Prepares the data matrix X and the dependence structures U and Sigma for clustering and testing. If Sigma is not provided, it is estimated using an i.i.d. sample Y of the same variables,
with an associated dependence structure UY. Sample splitting can be used to generate Y from X when observations are independent.
Checks are performed to ensure the compatibility of the dimensions of the data and dependence structures, and to verify the positive-definiteness of U and Sigma.
Usage
setup.model(
X,
U = NULL,
Sigma = NULL,
Y = NULL,
UY = NULL,
precUY = NULL,
sample_split = FALSE,
nY = NULL
)Arguments
- X
Data matrix of size \(n \times p\) containing the observations and variables to be clustered and tested.
- U
Optional \(n \times n\) positive-definite matrix representing the dependence structure among observations in
X. If not provided, observations are considered independent with unit variance.- Sigma
Optional \(p \times p\) positive-definite matrix representing the dependence structure among variables in
X. If not provided, it is estimated usingYandUY.- Y
Optional \(n_Y \times p\) data matrix containing an i.i.d. sample of the same variables as in
X, used to estimateSigmawhen it is not provided. If not provided andsample_split = TRUE,Yis generated by sample splitting fromX.- UY
Optional \(n_Y \times n_Y\) positive-definite matrix representing the dependence structure among observations in
Y. If not provided, observations inYare considered independent with unit variance.- precUY
Optional \(n_Y \times n_Y\) positive-definite matrix representing the inverse of
UY. IfUYis provided butprecUYis not,precUYis computed as the inverse ofUY. If neitherUYnorprecUYis provided, observations inYare considered independent with unit variance.- sample_split
Logical indicating whether to generate
Yby sample splitting fromXwhenSigmais not provided. IfTRUE,Yis generated by randomly splitting the observations inXinto two disjoint sets, one for clustering and testing, and the other for estimatingSigma. IfFALSE, an i.i.d. sampleYmust be provided to estimateSigma.- nY
Optional integer specifying the number of observations in
Ywhensample_split = TRUE. If not provided, it defaults to half of the sample size ofX.
Value
A list containing the following elements:
- X
Data matrix of size \(n \times p\) containing the observations and variables to be clustered and tested. If
sample_split = TRUE,Xcontains only the observations used for clustering and testing after sample splitting.- U
\(n \times n\) positive-definite matrix representing the dependence structure among observations in
X. If not provided, it is set to the identity matrix.- Sigma
\(p \times p\) positive-definite matrix representing the dependence structure among variables in
X. If not provided, it is estimated usingYandUY.
See also
Other Utilities:
ARI(),
is.CS(),
preserve.cl()
Examples
# Example with independent observations and known Sigma
X <- matrix(rnorm(100 * 5), nrow = 100, ncol = 5)
Sigma <- diag(5)
setup_result <- setup.model(X = X, Sigma = Sigma)
#> U is not provided: observations are considered independent with unit variance.
print(setup_result)
#> $X
#> 100 x 5 Matrix of class "dgeMatrix"
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1.51167228 -1.514497008 1.11343318 -0.722753124 -1.403933837
#> [2,] -0.47569828 -0.061707422 0.83739440 -0.629164665 1.440893147
#> [3,] 0.79791644 -0.147270790 0.31451677 -1.816206055 -0.981359991
#> [4,] -0.97400256 1.541593069 0.22221807 -0.259289098 1.474244904
