504 0.0537303709 -0.0263094233 -0.0073732669 -0.013651922
[7,] -0.0017927970 -0.0467460667 -0.1201028093 -0.1094325499 0.016322992
[8,] -0.0341970371 -0.0300731633 -0.0002240495 -0.0612157806 -0.015262483
[9,] 0.0281958633 0.0435890812 -0.0390541420 -0.0268566488 -0.014625371
[10,] -0.0277719780 -0.0314850595 -0.0525752627 0.0888087969 -0.048481772
[11,] -0.0760039676 0.0105179693 -0.0397071441 0.0606544402 0.035356891
[12,] -0.0342879894 0.0007839686 0.0208350033 0.0524484500 -0.015430158
[13,] -0.0275185079 -0.0332165543 -0.0832866314 -0.0227418290 -0.089261953
[14,] -0.0275665886 -0.0821717870 -0.0726997484 -0.0436966599 0.001474022
[15,] 0.0594430898 -0.0155215242 0.0238179391 0.0233269783 0.008146694
[16,] -0.0693806953 -0.0349822950 -0.0042269645 0.0353523621 -0.070733287
[17,] -0.0157527962 -0.0230991065 -0.0134778603 -0.0007168739 0.041573421
[18,] -0.0231700596 0.0733213615 -0.0290025414 0.0309943168 0.026840508
[19,] -0.0223204147 -0.0882077533 0.0127000024 -0.0680273128 -0.013326041
[20,] -0.0673101512 -0.0012371239 -0.0216796701 -0.0624619682 -0.047940644
[21,] 0.4532971502 0.0644351186 0.0117196765 -0.0685999229 0.026658331
[22,] 0.0644351186 0.6160581543 -0.0218699972 0.0082284333 -0.017647925
[23,] 0.0117196765 -0.0218699972 0.5446348853 -0.0539038024 0.061642592
[24,] -0.0685999229 0.0082284333 -0.0539038024 0.5040169689 -0.028800508
[25,] 0.0266583306 -0.0176479248 0.0616425925 -0.0288005079 0.421022540
[26,] 0.0186500856 -0.0382695381 -0.0493117288 -0.0801929872 -0.013104310
[27,] -0.0434059113 -0.0464708452 -0.0088144800 0.0237304616 -0.034369816
[28,] -0.0033670071 -0.0500548108 -0.0297257183 -0.0598375885 0.024898151
[29,] -0.0331165397 -0.0285900408 -0.0496219980 -0.0499339053 -0.054230045
[30,] -0.0122976044 -0.0687115601 0.0133813306 -0.0390024451 -0.004133183
[,26] [,27] [,28] [,29] [,30]
[1,] 0.0226278997 0.0027295912 -0.109946516 -0.070063528 -0.006879060
[2,] 0.0026644839 -0.0680819648 0.013696196 0.053344137 0.033022196
[3,] 0.0439849581 -0.0063512455 -0.027754359 0.033888743 0.023334983
[4,] 0.0130663368 -0.0142288817 0.055696333 0.095914955 0.054798581
[5,] 0.0007928886 -0.0204527025 -0.071108707 -0.021818603 -0.060238316
[6,] -0.0827106872 -0.0214432388 -0.051874188 -0.082667195 0.020551930
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[15,] 0.0605548311 -0.0217700949 0.007556836 -0.001052312 -0.062882603
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[17,] -0.0772820356 0.0251568877 -0.036997342 -0.047794720 -0.086318992
[18,] 0.0177333782 -0.1140944587 0.015537007 0.007195362 -0.044083002
[19,] -0.0624266560 0.0375128122 -0.073801270 0.027748285 -0.022944666
[20,] -0.0182678436 -0.0474202299 -0.088193801 0.004433983 -0.047298915
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[26,] 0.4351013787 0.0475890369 0.037764022 -0.013057857 0.027976302
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[30,] 0.0279763019 -0.0023006234 0.057726422 -0.054262369 0.432810277
$eigenvalues
[1] 1.061808e+00 9.277102e-01 8.822273e-01 8.511844e-01 8.197691e-01
[6] 7.907631e-01 7.706703e-01 6.877436e-01 6.519147e-01 6.220092e-01
[11] 5.947820e-01 5.754436e-01 5.527508e-01 5.064458e-01 4.825394e-01
[16] 4.619910e-01 4.444526e-01 4.113546e-01 3.858443e-01 3.417123e-01
[21] 3.133358e-01 2.686268e-01 2.617619e-01 2.381449e-01 2.299887e-01
[26] 2.082447e-01 1.806557e-01 1.503149e-01 1.378124e-01 1.398867e-16
$eigenvectors
