lcca.linear.Rd
Current version is implemented for only the linear trajectory.
lcca.linear(
x,
y,
varthresh = 0.95,
projectthresh = 1,
method = "Wilks",
verbose = FALSE
)
object for input list(x, time, J, I, visit)
(default=1) threshold for the dimension reduction projection in lfpca.
(defualt='Wilks') test statistic to be used. "Wilks","Hotelling", "Pillai", or "Roy".
(default=FALSE) print all details
(default=0.95) threshold to detemined the number of components of lpcs.
(defult=FALSE)
ccor xcv_x0: Longitudinal Canonical vector for the intercept for x xcv_x1: Longitudinal Canonical vector for the slope for x xcv_y0: Longitudinal Canonical vector for the intercept for y xcv_y1: Longitudinal Canonical vector for the slope for y
set.seed(12345678)
r=0.8
mu = c(0,0,0,0,0,0)
stddev = rep(c(8,4,2),2)
cormatx = diag(1,6,6)
cormatx[1,5] <- r
cormatx[5,1] <- r
covmatx = stddev %*% t(stddev) * cormatx
## Generate scores
xi = mvrnorm(n = 100, mu = mu, Sigma = covmatx, empirical = FALSE)
I=100
## X
visit.X =rpois(I,1)+3
time.X = unlist(lapply(visit.X, function(x) scale(c(0,cumsum(rpois(x-1,1)+1)))))
J.X = sum(visit.X)
xi.X = xi[,1:3]
V.x=144
phix0 = matrix(0,V.x,3); phix0[1:12, 1]<-.1; phix0[1:12 + 12, 2]<-.1; phix0[1:12 + 12*2, 3]<-.1
phix1 = matrix(0,V.x,3); phix1[1:12 + 12*3, 1]<-.1; phix1[1:12 + 12*4, 2]<-.1; phix1[1:12 + 12*5, 3]<-.1
phixw = matrix(0,V.x,3); phixw[1:12 + 12*6, 1]<-.1; phixw[1:12 + 12*7, 2]<-.1; phixw[1:12 + 12*8, 3]<-.1
zeta.X = t(matrix(rnorm(J.X*3), ncol=J.X)*c(8,4,2))*2
X = phix0 %*% t(xi.X[rep(1:I, visit.X),]) + phix1 %*% t(time.X * xi.X[rep(1:I, visit.X),]) + phixw %*% t(zeta.X) + matrix(rnorm(V.x*J.X, 0, .1), V.x, J.X)
## Y
visit.Y=rpois(I,1)+3
time.Y = unlist(lapply(visit.Y, function(x) scale(c(0,cumsum(rpois(x-1,1)+1)))))
K.Y = sum(visit.Y)
V.y=81
phiy0 = matrix(0,V.y,3); phiy0[1:9, 1]<-.1; phiy0[1:9 + 9, 2]<-.1; phiy0[1:9 + 9*2, 3]<-.1
phiy1 = matrix(0,V.y,3); phiy1[1:9 + 9*3, 1]<-.1; phiy1[1:9 + 9*4, 2]<-.1; phiy1[1:9 + 9*5, 3]<-.1
phiyw = matrix(0,V.y,3); phiyw[1:9 + 9*6, 1]<-.1; phiyw[1:9 + 9*7, 2]<-.1; phiyw[1:9 + 9*8, 3]<-.1
zeta.Y = t(matrix(rnorm(K.Y*3), ncol=K.Y)*c(8,4,2))*2
xi.Y = xi[,4:6]
Y = phiy0 %*% t(xi.Y[rep(1:I, visit.Y),]) + phiy1 %*% t(time.Y * xi.Y[rep(1:I, visit.Y),]) + phiyw %*% t(zeta.Y) + matrix(rnorm(V.y*K.Y ,0, .1), V.y, K.Y)
x = list(X=X, time=time.X, I=I, J=sum(visit.X),visit=visit.X)
y = list(X=Y, time=time.Y, I=I, J=sum(visit.Y),visit=visit.Y)
re = lcca.linear(x=x,y=y)
#> Wilks' Lambda, using F-approximation (Rao's F):
#> stat approx df1 df2 p.value
#> 1 to 4: 0.3635147 6.913769391 16 281.7023 2.345901e-13
#> 2 to 4: 0.9176709 0.904261906 9 226.4882 5.222746e-01
#> 3 to 4: 0.9749770 0.599311064 4 188.0000 6.635830e-01