#> [5,] 0.68937270 -0.981855669 -0.84361539 0.334632273 -0.991197245
#> [6,] -0.95583910 0.496578173 0.44380533 -1.427167613 -0.094497345
#> [7,] -1.23170706 1.696947881 0.05579711 1.938628233 -2.875141684
#> [8,] -0.95689188 -0.260736309 0.06797239 -0.759530213 -0.246866101
#> [9,] -0.86978287 -0.705928586 -0.20196174 -2.278776142 0.014744485
#> [10,] -0.91068068 -0.161178506 -1.15801525 -0.114050766 -1.919087703
#> [11,] 0.74127631 0.501321828 -0.59274327 2.351856666 -0.287813744
#> [12,] 0.06851153 -1.013539670 0.76606538 1.596320803 -0.346637445
#> [13,] -0.32375075 1.614752235 0.03892812 1.277445511 -1.839588585
#> [14,] -1.08650305 0.005641985 0.01464681 0.788970858 0.898588941
#> [15,] -1.01592895 -2.904899060 -0.18631697 0.461465382 -1.212855011
#> [16,] -0.76779018 -1.107164819 1.40059083 -0.438069134 -0.218964232
#> [17,] -1.11972006 1.547566933 0.01848557 -1.507807009 0.564268161
#> [18,] -0.44817424 -0.976830350 0.24919601 -2.222946131 -0.525434376
#> [19,] 0.47173637 -0.101503448 0.14922074 -1.178672442 0.744374225
#> [20,] -1.18049068 0.042650250 -0.96323318 -1.782760224 0.128981753
#> [21,] 1.47025700 -1.596718014 -0.06646677 -0.987919139 1.488274257
#> [22,] -1.31142059 0.490967373 1.28692204 0.728488688 -0.662681951
#> [23,] -0.09652492 0.421603365 0.45812526 -0.884684915 -1.160655001
#> [24,] 2.36971991 1.873903899 -1.45202829 -1.538441417 0.358774234
#> [25,] 0.89062648 1.034514324 0.07734228 -1.044375407 -0.194846384
#> [26,] -0.25218316 0.081810310 0.55989527 -1.718136190 -0.295282008
#> [27,] -0.86576375 -0.082523762 -0.07494657 0.803757539 0.496640424
#> [28,] 0.58258600 0.606073431 0.78269770 -1.501787170 0.484912788
#> [29,] -0.01252935 -0.887420145 -0.17266856 -0.145499071 0.018784501
#> [30,] -0.37485476 0.105421390 -1.05129378 0.579458612 0.634774565
#> [31,] 0.31788574 0.352874473 0.72945128 1.201525576 0.754444088
#> [32,] -0.48880563 0.550393358 0.26266524 1.893910787 0.833589035
#> [33,] 2.65865803 -1.134330969 0.54365786 -1.760226343 0.965761296
#> [34,] 1.68027820 1.462351539 1.04106030 0.924546803 1.293879968
#> [35,] 0.77958401 0.702116711 0.19750615 -0.556542168 -0.136551021
#> [36,] 0.71324052 2.507111148 -1.62957829 -0.180584138 -0.440138688
#> [37,] -0.54288194 -1.890027144 0.12104023 1.447440285 -1.227283914
#> [38,] 0.88577837 -0.589812790 -1.63742195 -0.607131453 -0.237653068
#> [39,] -0.34859468 -1.714502297 -0.53104311 0.679362430 -0.926858157
#> [40,] -1.00805458 -0.420997898 0.95367979 -0.093557640 0.411235356
#> [41,] 1.88318254 0.310141377 -1.72065066 -0.490086292 -0.198864577
#> [42,] -0.92897108 1.702570586 0.10632062 1.410659383 -0.557449639
#> [43,] -0.29419645 -0.443384804 -0.60866850 -0.224573790 -0.977157122
#> [44,] -0.61495027 -1.198597083 -0.30119698 -0.212495490 0.060735249
#> [45,] -0.94707579 -0.307380914 0.97620252 0.696378474 -0.597229480
#> [46,] 0.59897515 0.621054203 0.45600867 0.915182505 -1.258948697
#> [47,] -1.52361488 0.181902191 1.29440807 -0.923374316 -1.410047202
#> [48,] -0.20618900 1.318400931 -1.13320221 1.146873263 1.101304079
#> [49,] -0.57429541 -0.298909313 -0.86946035 -0.635865043 -0.677242026
#> [50,] -1.39016604 -1.648221742 -0.75497029 -0.886443308 -0.762173508
#> [51,] -0.07041738 0.951498470 -0.12963535 -2.333136685 -0.291748602
#> [52,] -0.43087953 -1.113122953 -1.00180134 -0.145490805 -0.575188529
#> [53,] -0.59222537 0.616966476 -0.81986828 0.316964024 -0.443941868
#> [54,] 0.98111616 0.513493716 -0.97455247 -0.707469988 -0.312570444
#> [55,] 0.53240936 0.369459104 0.60430941 1.242155558 -0.603004426