[,1] [,2] [,3] [,4] [,5]
[1,] -0.052316361 0.060451073 0.1006870010 0.48227679 -0.21348012
[2,] -0.155470384 0.203357995 -0.0275309122 -0.21519157 0.05388104
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[5,] -0.165277299 0.320601766 0.2469046137 -0.06857183 0.01958251
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[12,] -0.069315515 -0.20354419 -0.150216126 -0.083352087 0.260871175
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[25,] 0.131137027 -0.18086519 0.094820785 0.244082790 -0.035904702
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[30,] 0.216840762 -0.03895512 -0.078259696 0.196046961 -0.130035731
[,11] [,12] [,13] [,14] [,15]
[1,] 0.15260827 0.267581597 0.005945827 -0.0236835192 -0.03069905
[2,] 0.15546316 0.286869750 0.003762796 -0.0622401641 -0.06531948
[3,] -0.07132687 -0.032799026 0.097256678 -0.1685859653 -0.10657037
[4,] 0.20003372 -0.197647449 0.192537177 0.2325128844 -0.09177355
[5,] -0.17234531 0.110598654 0.218667748 0.1190256129 -0.05378590
[6,] -0.18379091 -0.269188835 -0.031305307 0.0840819338 0.12928748
[7,] -0.03930230 0.010002596 0.016306507 0.0756240791 0.12719770
[8,] -0.24798328 -0.260927246 -0.058143197 -0.0401798425 -0.09412939
[9,] 0.10444951 -0.261266760 -0.044455627 0.0006819437 -0.09291844
[10,] -0.11774031 0.008602138 -0.470978890 -0.1714307518 0.13927355
[11,] -0.15911679 0.113127348 0.346105090 -0.1989162588 -0.21886994
[12,] 0.41290722 -0.006708457 -0.059896604 -0.0692514642 -0.12884883
[13,] -0.44969529 0.249213032 -0.070277477 0.2933690276 -0.43349999
[14,] 0.06825560 -0.045774205 0.241320621 -0.2576082002 0.01052903
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[19,] 0.11114967 -0.112041969 -0.255536862 -0.0306157349 0.21260310
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[22,] 0.16108067 -0.005199906 0.097311938 0.0524925156 -0.22578883
[23,] 0.08040149 0.036613763 -0.271326190 0.2275175465 -0.26132905
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[30,] -0.10841549 0.004481332 -0.455849089 -0.1045247595 -0.18219395
[,16] [,17] [,18] [,19] [,20]
[1,] -0.302978265 0.04648511 0.235505855 -0.288643921 0.192834248
[2,] -0.084266970 0.19187672 0.095042709 -0.084371641 -0.078414558
[3,] 0.079219250 0.19144928 0.107188972 0.235473571 -0.134236048
[4,] 0.043632514 0.22050840 -0.295578638 -0.187165659 0.238403771
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[8,] -0.035612133 -0.01031782 -0.004532902 -0.516259111 -0.052461052
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[11,] -0.242450241 0.08247082 -0.107506811 0.044027635 0.234061902
[12,] 0.218491806 -0.11026230 -0.238010042 0.233712162 -0.181370170
[13,] -0.121571538 -0.06515895 -0.039301537 0.265140723 -0.129018638
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[15,] 0.004238635 0.12918906 -0.253472990 0.048554282 -0.333163378
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[22,] 0.158762039 -0.26302208 0.112171258 0.056978476 0.165182298
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[30,] 0.073916877 0.09289579 -0.150263241 0.083721202 0.361052742
[,21] [,22] [,23] [,24] [,25]
[1,] 0.10430404 -0.010778023 -0.248404880 0.080521994 -0.370697127
[2,] -0.06705513 0.250115784 -0.014259023 -0.220338848 0.052650654
[3,] 0.08183476 -0.154069944 0.159235955 -0.263602323 0.209819150
[4,] -0.04262406 -0.298178194 0.066380979 0.015409588 0.069607108
[5,] 0.36451827 0.145547867 0.094219205 0.229636791 0.076174289