#> 4 to 4: 0.9999414 0.005566361 1 95.0000 9.406834e-01
re
#> $tests
#> $tests$id
#> [1] "Wilks"
#>
#> $tests$stat
#> [1] 0.3635147 0.9176709 0.9749770 0.9999414
#>
#> $tests$approx
#> [1] 6.913769391 0.904261906 0.599311064 0.005566361
#>
#> $tests$df1
#> [1] 16 9 4 1
#>
#> $tests$df2
#> [1] 281.7023 226.4882 188.0000 95.0000
#>
#> $tests$p.value
#> [1] 2.345901e-13 5.222746e-01 6.635830e-01 9.406834e-01
#>
#> $tests$r
#> [1] 0.7770923 0.2424396 0.1580058 0.0076544
#>
#>
#> $ccor.dim
#> [1] 1
#>
#> $ccor
#> [1] 0.7770923
#>
#> $xcv_x0
#> [,1]
#> [1,] -5.240458e-02
#> [2,] -5.121346e-02
#> [3,] -5.281954e-02
#> [4,] -5.250476e-02
#> [5,] -5.162357e-02
#> [6,] -5.146379e-02
#> [7,] -5.309163e-02
#> [8,] -5.314932e-02
#> [9,] -5.160490e-02
#> [10,] -5.122553e-02
#> [11,] -5.311918e-02
#> [12,] -5.154821e-02
#> [13,] -3.697314e-03
#> [14,] -3.578033e-03
#> [15,] -3.526340e-03
#> [16,] -5.019905e-03
#> [17,] -4.005135e-03
#> [18,] -4.105053e-03
#> [19,] -4.087958e-03
#> [20,] -3.603200e-03
#> [21,] -4.762419e-03
#> [22,] -3.327134e-03
#> [23,] -4.107509e-03
#> [24,] -4.726038e-03
#> [25,] 9.177084e-03
#> [26,] 9.409618e-03
#> [27,] 9.631838e-03
#> [28,] 1.019491e-02
#> [29,] 1.038734e-02
#> [30,] 9.599668e-03
#> [31,] 9.933208e-03
#> [32,] 8.924947e-03
#> [33,] 1.045960e-02
#> [34,] 1.017450e-02
#> [35,] 9.659505e-03
#> [36,] 9.736108e-03
#> [37,] -8.583329e-04
#> [38,] -3.837461e-04
#> [39,] -1.572281e-03
#> [40,] -5.510319e-04
#> [41,] -1.396470e-03
#> [42,] 4.245864e-04
#> [43,] -9.530606e-04
#> [44,] -1.761365e-04
#> [45,] -2.497254e-04
#> [46,] 2.985649e-04
#> [47,] 1.041726e-03
#> [48,] -6.748502e-04
#> [49,] -5.239793e-04
#> [50,] -5.905928e-06
#> [51,] 3.401799e-04
#> [52,] -4.313707e-04
#> [53,] -1.301769e-04
#> [54,] -8.990692e-04
#> [55,] -1.087787e-04
#> [56,] -4.575808e-04
#> [57,] 6.172353e-04
#> [58,] -9.927459e-04
#> [59,] -1.161591e-03
#> [60,] -1.447779e-04
#> [61,] -6.160998e-04
#> [62,] 1.139509e-03
#> [63,] -1.235321e-03
#> [64,] -6.992568e-04
#> [65,] -1.762374e-04
#> [66,] 1.733414e-03
#> [67,] -2.174736e-04
#> [68,] -6.148850e-04
#> [69,] 5.907092e-04
#> [70,] -8.222421e-04
#> [71,] 7.182849e-05
#> [72,] 1.711529e-03
#> [73,] 2.051787e-02
#> [74,] 1.980696e-02
#> [75,] 2.015651e-02
#> [76,] 1.948428e-02
#> [77,] 2.005626e-02
#> [78,] 2.057709e-02
#> [79,] 2.177505e-02
#> [80,] 2.038227e-02
#> [81,] 2.163555e-02
#> [82,] 2.081181e-02
#> [83,] 2.074497e-02
#> [84,] 2.153904e-02
#> [85,] -2.293309e-03
#> [86,] -2.106100e-03
#> [87,] -1.459963e-03
#> [88,] -3.571095e-03
#> [89,] -2.168368e-03
#> [90,] -1.729366e-03
#> [91,] -2.911988e-03
#> [92,] -1.310539e-03
#> [93,] -3.162737e-03
#> [94,] -1.479016e-03
#> [95,] -2.757131e-03
#> [96,] -1.385267e-03
