MODEL REGRESI MULTIVARIAT NORMAL DAN KANONIK
Oleh: Andi Syaiful Rahmat
REGRESI LINEAR MULTIVARIAT NORMAL
A. Uji Distribusi Multivariat Normal Menggunakan Uji Mahalanobis Sintaks
library('mvnormtest')
x <- c(205, 206, 254, 246, 201, 291, 234, 209, 204, 216, 245, 286, 312, 265, 322)
y <- c(26, 28, 35, 31, 21, 49, 30, 30, 24, 31, 32, 47, 54, 40, 42)
z <- c(159, 164, 198, 184, 150, 208, 184, 154, 149, 175, 192, 201, 248, 166, 287)
mtx_A <- matrix(c(x, y, z), ncol = 3)
n <- length(x)
mtx_mean <- apply(mtx_A, 2, mean)
mtx_cov <- var(mtx_A)
distance_mahalanobis <- sort(mahalanobis(mtx_A, center = mtx_mean, cov = mtx_cov))
n <- length(distance_mahalanobis)
p <- (1:n - 0.5) / n
chi <- qchisq(p, df = ncol(mtx_A))
win.graph()
plot(distance_mahalanobis, chi, type = "p")
Interpretasi: Berdasarkan hasil yang diperoleh, terlihat bahwa visualisasi grafik scatter plot dengan menggunakan jarak mahalanobis menunjukkan kumpulan data mendekati garis lurus sehingga dapat disimpulkan bahwa data mengikuti distribusi multivariat normal.
B. Uji Distribusi Multivariat Normal Menggunakan Uji Shapiro Wilk
Y <- t(mtx_A[1:n,1:3])
mshapiro.test(Y)##
## Shapiro-Wilk normality test
##
## data: Z
## W = 0.72927, p-value = 0.0005203Interpretasi: Berdasarkan hasil analisis dengan menggunakan uji shapiro wilk, diperoleh nilai p-value sebesar 0,0005203 dimana nilai ini lebih kecil dari nilai taraf signifikansi (0,05). Sehingga dapat disimpulkan bahwa data tidak berdistribusi multivariat normal.
C. Uji Distribusi Multivariat Normal Menggunakan Korelasi
cor(chi, distance_mahalanobis, method = 'pearson')## [1] 0.9787523Interpretasi: Berdasarkan hasil analisis dengan menggunakan uji korelasi pearson dari jarak mahalanobis, diperoleh nilai 0,9787523 dimana nilai ini mendekati 1. Sehingga dapat disimpulkan bahwa data memiliki korelasi yang sangat tinggi dan mengikuti distribusi multivariat normal.
D. Model Regresi Linear Multivariat Normal
N <- length(y)
X1 <- x
Y1 <- y
Y2 <- z
Y <- cbind(Y1, Y2)
dfRegr <- data.frame(X1, Y1, Y2)
(fit <- lm(cbind(Y1, Y2) ~ X1, data = dfRegr))##
## Call:
## lm(formula = cbind(Y1, Y2) ~ X1, data = dfRegr)
##
## Coefficients:
## Y1 Y2
## (Intercept) -18.4585 -17.7721
## X1 0.2156 0.8348Interpretasi: Berdasarkan hasil analisis, diperoleh model regresi linear multivariat adalah sebagai berikut:
Y_1 = -18,4585 + 0,2156
Y_2 = -17,7721 + 0,8348
E. Statistik Uji
summary(manova(fit), test = 'Hotelling-Lawley')## Df Hotelling-Lawley approx F num Df den Df Pr(>F)
## X1 1 19.716 118.29 2 12 1.265e-08 ***
## Residuals 13
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(manova(fit), test = 'Wilks')## Df Wilks approx F num Df den Df Pr(>F)
## X1 1 0.048272 118.29 2 12 1.265e-08 ***
## Residuals 13
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(manova(fit), test = 'Roy')## Df Roy approx F num Df den Df Pr(>F)
## X1 1 19.716 118.29 2 12 1.265e-08 ***
## Residuals 13
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(manova(fit), test = 'Pillai')## Df Pillai approx F num Df den Df Pr(>F)
## X1 1 0.95173 118.29 2 12 1.265e-08 ***
## Residuals 13
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Interpretasi: Berdasarkan hasil statistik uji dengan menggunakan pengujian Hotelling Lawley, Wilks, Roy, Pillai, diperoleh nilai p-value yang lebih kecil dari nilai taraf signifikansi (0,05). Sehingga dapat disimpulkan bahwa model signifikan dan variabel X_1 berpengaruh signifikan terhadap Y_1 dan Y_2.