[6,] -0.21430608 -0.046499511 -0.006297900 -0.206207869 -0.519122823
[7,] 0.45925730 0.095045252 -0.302307007 -0.019521455 -0.008106335
[8,] -0.06677337 0.165926716 0.033812848 0.212819588 0.197241807
[9,] 0.15914124 0.023604879 0.204471067 -0.010524172 0.007817897
[10,] 0.18873102 -0.418202210 0.088198235 -0.079334739 -0.082495371
[11,] 0.29717878 -0.186137629 -0.100361578 -0.209404061 0.054394846
[12,] 0.01697561 -0.054821428 0.094814546 0.002888653 0.113323231
[13,] -0.21077219 0.033058148 0.172851846 0.087546419 -0.157931896
[14,] -0.44164774 -0.178147916 -0.177039087 -0.106930830 0.278583379
[15,] -0.22928351 -0.213152691 -0.425879948 0.214952377 0.037969156
[16,] 0.07745050 -0.153209027 0.260086251 0.303479952 0.094342816
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[18,] -0.03547374 -0.016188175 0.008870007 -0.244146999 0.065142862
[19,] 0.06402456 -0.086702984 0.061509830 0.032902037 -0.055523393
[20,] -0.15656334 0.116770900 -0.075487639 0.053327199 -0.129387131
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[,26] [,27] [,28] [,29] [,30]
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[16,] -0.153093663 -0.071241304 -0.002158922 -0.007270822 -0.1825742
[17,] -0.076564537 0.397223695 0.140219067 -0.113954414 -0.1825742
[18,] 0.119673677 0.060580859 0.213002205 -0.392857450 -0.1825742
[19,] 0.058245261 0.277228254 0.283570649 0.268001882 -0.1825742
[20,] -0.303666383 -0.349483839 0.142228793 -0.141783417 -0.1825742
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[26,] -0.075498343 0.164622788 -0.269775388 0.203203469 -0.1825742
[27,] 0.238980218 -0.330329119 0.136583184 -0.209117902 -0.1825742
[28,] -0.102176913 0.095629431 0.198618375 -0.028459840 -0.1825742
[29,] -0.132570477 -0.045984634 -0.339787294 -0.167374869 -0.1825742
[30,] -0.069305205 0.103893069 -0.203435054 -0.217226641 -0.1825742
$topK
[1] 2
$TW.stat
TW1 TW2 TW3 TW4 TW5 TW6 TW7
-1.2819870 -2.9899815 -3.0960090 -2.8923396 -2.6777464 -2.3727005 -1.7566232
TW8 TW9 TW10 TW11 TW12 TW13 TW14
-2.8938323 -2.9842973 -2.9426116 -2.8322269 -2.4496598 -2.0954053 -2.5480111
TW15 TW16 TW17 TW18 TW19 TW20 TW21
-2.3561102 -1.9973977 -1.4000072 -1.2622768 -0.7700852 -1.1296115 -1.0348205
TW22 TW23 TW24 TW25 TW26 TW27 TW28
-2.3009282 -1.6129168 -1.8711287 -1.0970003 -0.7496939 -0.5688249 -0.9160335
TW29
NaN
$topK.eigenvalues
[1] 1.0618076 0.9277102
$topK.eigenvectors
[,1] [,2]
[1,] -0.052316361 0.060451073
[2,] -0.155470384 0.203357995
[3,] -0.283658854 0.012037621
[4,] -0.251370763 -0.088312791
[5,] -0.165277299 0.320601766
[6,] 0.081874647 0.121198747
[7,] 0.062373463 -0.009972512
[8,] 0.027196470 -0.059333572
[9,] -0.136622044 0.005144760
[10,] -0.191498047 -0.069468261
[11,] 0.344664298 -0.028486800
[12,] 0.261463541 -0.030004292
[13,] -0.001028412 -0.121306169
[14,] -0.070320996 0.234651147
[15,] -0.048070914 -0.204739867
[16,] 0.277020274 0.254364666
[17,] 0.407803972 0.079343302
[18,] 0.221831107 -0.446192331
[19,] 0.184902973 0.202032385
[20,] -0.021137647 0.360879677
[21,] -0.046007927 -0.125965433
[22,] 0.127284697 -0.286992678
[23,] 0.024195836 0.165705043
[24,] 0.129681700 -0.116744522
[25,] 0.096536618 -0.069019214
[26,] -0.219856804 -0.129941108
[27,] -0.019563946 0.137858977
[28,] -0.136443593 -0.275019804
[29,] -0.249979894 -0.104318042
[30,] -0.198205711 0.008190238
$runtime
elapsed
0.014
[1] TRUE TRUE TRUE
AssocTests documentation built on Jan. 13, 2021, 5:09 a.m.