#> [97,] -4.876773e-03
#> [98,] -2.812057e-03
#> [99,] -2.932701e-03
#> [100,] -3.891947e-03
#> [101,] -1.875466e-03
#> [102,] -3.712810e-03
#> [103,] -2.989562e-03
#> [104,] -4.248513e-03
#> [105,] -3.250476e-03
#> [106,] -2.644392e-03
#> [107,] -2.654437e-03
#> [108,] -1.791128e-03
#> [109,] 5.511383e-04
#> [110,] -7.935502e-04
#> [111,] -8.379491e-04
#> [112,] -7.219404e-04
#> [113,] 1.114718e-03
#> [114,] -2.637650e-04
#> [115,] 9.618236e-04
#> [116,] -8.783366e-04
#> [117,] 1.527783e-03
#> [118,] -9.448495e-04
#> [119,] -1.005080e-04
#> [120,] -3.787867e-04
#> [121,] 8.692029e-04
#> [122,] 3.856886e-04
#> [123,] -6.433996e-04
#> [124,] 4.663477e-04
#> [125,] 8.197149e-04
#> [126,] -2.456516e-04
#> [127,] -1.212015e-04
#> [128,] 5.907830e-05
#> [129,] -8.047157e-04
#> [130,] 7.023068e-04
#> [131,] 5.430844e-04
#> [132,] 2.417548e-04
#> [133,] -1.610971e-03
#> [134,] -8.653542e-04
#> [135,] 3.220282e-04
#> [136,] 4.664442e-04
#> [137,] 8.285327e-04
#> [138,] -7.887992e-04
#> [139,] -1.751198e-03
#> [140,] -4.224397e-04
#> [141,] 8.877716e-05
#> [142,] 8.005640e-04
#> [143,] 5.859152e-04
#> [144,] 5.139042e-04
#>
#> $xcv_x1
#> [,1]
#> [1,] -7.507811e-04
#> [2,] -1.572859e-03
#> [3,] -7.527726e-04
#> [4,] -7.619821e-04
#> [5,] 6.504041e-04
#> [6,] 1.463867e-03
#> [7,] 5.446627e-05
#> [8,] 9.539625e-05
#> [9,] -1.147493e-03
#> [10,] -8.025226e-04
#> [11,] -2.341298e-03
#> [12,] -5.276036e-04
#> [13,] 7.505225e-04
#> [14,] 5.788080e-04
#> [15,] -1.203492e-03
#> [16,] 6.432623e-04
#> [17,] 2.904233e-04
#> [18,] 6.186078e-04
#> [19,] 9.474854e-04
#> [20,] -6.447103e-04
#> [21,] 2.073490e-04
#> [22,] 1.656986e-04
#> [23,] -8.091541e-04
#> [24,] -1.202719e-04
#> [25,] 1.101125e-03
#> [26,] -8.558459e-04
#> [27,] 8.387028e-04
#> [28,] 6.484049e-05
#> [29,] 4.880481e-04
#> [30,] -4.152245e-04
#> [31,] 4.479064e-04
#> [32,] 7.282962e-04
#> [33,] -2.352861e-04
#> [34,] 1.885000e-03
#> [35,] -1.527236e-03
#> [36,] 1.601158e-03
#> [37,] -5.535664e-02
#> [38,] -5.446659e-02
#> [39,] -5.341987e-02
#> [40,] -5.390930e-02
#> [41,] -5.349713e-02
#> [42,] -5.378800e-02
#> [43,] -5.460786e-02
#> [44,] -5.388483e-02
#> [45,] -5.347298e-02
#> [46,] -5.416128e-02
#> [47,] -5.493500e-02
#> [48,] -5.401589e-02
#> [49,] -5.627733e-03
#> [50,] -5.708574e-03
#> [51,] -3.889033e-03
#> [52,] -5.276997e-03
#> [53,] -4.211039e-03
#> [54,] -6.157294e-03
#> [55,] -1.770175e-03
#> [56,] -4.725905e-03
#> [57,] -5.516828e-03
#> [58,] -3.581518e-03
#> [59,] -4.729501e-03
#> [60,] -5.064211e-03
#> [61,] 9.278862e-03
#> [62,] 8.734523e-03
#> [63,] 8.411876e-03
#> [64,] 1.052318e-02
#> [65,] 9.766372e-03
#> [66,] 1.043241e-02
#> [67,] 1.148311e-02
#> [68,] 9.378426e-03
#> [69,] 1.060483e-02