#> [56,] -0.09045612 1.723894131 0.54878759 0.620152195 -1.093934720
#> [57,] 0.15649049 -0.206144567 0.91643266 0.099903068 0.714706191
#> [58,] -0.73731169 -1.314195140 2.66156637 1.807703488 -0.108812263
#> [59,] -0.20134121 0.063474096 -0.18025707 -1.502429979 -1.443797935
#> [60,] 1.10217660 -0.231977451 0.68501477 0.285640465 0.806123264
#> [61,] -0.01674826 0.635060328 3.26641452 0.845706964 -1.739835078
#> [62,] 0.16178863 1.634644285 0.56060046 -0.995342638 -0.401320309
#> [63,] 2.02476139 -1.808327579 -0.06901730 -0.256854125 -0.287582489
#> [64,] -0.70369425 -0.213885951 -0.97244294 -0.055856043 -0.938407400
#> [65,] 0.96079238 0.070366141 -0.54658659 -0.445005240 0.287667139
#> [66,] 1.79048505 0.549707670 -1.68869233 0.069695103 -1.505401124
#> [67,] -1.06416516 -0.696823546 -1.57237270 -0.154671706 1.519297013
#> [68,] 0.01763655 0.390565942 -0.40498716 -0.831263459 0.367409356
#> [69,] -0.38990863 0.381411259 0.31928642 0.761544352 1.699862409
#> [70,] -0.49083275 -0.012372770 0.04042768 -0.576506933 0.644196977
#> [71,] -1.04571765 -0.124434986 -0.39000956 -0.626368228 -1.687801029
#> [72,] -0.89621126 1.466744593 -1.81922223 0.481335326 0.647645994
#> [73,] 1.26938716 0.673928676 0.65918071 1.695271084 0.448794227
#> [74,] 0.59384095 1.956425263 0.45962167 -1.761226294 1.026302158
#> [75,] 0.77563432 -0.269041012 1.61662634 0.198013015 1.074978223
#> [76,] 1.55737038 -1.244551518 -1.85619049 0.397349099 0.458309613
#> [77,] -0.36540180 -0.395702923 -0.28682388 0.029225495 0.631586758
#> [78,] 0.81655645 0.097396655 1.75032189 2.560273389 -0.580466398
#> [79,] -0.06063478 -0.238386950 0.11641361 1.257127712 1.584192142
#> [80,] -0.50137832 -0.411827957 1.38425316 -0.534537686 -1.763992940
#> [81,] 0.92606273 -1.577218049 0.57422091 -0.625227429 -1.880621970
#> [82,] 0.03693769 -0.797276101 0.13649081 0.913848687 -1.291719044
#> [83,] -1.06620017 -1.096236783 0.91421599 1.007199535 0.909670446
#> [84,] -0.23845635 0.308308749 -1.80082632 0.719291823 -1.107755682
#> [85,] 1.49522344 0.344795124 -0.33988064 -0.604711661 -0.384123875
#> [86,] 1.17215855 1.539648088 0.60626457 0.539054406 0.082734834
#> [87,] -1.45770721 -0.329514192 1.34113031 -0.076830886 -0.483882474
#> [88,] 0.09505623 0.948389351 0.76728729 1.849919560 -2.084741125
#> [89,] 0.84766496 -0.479255587 0.19372567 -0.854907551 1.167586964
#> [90,] -1.62436453 -1.514886795 1.14056669 0.032637295 -0.076825771
#> [91,] 1.40856336 0.434536656 0.01386480 -1.025059481 0.530421395
#> [92,] -0.54176036 -0.519536667 -1.10530591 -0.982249076 0.004908796
#> [93,] 0.27866472 -0.834559033 -0.02516264 0.004101957 -0.530231430
#> [94,] -0.19397274 -0.756647609 -0.16367334 -0.233427178 1.514866654
#> [95,] 1.57615818 1.089503495 0.37005975 -0.498888219 0.815459636
#> [96,] -1.47554764 1.572432917 -0.38082454 1.549712963 -1.506521863
#> [97,] -0.14460821 1.007364366 0.65295237 0.087496917 -1.157180172
#> [98,] -0.95320315 -0.273157993 2.06134181 1.318701131 1.301554937
#> [99,] 0.40654273 -1.309679542 -1.79664494 -0.981224119 -0.905640775
#> [100,] 2.22926220 0.222573831 0.58407712 -0.245622588 0.015563481
#>
#> $U
#> 100 x 100 diagonal matrix of class "ddiMatrix", with diagonal entries
#> [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
#> [38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
#> [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
#>
#> $Sigma
#> 5 x 5 diagonal matrix of class "ddiMatrix"
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1 . . . .