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Description Usage Arguments Details Value Author(s) References Examples
View source: R/EigenStrat_main.R
Description
Find the eigenvectors of the similarity matrix among the subjects used for correcting for population stratification in the population-based genetic association studies.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | eigenstrat(
genoFile,
outFile.Robj = "out.list",
outFile.txt = "out.txt",
rm.marker.index = NULL,
rm.subject.index = NULL,
miss.val = 9,
num.splits = 10,
topK = NULL,
signt.eigen.level = 0.01,
signal.outlier = FALSE,
iter.outlier = 5,
sigma.thresh = 6
)
|
Arguments
genoFile |
a txt file containing the genotypes (0, 1, 2, or 9). The element of the file in Row i and Column j represents the genotype at the ith marker of the jth subject. 0, 1, and 2 denote the number of risk alleles, and 9 (default) is for the missing genotype. |
outFile.Robj |
the name of an R object for saving the list of
the results which is the same as the return value of this
function. The default is " |
outFile.txt |
a txt file for saving the eigenvectors corresponding to the top significant eigenvalues. |
rm.marker.index |
a numeric vector for the indices of the
removed markers. The default is |
rm.subject.index |
a numeric vector for the indices of the
removed subjects. The default is |
miss.val |
the number representing the missing data in the
input data. The default is |
num.splits |
the number of groups into which the markers are
split. The default is |
topK |
the number of eigenvectors to return. If |
signt.eigen.level |
a numeric value which is the significance
level of the Tracy-Widom test. It should be |
signal.outlier |
logical. If |
iter.outlier |
a numeric value that is the iteration time for
finding the outliers of the subjects. The default is |
sigma.thresh |
a numeric value that is the lower limit for
eliminating the outliers. The default is |
Details
Suppose that a total of n cases and controls are randomly enrolled in the source population and a panel of m single-nucleotide polymorphisms are genotyped. The genotype at a marker locus is coded as 0, 1, or 2, with the value corresponding to the copy number of risk alleles. All the genotypes are given in the form of a m*n matrix, in which the element in the ith row and the jth column represents the genotype of the jth subject at the ith marker. This function calculates the top eigenvectors or the eigenvectors with significant eigenvalues of the similarity matrix among the subjects to infer the potential population structure. See also tw.
Value
eigenstrat returns a list, which contains the following components:
num.markers | the number of markers excluding the removed markers. | ||
num.subjects | the number of subjects excluding the outliers. | ||
rm.marker.index | the indices of the removed markers. | ||
rm.subject.index | the indices of the removed subjects. | ||
TW.level | the significance level of the Tracy-Widom test. | ||
signal.outlier | dealing with the outliers in the subjects or not. | ||
iter.outlier | the iteration time for finding the outliers. | ||
sigma.thresh | the lower limit for eliminating the outliers. | ||
num.outliers | the number of outliers. | ||
outliers.index | the indices of the outliers. | ||
num.used.subjects | the number of the used subjects. | ||
used.subjects.index | the indices of the used subjects. | ||
similarity.matrix | the similarity matrix among the subjects. | ||
eigenvalues | the eigenvalues of the similarity matrix. | ||
eigenvectors | the eigenvectors corresponding to the eigenvalues. | ||
topK | the number of significant eigenvalues. | ||
TW.stat | the observed values of the Tracy-Widom statistics. | ||
topK.eigenvalues | the top eigenvalues. | ||
topK.eigenvectors | the eigenvectors corresponding to the top eigenvalues. | ||
runtime | the running time of this function. |
Author(s)
Lin Wang, Wei Zhang, and Qizhai Li.
References
Lin Wang, Wei Zhang, and Qizhai Li. AssocTests: An R Package for Genetic Association Studies. Journal of Statistical Software. 2020; 94(5): 1-26.
AL Price, NJ Patterson, RM Plenge, ME Weinblatt, NA Shadick, and D Reich. Principal Components Analysis Corrects for Stratification in Genome-Wide Association Studies. Nature Genetics. 2006; 38(8): 904-909.
N Patterson, AL Price, and D Reich. Population Structure and Eigenanalysis. PloS Genetics. 2006; 2(12): 2074-2093.
CA Tracy and H Widom. Level-Spacing Distributions and the Airy Kernel. Communications in Mathematical Physics. 1994; 159(1): 151-174.