KORELASI KANONIK
A. Load Dataset
library(CCA)
data(nutrimouse)
X <- as.matrix(nutrimouse$gene[, 1:10])
Y <- as.matrix(nutrimouse$lipid)B. Plot Korelasi Kanonik
res.cc <- cc(X,Y)
plot(res.cc$cor, type = 'b')
plt.cc(res.cc)
Interpretasi: Berdasarkan hasil yang diperoleh, terlihat bahwa hasil plot korelasi kanonik dan korelasi variabel memiliki hubungan sangat kuat yang bersifat negatif dan berhubungan timbal balik. Selain itu, berdasarkan hasil plot korelasi kanonik terlihat sebaran data berada di area yang tidak sama sehingga tidak terbentuk cluster yang berbeda.
C. Menampilkan Nilai Korelasi Kanonik
res.cc$cor## [1] 0.9906993 0.9848735 0.9388864 0.9191073 0.8149742 0.7234679 0.6413248
## [8] 0.6057535 0.5469842 0.3607641D. Menampilkan Penaksir Koefisien
res.cc$xcoef## [,1] [,2] [,3] [,4] [,5] [,6]
## X36b4 -3.3748490 0.5817180 7.3528185 -2.75182972 -4.9593593 1.2664888
## ACAT1 1.3694057 4.1938419 2.1951887 13.24670653 -7.5278797 -5.8494391
## ACAT2 0.7236782 3.9928812 3.3376630 -3.88120599 0.2721882 -1.3012874
## ACBP 0.5927870 -6.8394169 2.3324859 8.39766198 1.6286876 6.7585683
## ACC1 -4.3801037 0.2876008 12.4601621 0.06732809 -10.6656173 -11.1335523
## ACC2 6.2221772 6.3953635 -5.8302868 6.38871606 5.9636507 3.4410507
## ACOTH 2.2727330 5.7611549 -12.5677715 -0.14230685 -2.8360377 5.2129368
## ADISP -4.6789126 -15.2268608 -0.9922763 -12.92907435 19.0493396 13.2687852
## ADSS1 -6.5906498 -1.1136249 3.1095779 0.32327939 -6.3302874 6.5385794
## ALDH3 8.6967435 1.4525302 -6.7672495 -9.52990178 -3.1463163 -0.7954847
## [,7] [,8] [,9] [,10]
## X36b4 6.3851965 -13.159138 4.2742659 4.4254371
## ACAT1 -13.4240634 -3.626869 1.0896599 24.6456754
## ACAT2 -1.9046485 3.179304 0.6021537 1.2924147
## ACBP -5.8552684 -5.704047 -5.3662421 -8.1207642
## ACC1 2.8192415 18.135016 9.6545142 -4.3084105
## ACC2 3.7490920 -3.765147 3.5499524 -1.0737214
## ACOTH -4.5231792 -7.195705 -2.2929182 -17.4098041
## ADISP -3.0669710 6.181938 12.9466045 -10.0293360
## ADSS1 3.8113885 4.131253 -17.8846096 11.9375988
## ALDH3 0.6880137 2.103283 0.7149102 0.6075842E. Menampilkan Penaksir Koefisien Bagi Variabel Y
res.cc$ycoef## [,1] [,2] [,3] [,4] [,5] [,6]
## C14.0 18.25835 9.531869 -8.951338 -14.480970 -5.83576334 -19.90462
## C16.0 18.39114 8.012748 -8.054978 -15.317120 -2.45444921 -21.44894
## C18.0 18.48383 7.761822 -8.499797 -15.391899 -2.11398881 -21.18489
## C16.1n.9 17.47713 5.438128 -12.606433 -14.858517 -0.06442915 -20.95551
## C16.1n.7 18.49964 8.146145 -8.272064 -15.149249 -1.66908125 -22.21911
## C18.1n.9 18.55467 8.335579 -8.233188 -14.956342 -2.73010007 -21.41944
## C18.1n.7 18.17675 7.754032 -7.317378 -15.903060 -2.60918722 -20.94234
## C20.1n.9 17.48909 10.199644 -7.607889 -18.499439 