#> [2,] . 1 . . .
#> [3,] . . 1 . .
#> [4,] . . . 1 .
#> [5,] . . . . 1
#>
# Example with dependent observations and unknown Sigma, using sample splitting
X <- matrix(rnorm(100 * 5), nrow = 100, ncol = 5)
U <- matrix(0.3, nrow = 100, ncol = 100)
diag(U) <- 1
setup_result <- setup.model(X = X, U = U, sample_split = TRUE)
#> Sigma not provided: plugging an over-estimate.
print(setup_result)
#> $X
#> 50 x 5 Matrix of class "dgeMatrix"
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] -0.510742458 -1.08542241 -0.65483531 0.24195408 -2.302512517
#> [2,] -0.291842736 0.95983242 1.18657520 0.07035250 1.175894863
#> [3,] 0.649421934 -0.25639230 0.95086737 -0.39223091 -0.501007298
#> [4,] 1.276020709 -0.98214721 0.20017731 -0.28355300 0.387769029
#> [5,] -0.047611220 0.32690556 -0.84719049 -1.16580298 -1.817656629
#> [6,] -0.003580270 1.18372412 0.69510462 -2.05653763 1.366606514
#> [7,] -2.034572643 -0.08861692 -1.57291787 -0.15417450 0.190588625
#> [8,] 1.963858056 0.08681257 -1.15491866 1.21615086 -1.405579071
#> [9,] 0.706528773 -0.29500503 -0.92520123 -0.51117114 2.172244168
#> [10,] -0.162257551 0.38454372 -0.82843838 -0.21273973 -0.261532000
#> [11,] 0.780699292 -0.28596579 1.41644085 -3.08236362 -0.910911965
#> [12,] -0.429033676 1.95027779 2.96174336 0.32559371 -1.658033573
#> [13,] 0.508776266 0.96445407 -0.15782718 -0.56553782 0.400994752
#> [14,] -1.446889743 1.03840459 1.81942527 0.69889868 -2.348004883
#> [15,] 1.019512829 1.76887362 0.86374255 0.88071510 0.730477590
#> [16,] 1.178546976 -0.57165015 -1.56644322 -0.22775497 0.755255204
#> [17,] -0.010258765 -1.47028289 0.51545597 0.13630075 0.788566380
#> [18,] 0.268624871 -1.11036644 0.69621951 1.84340823 -0.342063446
#> [19,] 1.342028872 0.25440339 0.02542110 -1.40539172 1.823848892
#> [20,] -0.937000891 -2.71592529 2.24535874 0.79415451 -0.971565897
#> [21,] -0.711413598 -0.05667276 1.24835851 1.35439733 -1.278265506
#> [22,] -0.943514417 -1.30942995 0.24555952 -1.03745248 0.046567748
#> [23,] -0.274367308 -0.70669129 -0.77872356 -0.03617214 -0.908244134
#> [24,] 0.154468494 1.03389167 -1.79088618 -0.55435061 -0.218683231
#> [25,] -1.288653202 1.97276097 -0.16752386 -0.55886675 -0.155295420
#> [26,] 1.323700599 0.73824255 -0.01702340 -0.90795985 1.769289381
#> [27,] -0.376196737 0.92380003 -0.73357178 -0.73898176 0.156912588
#> [28,] 0.783127640 2.15270084 -1.38185471 -0.09776513 -0.571797205
#> [29,] 0.229284475 1.02950822 -0.78631016 0.95706366 0.340690847
#> [30,] 0.336850949 1.37715475 -0.74248224 0.55933417 0.735364418
#> [31,] -0.647231999 0.91481105 -0.39098025 -0.49770072 -1.024828130
#> [32,] 1.161751761 -0.15173862 -0.89040559 0.08633493 -1.915180723
#> [33,] -0.682467580 0.86857743 0.37183911 -0.96991802 1.135716960
#> [34,] -0.584849244 -1.22233197 -0.02454386 0.75550915 -1.157504888
#> [35,] 1.129936001 -0.71144470 -0.91768924 -0.70325229 0.496621993
#> [36,] 0.581201043 -1.42403167 -0.59188422 -0.28685156 -1.331908129
#> [37,] 0.379293067 -1.66934441 -0.37099306 1.84110689 1.592628620
#> [38,] -0.310740876 1.37923613 0.08792426 -0.15676431 0.061958081
#> [39,] 0.886390001 -0.91967458 -0.03472634 -1.38980264 -0.145945861
#> [40,] -1.641864750 -0.50449004 1.80637427 -1.47310399 -0.343735779
#> [41,] 0.156056926 0.52798878 -1.63913684 0.25041991 -0.002131136
#> [42,] -0.287458172 -0.46203636 2.59577184 -1.97539996 -0.814033523
#> [43,] 0.003854672 1.51344748 -0.16576500 -1.47314013 -0.628854148
#> [44,] 0.980223359 -0.43053694 1.44433440 -1.40341629 -0.953274417
#> [45,] 1.511868401 -1.34572179 0.10619132 0.42196879 -0.766182568
#> [46,] -0.645182435 -0.39889130 -1.51103873 -1.15594311 -0.808773130
#> [47,] 0.567249697 1.31560505 -0.88018810 1.38545119 0.714887190
#> [48,] 0.455884554 -0.44449642 1.06875896 -0.63849508 -0.768700129
#> [49,] -1.197934626 0.56618308 1.16673686 0.23980445 -1.877124097
#> [50,] -2.018180550 0.29032567 2.02995850 -1.00077442 -0.770522589
#>
#> $U
#> 50 x 50 Matrix of class "dsyMatrix"
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#> [1,] 1.0 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [2,] 0.3 1.0 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [3,] 0.3 0.3 1.0 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [4,] 0.3 0.3 0.3 1.0 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [5,] 0.3 0.3 0.3 0.3 1.0 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [6,] 0.3 0.3 0.3 0.3 0.3 1.0 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [7,] 0.3 0.3 0.3 0.3 0.3 0.3 1.0 0.3 0.3 0.3 0.3 0.3 0.3
#> [8,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1.0 0.3 0.3 0.3 0.3 0.3
#> [9,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1.0 0.3 0.3 0.3 0.3
#> [10,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1.0 0.3 0.3 0.3
#> [11,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1.0 0.3 0.3
#> [12,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1.0 0.3
#> [13,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1.0