Examples
1 2 3 4 5 6 7 8 9 | eigenstratG.eg <- matrix(rbinom(3000, 2, 0.5), ncol = 30)
write.table(eigenstratG.eg, file = "eigenstratG.eg.txt", quote = FALSE,
sep = "", row.names = FALSE, col.names = FALSE)
eigenstrat(genoFile = "eigenstratG.eg.txt", outFile.Robj = "eigenstrat.result.list",
outFile.txt = "eigenstrat.result.txt", rm.marker.index = NULL,
rm.subject.index = NULL, miss.val = 9, num.splits = 10,
topK = NULL, signt.eigen.level = 0.01, signal.outlier = FALSE,
iter.outlier = 5, sigma.thresh = 6)
file.remove("eigenstratG.eg.txt", "eigenstrat.result.list", "eigenstrat.result.txt")
|
Example output
Loading required package: cluster
Loading required package: mvtnorm
Loading required package: combinat
Attaching package: ‘combinat’
The following object is masked from ‘package:utils’:
combn
Loading required package: fExtremes
Loading required package: timeDate
Loading required package: timeSeries
Loading required package: fBasics
Loading required package: fGarch
$num.markers
[1] 100
$num.subjects
[1] 30
$rm.marker.index
NULL
$rm.subject.index
NULL
$TW.level
[1] 0.01
$signal.outlier
[1] FALSE
$iter.outlier
[1] 5
$sigma.thresh
[1] 6
$num.outliers
NULL
$outliers.index
NULL
$num.used.subjects
[1] 30
$used.subjects.index
[1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
[26] 26 27 28 29 30
$similarity.matrix
[,1] [,2] [,3] [,4] [,5]
[1,] 0.504823019 -0.002065908 0.019716344 0.017508800 -0.0234256469
[2,] -0.002065908 0.412586495 0.099376365 -0.030928017 -0.0151805797
[3,] 0.019716344 0.099376365 0.435454075 -0.001681213 -0.0036751697
[4,] 0.017508800 -0.030928017 -0.001681213 0.478222477 0.0356755506
[5,] -0.023425647 -0.015180580 -0.003675170 0.035675551 0.5080335960
[6,] -0.066815778 -0.014831689 0.045039495 -0.003358736 0.0097408427
[7,] -0.026632986 -0.027218554 -0.035487456 -0.056671432 -0.0305276893
[8,] -0.008763545 -0.029820411 0.052253502 -0.058023810 0.0169058163
[9,] 0.022021391 -0.036684528 0.003397999 0.026334665 -0.0709783066
[10,] -0.042784836 -0.002412424 0.009613859 0.009292651 0.0143934186
[11,] -0.059843402 -0.010238596 -0.059249078 -0.038370832 -0.0216584848
[12,] 0.113093129 -0.080305260 -0.038139493 -0.009161599 -0.0509788261
[13,] 0.017808402 -0.053373534 -0.032172434 -0.040343938 -0.0357359304
[14,] 0.038678751 -0.032034676 -0.030302322 -0.002340386 0.0652665953
[15,] -0.036695494 0.003365073 0.014793146 -0.014337428 -0.0083887407
[16,] -0.014196467 0.067742857 -0.064371596 -0.032900700 -0.0491801549
[17,] -0.062225225 -0.031676494 -0.142514178 -0.066837198 -0.0853605091
[18,] -0.069168315 -0.118779083 -0.137058403 -0.028054484 -0.1221967780
[19,] -0.026119427 -0.017034170 -0.055331901 -0.138344811 -0.0396886184
[20,] -0.082771705 0.089593870 -0.060927776 -0.069476878 0.0657200786
[21,] 0.043654299 -0.046787529 -0.035934168 -0.056091098 -0.0002480018
[22,] -0.041840028 -0.043453304 0.050279034 -0.092508728 -0.0847862815
[23,] -0.021670032 -0.012699839 -0.041203777 -0.033862616 0.1362988064
[24,] 0.017667074 -0.073906804 -0.032537717 0.059584200 -0.0155739114
[25,] -0.048420802 -0.027878309 -0.026440215 -0.058571764 -0.0216256351
[26,] 0.022627900 0.002664484 0.043984958 0.013066337 0.0007928886
[27,] 0.002729591 -0.068081965 -0.006351246 -0.014228882 -0.0204527025
[28,] -0.109946516 0.013696196 -0.027754359 0.055696333 -0.0711087070
[29,] -0.070063528 0.053344137 0.033888743 0.095914955 -0.0218186030
[30,] -0.006879060 0.033022196 0.023334983 0.054798581 -0.0602383162
[,6] [,7] [,8] [,9] [,10]