#> [70,] 9.676407e-03
#> [71,] 9.579854e-03
#> [72,] 1.109840e-02
#> [73,] 8.911571e-03
#> [74,] 8.256658e-03
#> [75,] 9.986911e-03
#> [76,] 7.217593e-03
#> [77,] 8.292849e-03
#> [78,] 8.352344e-03
#> [79,] 8.940095e-03
#> [80,] 7.813016e-03
#> [81,] 8.741793e-03
#> [82,] 9.452739e-03
#> [83,] 8.025833e-03
#> [84,] 1.015984e-02
#> [85,] -3.841968e-03
#> [86,] -3.785574e-03
#> [87,] -3.296713e-03
#> [88,] -4.735503e-03
#> [89,] -3.062659e-03
#> [90,] -4.551920e-03
#> [91,] -4.438180e-03
#> [92,] -4.608802e-03
#> [93,] -2.092710e-03
#> [94,] -4.795350e-03
#> [95,] -2.970079e-03
#> [96,] -2.763033e-03
#> [97,] -8.263363e-03
#> [98,] -6.487589e-03
#> [99,] -8.086401e-03
#> [100,] -7.514088e-03
#> [101,] -6.920517e-03
#> [102,] -8.354038e-03
#> [103,] -6.980921e-03
#> [104,] -7.529404e-03
#> [105,] -6.047182e-03
#> [106,] -7.960900e-03
#> [107,] -6.923776e-03
#> [108,] -7.578885e-03
#> [109,] 9.632540e-04
#> [110,] -1.694938e-03
#> [111,] -2.040445e-03
#> [112,] -4.980857e-04
#> [113,] 3.208232e-04
#> [114,] 7.657372e-04
#> [115,] 1.828987e-04
#> [116,] 5.660768e-04
#> [117,] -5.549719e-04
#> [118,] -3.533345e-04
#> [119,] -7.872822e-04
#> [120,] 2.710043e-04
#> [121,] 1.182603e-04
#> [122,] -1.163531e-04
#> [123,] 2.239494e-04
#> [124,] -3.647398e-04
#> [125,] -1.385291e-03
#> [126,] 2.505571e-04
#> [127,] 1.030736e-04
#> [128,] 4.856185e-04
#> [129,] 3.515498e-04
#> [130,] -3.814922e-04
#> [131,] 3.799971e-05
#> [132,] -3.622948e-04
#> [133,] -1.181772e-03
#> [134,] 1.196584e-04
#> [135,] -1.748409e-03
#> [136,] 6.940279e-04
#> [137,] 2.336499e-04
#> [138,] -5.759745e-04
#> [139,] -2.130494e-04
#> [140,] -6.125097e-04
#> [141,] -1.419526e-03
#> [142,] -5.823073e-04
#> [143,] -2.194133e-03
#> [144,] 1.291580e-03
#>
#> $xcv_y0
#> [,1]
#> [1,] 0.0081296799
#> [2,] -0.0007121821
#> [3,] -0.0046971487
#> [4,] -0.0060979262
#> [5,] 0.0033765720
#> [6,] -0.0093518843
#> [7,] -0.0010939603
#> [8,] -0.0064676004
#> [9,] -0.0007633369
#> [10,] -0.1360628505
#> [11,] -0.1439140406
#> [12,] -0.1394703811
#> [13,] -0.1467906922
#> [14,] -0.1334887662
#> [15,] -0.1437964509
#> [16,] -0.1327310593
#> [17,] -0.1322796955
#> [18,] -0.1403573404
#> [19,] 0.0499203528
#> [20,] 0.0447663780
#> [21,] 0.0529169043
#> [22,] 0.0496646908
#> [23,] 0.0530201680
#> [24,] 0.0550746144
#> [25,] 0.0515301566
#> [26,] 0.0523687091
#> [27,] 0.0490540908
#> [28,] 0.0033611182
#> [29,] 0.0010679894
#> [30,] 0.0049976316
#> [31,] -0.0049667013
#> [32,] -0.0013752645
#> [33,] -0.0023629180
#> [34,] -0.0030392105
#> [35,] -0.0002020371
#> [36,] -0.0011130012
#> [37,] 0.0037422586
#> [38,] 0.0005803851
#> [39,] -0.0035352086
#> [40,] -0.0013307573
#> [41,] 0.0056856888
#> [42,] -0.0035797176
#> [43,] -0.0063618169