#> [14,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [15,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [16,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [17,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [18,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [19,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [20,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [21,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [22,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [23,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [24,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [25,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [26,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [27,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [28,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [29,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [30,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [31,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [32,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [33,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [34,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [35,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [36,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [37,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [38,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [39,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [40,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [41,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [42,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [43,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [44,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [45,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [46,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [47,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [48,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [49,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [50,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]
#> [1,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [2,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [3,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [4,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [5,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [6,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [7,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [8,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [9,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [10,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [11,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [12,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [13,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [14,] 1.0 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [15,] 0.3 1.0 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [16,] 0.3 0.3 1.0 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [17,] 0.3 0.3 0.3 1.0 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [18,] 0.3 0.3 0.3 0.3 1.0 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [19,] 0.3 0.3 0.3 0.3 0.3 1.0 0.3 0.3 0.3 0.3 0.3 0.3
#> [20,] 0.3 0.3 0.3 0.3 0.3 0.3 1.0 0.3 0.3 0.3 0.3 0.3
#> [21,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1.0 0.3 0.3 0.3 0.3
#> [22,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1.0 0.3 0.3 0.3
#> [23,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1.0 0.3 0.3
#> [24,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1.0 0.3
#> [25,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1.0
#> [26,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [27,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [28,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [29,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [30,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [31,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [32,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [33,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [34,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [35,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [36,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [37,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [38,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [39,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [40,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [41,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [42,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [43,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [44,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [45,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [46,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [47,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [48,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [49,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [50,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37]
#> [1,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [2,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [3,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [4,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [5,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [6,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [7,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [8,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [9,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [10,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [11,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [12,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [13,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [14,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [15,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [16,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [17,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [18,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [19,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [20,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [21,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [22,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [23,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [24,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [25,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [26,] 1.0 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [27,] 0.3 1.0 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [28,] 0.3 0.3 1.0 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [29,] 0.3 0.3 0.3 1.0 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [30,] 0.3 0.3 0.3 0.3 1.0 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [31,] 0.3 0.3 0.3 0.3 0.3 1.0 0.3 0.3 0.3 0.3 0.3 0.3