[1,] -0.066815778 -0.026632986 -0.0087635446 0.022021391 -0.042784836
[2,] -0.014831689 -0.027218554 -0.0298204110 -0.036684528 -0.002412424
[3,] 0.045039495 -0.035487456 0.0522535017 0.003397999 0.009613859
[4,] -0.003358736 -0.056671432 -0.0580238101 0.026334665 0.009292651
[5,] 0.009740843 -0.030527689 0.0169058163 -0.070978307 0.014393419
[6,] 0.448431389 0.048814001 0.0474228188 -0.060570417 -0.066232519
[7,] 0.048814001 0.453903209 -0.0448537419 -0.002712878 -0.048449226
[8,] 0.047422819 -0.044853742 0.4797587923 -0.065700064 -0.009139813
[9,] -0.060570417 -0.002712878 -0.0657000644 0.496668869 -0.026233145
[10,] -0.066232519 -0.048449226 -0.0091398134 -0.026233145 0.524024931
[11,] -0.034360623 -0.065362631 -0.0066046443 -0.076721608 -0.079800805
[12,] -0.045288911 -0.004542875 0.0018622741 -0.054898551 -0.069553132
[13,] -0.056178396 0.032632612 -0.0186640743 0.032816688 0.007036464
[14,] 0.022286521 0.052514456 -0.0509239054 0.012660066 -0.042942126
[15,] -0.062242837 -0.081032007 0.0067323337 -0.042571126 0.013452650
[16,] 0.094116785 0.010716276 -0.0811530550 -0.090376333 -0.084227388
[17,] -0.013453776 0.052765280 -0.0061432520 -0.075267516 -0.011026785
[18,] -0.042797230 0.088235398 0.0354482418 -0.024066459 -0.028497432
[19,] -0.013148117 -0.032202733 0.0454802042 0.008245440 -0.057009815
[20,] -0.045692356 0.002279193 -0.0601217646 0.066753756 0.058907872
[21,] 0.020867150 -0.001792797 -0.0341970371 0.028195863 -0.027771978
[22,] 0.053730371 -0.046746067 -0.0300731633 0.043589081 -0.031485059
[23,] -0.026309423 -0.120102809 -0.0002240495 -0.039054142 -0.052575263
[24,] -0.007373267 -0.109432550 -0.0612157806 -0.026856649 0.088808797
[25,] -0.013651922 0.016322992 -0.0152624826 -0.014625371 -0.048481772
[26,] -0.082710687 0.008527775 -0.0352237165 -0.035076475 -0.037797421
[27,] -0.021443239 -0.033258645 -0.0139609811 0.079339200 -0.036284516
[28,] -0.051874188 -0.024122043 0.0039739171 -0.063976005 0.021964853
[29,] -0.082667195 -0.003186706 -0.0050250780 -0.011714463 0.032824875
[30,] 0.020551930 0.027624634 -0.0547435302 -0.001938980 0.022385085
[,11] [,12] [,13] [,14] [,15]
[1,] -0.059843402 0.1130931286 0.017808402 0.038678751 -0.036695494
[2,] -0.010238596 -0.0803052603 -0.053373534 -0.032034676 0.003365073
[3,] -0.059249078 -0.0381394932 -0.032172434 -0.030302322 0.014793146
[4,] -0.038370832 -0.0091615986 -0.040343938 -0.002340386 -0.014337428
[5,] -0.021658485 -0.0509788261 -0.035735930 0.065266595 -0.008388741
[6,] -0.034360623 -0.0452889112 -0.056178396 0.022286521 -0.062242837
[7,] -0.065362631 -0.0045428745 0.032632612 0.052514456 -0.081032007
[8,] -0.006604644 0.0018622741 -0.018664074 -0.050923905 0.006732334
[9,] -0.076721608 -0.0548985509 0.032816688 0.012660066 -0.042571126
[10,] -0.079800805 -0.0695531325 0.007036464 -0.042942126 0.013452650
[11,] 0.490527357 -0.0265183761 0.020555301 -0.050339978 0.016986796
[12,] -0.026518376 0.5401764223 -0.039715620 -0.029212923 -0.012044908
[13,] 0.020555301 -0.0397156196 0.503294346 0.006652993 -0.015493307
[14,] -0.050339978 -0.0292129225 0.006652993 0.474527884 -0.137034186
[15,] 0.016986796 -0.0120449082 -0.015493307 -0.137034186 0.455990956
[16,] 0.068854006 -0.0230079120 -0.044423142 0.015941229 -0.078910164
[17,] 0.093199320 0.0915409863 0.010685585 -0.074304333 -0.015147032
[18,] 0.055308924 -0.0162775178 0.041380480 -0.008161483 -0.011083954
[19,] 0.045510792 0.0670018982 -0.028257696 -0.015544949 -0.031942334
[20,] 0.001783388 -0.0685001847 -0.042695655 0.059286070 -0.046017270