#> [44,] -0.0022546061
#> [45,] -0.0030673160
#> [46,] 0.0008698282
#> [47,] -0.0003527553
#> [48,] -0.0056976938
#> [49,] -0.0012913905
#> [50,] 0.0051752148
#> [51,] -0.0043363013
#> [52,] -0.0012338536
#> [53,] -0.0054863084
#> [54,] -0.0058141976
#> [55,] 0.0242222743
#> [56,] 0.0178410720
#> [57,] 0.0240292814
#> [58,] 0.0199759251
#> [59,] 0.0224672074
#> [60,] 0.0123219022
#> [61,] 0.0202528591
#> [62,] 0.0222041339
#> [63,] 0.0130602136
#> [64,] 0.0911716002
#> [65,] 0.0857195197
#> [66,] 0.0966913558
#> [67,] 0.0898881321
#> [68,] 0.0928409603
#> [69,] 0.0975050878
#> [70,] 0.0951640689
#> [71,] 0.0905931149
#> [72,] 0.0950636233
#> [73,] 0.0158051577
#> [74,] 0.0152536382
#> [75,] 0.0114460203
#> [76,] 0.0153253537
#> [77,] 0.0169586381
#> [78,] 0.0079384420
#> [79,] 0.0098089403
#> [80,] 0.0051102139
#> [81,] 0.0115395775
#>
#> $xcv_y1
#> [,1]
#> [1,] -0.0056960564
#> [2,] 0.0027124152
#> [3,] -0.0025278197
#> [4,] 0.0008639328
#> [5,] 0.0008118146
#> [6,] -0.0078314871
#> [7,] 0.0014535092
#> [8,] -0.0099575303
#> [9,] -0.0063555415
#> [10,] 0.0113472290
#> [11,] 0.0122184361
#> [12,] -0.0020498337
#> [13,] -0.0003060191
#> [14,] 0.0028717174
#> [15,] 0.0065755128
#> [16,] -0.0064821738
#> [17,] 0.0078707601
#> [18,] -0.0014681876
#> [19,] 0.0014070242
#> [20,] 0.0015542097
#> [21,] -0.0027652749
#> [22,] 0.0043055865
#> [23,] -0.0011381039
#> [24,] -0.0019029225
#> [25,] 0.0010911985
#> [26,] 0.0030406700
#> [27,] 0.0031524983
#> [28,] -0.0029596656
#> [29,] -0.0075011522
#> [30,] -0.0017339975
#> [31,] -0.0012703328
#> [32,] -0.0016711133
#> [33,] -0.0082931902
#> [34,] -0.0016873109
#> [35,] -0.0033544943
#> [36,] -0.0047838727
#> [37,] -0.1239446099
#> [38,] -0.1329827450
#> [39,] -0.1276773264
#> [40,] -0.1273756574
#> [41,] -0.1294425675
#> [42,] -0.1273186424
#> [43,] -0.1348704603
#> [44,] -0.1304592317
#> [45,] -0.1321602473
#> [46,] 0.0525578713
#> [47,] 0.0539062406
#> [48,] 0.0535783299
#> [49,] 0.0555460352
#> [50,] 0.0586410181
#> [51,] 0.0514615985
#> [52,] 0.0567592613
#> [53,] 0.0578764355
#> [54,] 0.0577939657
#> [55,] -0.0279785412
#> [56,] -0.0276155613
#> [57,] -0.0212924005
#> [58,] -0.0306150263
#> [59,] -0.0309203871
#> [60,] -0.0287975250
#> [61,] -0.0291220940
#> [62,] -0.0318872678
#> [63,] -0.0297629824
#> [64,] 0.0113375016
#> [65,] 0.0042988262
#> [66,] 0.0047984061
#> [67,] 0.0125560896
#> [68,] 0.0008934148
#> [69,] 0.0052566070
#> [70,] 0.0075788399
#> [71,] 0.0084162275
#> [72,] 0.0087641349
#> [73,] 0.0223658083
#> [74,] 0.0268251171
#> [75,] 0.0158752671
#> [76,] 0.0266425126
#> [77,] 0.0191938803
#> [78,] 0.0209776762
#> [79,] 0.0171377535
#> [80,] 0.0147452503
#> [81,] 0.0230731125
#>
#> $scores
#> $scores$x