#> [32,] 0.3 0.3 0.3 0.3 0.3 0.3 1.0 0.3 0.3 0.3 0.3 0.3
#> [33,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1.0 0.3 0.3 0.3 0.3
#> [34,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1.0 0.3 0.3 0.3
#> [35,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1.0 0.3 0.3
#> [36,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1.0 0.3
#> [37,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1.0
#> [38,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [39,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [40,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [41,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [42,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [43,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [44,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [45,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [46,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [47,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [48,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [49,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [50,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49]
#> [1,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [2,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [3,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [4,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [5,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [6,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [7,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [8,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [9,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [10,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [11,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [12,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [13,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [14,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [15,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [16,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [17,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [18,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [19,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [20,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [21,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [22,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [23,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [24,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [25,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [26,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [27,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [28,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [29,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [30,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [31,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [32,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [33,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [34,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [35,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [36,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [37,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [38,] 1.0 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [39,] 0.3 1.0 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [40,] 0.3 0.3 1.0 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [41,] 0.3 0.3 0.3 1.0 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [42,] 0.3 0.3 0.3 0.3 1.0 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [43,] 0.3 0.3 0.3 0.3 0.3 1.0 0.3 0.3 0.3 0.3 0.3 0.3
#> [44,] 0.3 0.3 0.3 0.3 0.3 0.3 1.0 0.3 0.3 0.3 0.3 0.3
#> [45,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1.0 0.3 0.3 0.3 0.3
#> [46,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1.0 0.3 0.3 0.3
#> [47,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1.0 0.3 0.3
#> [48,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1.0 0.3
#> [49,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1.0
#> [50,] 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
#> [,50]
#> [1,] 0.3
#> [2,] 0.3
#> [3,] 0.3
#> [4,] 0.3
#> [5,] 0.3
#> [6,] 0.3
#> [7,] 0.3
#> [8,] 0.3
#> [9,] 0.3
#> [10,] 0.3
#> [11,] 0.3
#> [12,] 0.3
#> [13,] 0.3
#> [14,] 0.3
#> [15,] 0.3
#> [16,] 0.3
#> [17,] 0.3
#> [18,] 0.3
#> [19,] 0.3
#> [20,] 0.3
#> [21,] 0.3
#> [22,] 0.3
#> [23,] 0.3
#> [24,] 0.3
#> [25,] 0.3
#> [26,] 0.3
#> [27,] 0.3
#> [28,] 0.3
#> [29,] 0.3
#> [30,] 0.3
#> [31,] 0.3
#> [32,] 0.3
#> [33,] 0.3
#> [34,] 0.3
#> [35,] 0.3
#> [36,] 0.3
#> [37,] 0.3
#> [38,] 0.3
#> [39,] 0.3
#> [40,] 0.3
#> [41,] 0.3
#> [42,] 0.3
#> [43,] 0.3
#> [44,] 0.3
#> [45,] 0.3
#> [46,] 0.3
#> [47,] 0.3
#> [48,] 0.3
#> [49,] 0.3
#> [50,] 1.0
#>
#> $Sigma
#> 5 x 5 Matrix of class "dgeMatrix"
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1.05298886 -0.01938594 0.1622737 -0.25068013 0.29348222
#> [2,] -0.01938594 1.13578655 0.1895796 -0.05137562 -0.07415423
#> [3,] 0.16227371 0.18957962 1.2802447 -0.17181381 -0.27211392
#> [4,] -0.25068013 -0.05137562 -0.1718138 1.92973993 -0.02848115
#> [5,] 0.29348222 -0.07415423 -0.2721139 -0.02848115 1.28984099
#>