[21,] -0.076003968 -0.0342879894 -0.027518508 -0.027566589 0.059443090
[22,] 0.010517969 0.0007839686 -0.033216554 -0.082171787 -0.015521524
[23,] -0.039707144 0.0208350033 -0.083286631 -0.072699748 0.023817939
[24,] 0.060654440 0.0524484500 -0.022741829 -0.043696660 0.023326978
[25,] 0.035356891 -0.0154301580 -0.089261953 0.001474022 0.008146694
[26,] -0.084507008 -0.0246896258 0.012422638 -0.017528398 0.060554831
[27,] -0.013478857 -0.0458818025 -0.006774995 0.021315889 -0.021770095
[28,] 0.015880038 -0.0267500522 -0.039892156 -0.018345282 0.007556836
[29,] -0.076505040 -0.0966679637 -0.008684902 -0.016957757 -0.001052312
[30,] -0.095864150 -0.0758884513 0.033145746 -0.018496988 -0.062882603
[,16] [,17] [,18] [,19] [,20]
[1,] -0.0141964675 -0.0622252252 -0.0691683149 -0.026119427 -0.082771705
[2,] 0.0677428565 -0.0316764938 -0.1187790832 -0.017034170 0.089593870
[3,] -0.0643715963 -0.1425141782 -0.1370584027 -0.055331901 -0.060927776
[4,] -0.0329006996 -0.0668371982 -0.0280544844 -0.138344811 -0.069476878
[5,] -0.0491801549 -0.0853605091 -0.1221967780 -0.039688618 0.065720079
[6,] 0.0941167853 -0.0134537761 -0.0427972297 -0.013148117 -0.045692356
[7,] 0.0107162761 0.0527652802 0.0882353979 -0.032202733 0.002279193
[8,] -0.0811530550 -0.0061432520 0.0354482418 0.045480204 -0.060121765
[9,] -0.0903763329 -0.0752675160 -0.0240664589 0.008245440 0.066753756
[10,] -0.0842273885 -0.0110267847 -0.0284974322 -0.057009815 0.058907872
[11,] 0.0688540061 0.0931993204 0.0553089240 0.045510792 0.001783388
[12,] -0.0230079120 0.0915409863 -0.0162775178 0.067001898 -0.068500185
[13,] -0.0444231421 0.0106855849 0.0413804802 -0.028257696 -0.042695655
[14,] 0.0159412290 -0.0743043330 -0.0081614833 -0.015544949 0.059286070
[15,] -0.0789101640 -0.0151470317 -0.0110839544 -0.031942334 -0.046017270
[16,] 0.5823670493 0.0372928558 0.0004992043 0.020347005 -0.023763547
[17,] 0.0372928558 0.5690167773 -0.0682012530 -0.007131014 0.039497178
[18,] 0.0004992043 -0.0682012530 0.5631755789 0.007450219 -0.078427527
[19,] 0.0203470055 -0.0071310138 0.0074502192 0.474959738 0.065853303
[20,] -0.0237635465 0.0394971780 -0.0784275267 0.065853303 0.526096317
[21,] -0.0693806953 -0.0157527962 -0.0231700596 -0.022320415 -0.067310151
[22,] -0.0349822950 -0.0230991065 0.0733213615 -0.088207753 -0.001237124
[23,] -0.0042269645 -0.0134778603 -0.0290025414 0.012700002 -0.021679670
[24,] 0.0353523621 -0.0007168739 0.0309943168 -0.068027313 -0.062461968
[25,] -0.0707332869 0.0415734214 0.0268405081 -0.013326041 -0.047940644
[26,] -0.0800097273 -0.0772820356 0.0177333782 -0.062426656 -0.018267844
[27,] 0.0006960394 0.0251568877 -0.1140944587 0.037512812 -0.047420230
[28,] -0.0290762907 -0.0369973422 0.0155370072 -0.073801270 -0.088193801
[29,] -0.0705339035 -0.0477947203 0.0071953624 0.027748285 0.004433983
[30,] 0.0115279531 -0.0863189921 -0.0440830016 -0.022944666 -0.047298915
[,21] [,22] [,23] [,24] [,25]
[1,] 0.0436542994 -0.0418400282 -0.0216700320 0.0176670743 -0.048420802
[2,] -0.0467875292 -0.0434533036 -0.0126998388 -0.0739068044 -0.027878309
[3,] -0.0359341677 0.0502790345 -0.0412037771 -0.0325377170 -0.026440215
[4,] -0.0560910977 -0.0925087281 -0.0338626162 0.0595841996 -0.058571764
[5,] -0.0002480018 -0.0847862815 0.1362988064 -0.0155739114 -0.021625635
[6,] 0.0208671504 0.0537303709 -0.0263094233 -0.0073732669 -0.013651922
[7,] -0.0017927970 -0.0467460667 -0.1201028093 -0.1094325499 0.016322992
[8,] -0.0341970371 -0.0300731633 -0.0002240495 -0.0612157806 -0.015262483