6.57046104 -20.87297
## C20.3n.9 18.95541 8.971971 -9.106700 -13.449666 -2.53414184 -21.44272
## C18.2n.6 18.24963 8.135332 -7.912258 -15.571984 -2.56209042 -21.45624
## C18.3n.6 18.25139 8.421602 -7.833877 -16.088806 -2.62392210 -21.41660
## C20.2n.6 20.46932 9.020131 -9.674874 -8.291072 -6.02579329 -25.13346
## C20.3n.6 20.19757 8.541453 -9.423868 -19.559058 -3.49492074 -22.27412
## C20.4n.6 18.21923 8.347795 -7.682024 -15.083926 -2.65850088 -21.51743
## C22.4n.6 22.36806 4.990955 -17.969106 1.749075 0.76459980 -16.93832
## C22.5n.6 18.34621 8.477176 -8.293508 -16.402786 -3.95616647 -22.01979
## C18.3n.3 18.52855 8.152770 -8.487307 -15.381268 -2.43280758 -21.23006
## C20.3n.3 11.89230 10.722131 6.257866 -11.755138 -16.66337673 -24.61401
## C20.5n.3 18.79358 8.270673 -8.835837 -15.231939 -2.35666510 -21.44424
## C22.5n.3 18.62810 6.987050 -8.006177 -13.646691 -2.71383635 -22.25207
## C22.6n.3 18.34196 8.407695 -7.997997 -14.851378 -2.81437680 -21.33650
## [,7] [,8] [,9] [,10]
## C14.0 9.1601637 24.041827 26.23586 -14.50703
## C16.0 9.9146866 23.380585 24.83538 -11.99405
## C18.0 9.7993892 24.019798 24.55970 -12.11391
## C16.1n.9 15.0082477 30.273137 17.25814 -19.91616
## C16.1n.7 9.8445895 23.163750 23.84281 -12.09438
## C18.1n.9 9.5666731 22.918388 24.60547 -12.04711
## C18.1n.7 9.8069681 23.298547 25.66651 -12.49599
## C20.1n.9 9.1086056 25.290340 21.97497 -10.23310
## C20.3n.9 9.5409090 22.443193 24.24194 -14.00538
## C18.2n.6 9.8618092 23.588501 25.04873 -12.36980
## C18.3n.6 9.5235508 24.070609 24.48174 -12.20438
## C20.2n.6 10.7987975 17.966001 20.39902 -16.31464
## C20.3n.6 11.7807005 28.370651 23.02181 -14.87258
## C20.4n.6 9.8929260 22.612358 24.85997 -12.68596
## C22.4n.6 -0.1530453 3.263162 14.35357 -6.93795
## C22.5n.6 10.7328297 27.082963 25.38803 -11.37265
## C18.3n.3 9.9928397 22.770669 24.42168 -12.10238
## C20.3n.3 1.1504999 48.489272 40.66735 -25.20117
## C20.5n.3 9.7601761 22.108820 24.10900 -12.48905
## C22.5n.3 10.8456290 21.482942 25.00679 -12.21762
## C22.6n.3 9.3775041 22.986270 24.45812 -12.56643F. Menampilkan Koordinat Bagi Variat Kanonik
res.cc$scores## $xscores
## [,1] [,2] [,3] [,4] [,5] [,6]
## 1 1.242097873 -1.32073181 -0.544253142 -0.860104127 -0.018440941 -0.23142614
## 2 0.488885161 -2.03191478 0.324266139 -0.942704614 -0.933256190 0.73236181
## 3 0.852497081 -1.03663862 -0.450651837 0.350804793 -0.343689251 -1.88817244
## 4 0.637431091 0.42777568 0.374687983 -1.533260933 -1.139478415 -0.67440950
## 5 0.776070104 0.35818618 1.562988367 -1.196454567 1.353144113 0.21001974
## 6 1.230157511 0.36148325 0.322829820 1.409782773 0.347972649 0.43459660
## 7 0.936014623 -1.17036368 -1.486553053 -0.109308656 -0.003854736 0.04018232
## 8 