#> [1] -1.033560402 -1.825417558 2.411470232 0.057065829 -1.202058624
#> [6] 0.807877674 0.837386825 -1.330343997 -1.240722621 -2.671073328
#> [11] 0.584071316 0.319172316 0.548157656 -0.015175030 0.429559387
#> [16] -1.623070500 0.207317049 -2.023853045 -0.336319217 -0.484823825
#> [21] 0.293646023 2.143478921 0.283484831 0.532853970 2.247572489
#> [26] -0.396915523 -0.449590855 -1.535281369 0.455496575 0.434447381
#> [31] 0.550949052 1.264365108 -0.117905766 -1.322197623 -0.001990266
#> [36] -0.169378049 0.221089091 1.523622153 -0.055940800 0.609532557
#> [41] -0.405083263 -0.563034056 0.662082085 1.893857110 -0.747247774
#> [46] 0.736157947 -0.513880025 -2.087260185 0.351354950 -2.165879487
#> [51] 0.382208134 -1.100894694 -0.571719158 -0.709795910 0.192818860
#> [56] -0.375504359 0.136821268 0.988351178 -0.184143962 0.455601256
#> [61] 0.829727033 0.236987797 -0.929986042 -0.823152512 -0.142428546
#> [66] 0.577136117 -0.359060561 -0.448926239 0.046221214 0.912052061
#> [71] 1.571984499 0.982437444 -0.316074967 -1.126567907 -0.951285076
#> [76] 1.448258455 -0.096414598 0.902015275 -0.606921232 0.942581940
#> [81] -1.466091864 1.613133425 0.559548281 1.559845125 0.386193054
#> [86] 0.040842474 -0.387582380 -0.780522122 1.075027278 1.269216552
#> [91] 0.036206618 0.229919283 -0.798159392 -0.338457941 -0.832971778
#> [96] 0.957815797 0.505483301 -0.424563310 0.058141936 -1.213416444
#>
#> $scores$y
#> [1] -1.75073124 -1.35519030 2.38190712 0.44784929 -0.81679952 0.64684367
#> [7] 0.28846733 -0.50962650 -1.71214929 -2.31782618 0.28954627 0.01487763
#> [13] -1.18306872 -0.88424726 0.59663336 -1.78297933 0.87402454 -1.02907353
#> [19] -0.77445802 -0.11796074 0.63877484 1.64826569 0.90412172 1.04683246
#> [25] 1.48248602 -0.25155667 -0.71670287 -1.07010172 0.15519631 -0.44000766
#> [31] 1.02861275 1.05020140 -0.50197578 -0.18783979 0.08167653 -0.10658151
#> [37] 1.13451359 0.57369410 -0.04651363 0.09024089 -0.20967284 -0.73192012
#> [43] 0.82177152 0.83488448 -0.21030837 1.52800560 -0.54197169 -0.74041418
#> [49] 1.15828192 -2.10699938 0.27387100 -1.36191168 -1.19323922 -0.57866142
#> [55] 0.57293781 -0.14543200 1.24055918 1.41068527 0.14510590 -0.17731410
#> [61] 1.19523757 0.01097175 -1.64332903 -0.30787260 -0.27594908 -1.18599330
#> [67] -1.24313865 0.48658436 0.46120924 0.74867386 1.17962691 1.78443459
#> [73] 0.08051452 -0.74372113 0.13035530 0.09786416 -0.55570469 1.29417261
#> [79] -0.33985051 1.04274959 -0.82023247 1.40961328 -0.14206371 1.85369215
#> [85] -0.36560488 -1.03876157 -0.23390584 0.17417254 1.77720926 1.38028300
#> [91] 0.70958310 -0.53554467 -1.05338167 0.17704992 -0.12314874 -1.13158691
#> [97] 1.02689410 -0.49406672 -0.45081650 -2.14385211
#>
#>