[9,] 0.0281958633 0.0435890812 -0.0390541420 -0.0268566488 -0.014625371
[10,] -0.0277719780 -0.0314850595 -0.0525752627 0.0888087969 -0.048481772
[11,] -0.0760039676 0.0105179693 -0.0397071441 0.0606544402 0.035356891
[12,] -0.0342879894 0.0007839686 0.0208350033 0.0524484500 -0.015430158
[13,] -0.0275185079 -0.0332165543 -0.0832866314 -0.0227418290 -0.089261953
[14,] -0.0275665886 -0.0821717870 -0.0726997484 -0.0436966599 0.001474022
[15,] 0.0594430898 -0.0155215242 0.0238179391 0.0233269783 0.008146694
[16,] -0.0693806953 -0.0349822950 -0.0042269645 0.0353523621 -0.070733287
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[12,] 0.160805992 -0.242695466 -0.219601281 -0.187121574 -0.1825742
[13,] 0.060640771 -0.173125687 0.125652366 0.064437529 -0.1825742
[14,] 0.011989449 0.141929423 -0.093161305 0.151687448 -0.1825742
[15,] -0.011567208 0.112007358 0.001404080 -0.022975700 -0.1825742
[16,] -0.153093663 -0.071241304 -0.002158922 -0.007270822 -0.1825742
[17,] -0.076564537 0.397223695 0.140219067 -0.113954414 -0.1825742
[18,] 0.119673677 0.060580859 0.213002205 -0.392857450 -0.1825742
[19,] 0.058245261 0.277228254 0.283570649 0.268001882 -0.1825742
[20,] -0.303666383 -0.349483839 0.142228793 -0.141783417 -0.1825742
[21,] -0.035221597 -0.288576084 0.039530450 -0.012772880 -0.1825742
[22,] 0.123716475 0.091600797 0.060077464 0.184480898 -0.1825742
[23,] -0.171867962 -0.070615310 -0.069194519 0.239371850 -0.1825742
[24,] -0.140465791 0.045031952 0.025208448 0.210664470 -0.1825742
[25,] 0.081804592 -0.180409995 0.071437575 -0.023518489 -0.1825742
[26,] -0.075498343 0.164622788 -0.269775388 0.203203469 -0.1825742
[27,] 0.238980218 -0.330329119 0.136583184 -0.209117902 -0.1825742
[28,] -0.102176913 0.095629431 0.198618375 -0.028459840 -0.1825742
[29,] -0.132570477 -0.045984634 -0.339787294 -0.167374869 -0.1825742
[30,] -0.069305205 0.103893069 -0.203435054 -0.217226641 -0.1825742
$topK
[1] 2
$TW.stat
TW1 TW2 TW3 TW4 TW5 TW6 TW7
-1.2819870 -2.9899815 -3.0960090 -2.8923396 -2.6777464 -2.3727005 -1.7566232
TW8 TW9 TW10 TW11 TW12 TW13 TW14
-2.8938323 -2.9842973 -2.9426116 -2.8322269 -2.4496598 -2.0954053 -2.5480111
TW15 TW16 TW17 TW18 TW19 TW20 TW21
-2.3561102 -1.9973977 -1.4000072 -1.2622768 -0.7700852 -1.1296115 -1.0348205
TW22 TW23 TW24 TW25 TW26 TW27 TW28
-2.3009282 -1.6129168 -1.8711287 -1.0970003 -0.7496939 -0.5688249 -0.9160335
TW29
NaN
$topK.eigenvalues
[1] 1.0618076 0.9277102
$topK.eigenvectors
[,1] [,2]
[1,] -0.052316361 0.060451073
[2,] -0.155470384 0.203357995
[3,] -0.283658854 0.012037621
[4,] -0.251370763 -0.088312791
[5,] -0.165277299 0.320601766
[6,] 0.081874647 0.121198747
[7,] 0.062373463 -0.009972512
[8,] 0.027196470 -0.059333572
[9,] -0.136622044 0.005144760
[10,] -0.191498047 -0.069468261
[11,] 0.344664298 -0.028486800
[12,] 0.261463541 -0.030004292
[13,] -0.001028412 -0.121306169
[14,] -0.070320996 0.234651147
[15,] -0.048070914 -0.204739867
[16,] 0.277020274 0.254364666
[17,] 0.407803972 0.079343302
[18,] 0.221831107 -0.446192331
[19,] 0.184902973 0.202032385
[20,] -0.021137647 0.360879677
[21,] -0.046007927 -0.125965433
[22,] 0.127284697 -0.286992678
[23,] 0.024195836 0.165705043
[24,] 0.129681700 -0.116744522
[25,] 0.096536618 -0.069019214
[26,] -0.219856804 -0.129941108
[27,] -0.019563946 0.137858977
[28,] -0.136443593 -0.275019804
[29,] -0.249979894 -0.104318042
[30,] -0.198205711 0.008190238
$runtime
elapsed
0.014
[1] TRUE TRUE TRUE
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