0.898609399 -1.37319950 0.256329394 0.480651678 0.588055605 -0.86135868
## 9 0.131416238 -0.06527504 1.216621765 -1.789277200 -2.580911585 -0.79150609
## 10 1.886288324 1.08431527 -1.214228134 1.665907911 -0.261155806 0.63730384
## 11 0.143333122 0.07576795 1.153324654 0.381147641 -1.832474170 0.10591115
## 12 0.746625813 0.55430165 0.296479818 0.031536889 -0.496646319 -1.50096970
## 13 0.395614197 -0.94421571 -0.876187355 1.336556648 0.577829229 0.17871056
## 14 0.204331012 0.24914989 0.923313916 -1.823237156 2.094749089 -0.51616967
## 15 0.323757446 -1.67764237 -0.273147797 -0.574736868 -0.217214233 1.42857216
## 16 0.783604596 -1.34473506 -1.754273317 -0.588838760 0.554349037 -0.35212221
## 17 2.220809544 1.51611465 1.287091459 0.380397701 0.900889514 -0.99690094
## 18 0.286101603 -0.26218451 1.187893737 -0.092064457 -1.405371822 0.67066965
## 19 1.567270752 0.45952330 1.156034159 0.893256111 0.250552821 1.06836371
## 20 0.966726471 0.08323253 0.034238448 -0.048077666 0.075688432 0.46721678
## 21 -0.638325852 1.44107265 0.044625139 -1.038069985 0.175444801 -0.50729169
## 22 -0.640105898 0.90324542 -1.042548131 0.532806895 0.574540819 -0.95169360
## 23 -1.517954028 -1.44013601 0.041627742 1.278190796 0.404342854 -1.42142946
## 24 -1.395124563 0.65732217 1.403992890 1.652596817 -1.086919193 -1.39401799
## 25 -1.169503077 -0.05134300 -1.015086381 0.467168272 0.125985374 -0.57492665
## 26 -0.477543084 1.10598117 0.231142500 1.111037147 -1.964618819 1.54068661
## 27 -0.900318888 0.78728718 0.164472557 -1.195013930 1.842642503 1.38162550
## 28 -0.782121571 0.85993056 -1.426412687 0.013334403 -0.803327338 0.08301912
## 29 -0.810435533 0.24829565 0.545395544 0.466016988 0.477469132 -0.69126979
## 30 -0.051437054 1.19915554 -2.240475547 -1.066965646 -0.156819224 0.08496980
## 31 -0.008879629 1.75763044 -0.007043267 -0.426718452 1.122398322 0.06886190
## 32 -0.850543921 -1.33717389 1.321900064 -0.243632000 0.009663020 2.31046649
## 33 -0.916579082 0.69654110 0.473208176 0.076866469 -0.214817475 -0.81511874
## 34 -0.361617579 -0.74245988 -0.613300266 -0.009051483 0.699157048 -0.64226849
## 35 -1.345172670 -0.12693017 0.528614794 0.108874298 1.001390927 -0.71966887
## 36 0.075913011 1.07037674 -0.929762382 1.380233335 0.272991555 2.42627415
## 37 -0.696948680 -0.23193204 -1.054580567 0.698735377 -0.503572563 -0.47073255
## 38 -1.346820162 -0.70266598 1.171564141 0.248882752 1.407491242 0.88188356
## 39 -1.221785259 0.87390174 -1.491279730 -2.242638129 -1.066630502 0.70688858
## 40 -1.662338443 -0.91104866 0.397140384 0.815368936 0.172450497 0.54286920
## [,7] [,8] [,9] [,10]
## 1 -0.97959852 -1.50861709 1.10072038 -1.25756470
## 2 0.74939610 0.75597689 -1.42730289 0.57690057
## 3 2.04973079 -0.65540962 0.05356618 0.24045064
## 4 0.20773968 0.61340194 -0.83487896 0.08111406
## 5 1.20280794 1.41344690 1.57938882 -0.44378089
## 6 1.40452663 0.81293272 1.61612789 -2.16308814
## 7 -0.04666510 1.59042281 0.28492748 0.60938931
## 8 0.41346119 -0.16447806 0.29597254 0.33076809
## 9 0.54339660 0.95253688 0.59974377 -0.54715378
## 10 0.21921625 0.62208854 -0.75587234 0.86554339
## 11 -2.63608112 -1.01784476 -0.47040555 -1.56361125
## 12 -0.88681053 0.63171857 -0.35434299 0.25922915
## 13 0.20541480 0.70414816 0.10517271 0.74469533
## 14 -0.79188208 -1.32384827 -0.39188321 0.98842227
## 15 0.16817207 -0.24869145 -0.69565247 -0.50559803
## 16 -2.26415766 0.37003624 -0.40104356 -0.36020822
## 17 0.03502314 -0.40946440 0.20634763 1.17385967
## 18 -0.37331285 -0.06978614 -0.16885528 2.16460584
## 19 -0.51754379 -1.65622543 0.62137146 0.40034605
## 20 0.98979401 -1.76010637 -2.37498615 -0.33728324
## 21 0.88295566 0.94114942 -0.27552401 -0.47028840
## 22 0.59040276 -0.62110604 0.31953870 -0.70584427
## 23 -0.05877332 -0.30910838 -0.34074446 -0.34189845
## 24 0.99449645 -1.88237776 -0.11371867 -0.45460594
## 25 -0.96973378 -0.36540098 -1.29105270 1.13235417
## 26 -0.60180598 0.84844339 1.01340287 0.31140743
## 27 0.38156641 0.13581838 -0.84582662 0.46226470
## 28 -0.92293924 -0.60329144 1.23013687 0.15433178
## 29 -0.31585311 -0.43418558 -1.27969413 -0.04399685
## 30 1.79323373 -0.60661806 -0.87534112 -1.74908117
## 31 -1.81932001 1.04836431 -0.41363043 -0.37005630
## 32 0.32760258 -0.07911568 0.51996373 -0.10614929
## 33 -0.59685816 2.46738188 -1.35040730 -0.91396696
## 34 -0.96858161 -0.29056614 2.52620952 -0.97830727
## 35 -0.09634101 0.41215435 1.59314556 2.31380235
## 36 0.12297728 -0.24744285 -0.18815764 0.12638715
## 37 0.19833350 1.26151231 0.40076943 0.70079878
## 38 -0.37463657 0.26678537 -0.41576363 -2.14679106
## 39 0.56688895 -1.74490458 1.51736991 1.08112299
## 40 1.17375792 0.15027005 -0.31879136 0.74148051
##
## $yscores
## [,1] [,2] [,3] [,4] [,5] [,6]
## 1 0.88058160 -1.08759878 -0.93074368 -0.814137063 0.051109311 -0.058894635
## 2 0.39212221 -1.87930485 0.02594305 -0.683840429 -0.544531474 -0.008329497
## 3 0.86722797 -0.84072982 -0.32680696 -0.287274359 -0.463647252 -0.137443781
## 4 0.65334586 0.39730476 0.73302308 -1.415780849 -1.834507671 -0.211879309
## 5 0.94124398 0.33667861 0.68466653 -1.673677963 1.075015903 -0.455329592
## 6 1.35799979 0.47360197 0.90033271 0.957248937 0.610506810 -0.160323505
## 7 0.94922090 -1.10021516 -0.77863830 -0.048867508 -0.457833110 -0.930564363
## 8 1.04360601 -1.55348601 -0.38301713 0.596256687 0.205254230 -1.122761946
## 9 0.07139738 -0.39568978 1.24825582 -1.007469213 -1.862087037 -0.500574825
## 10 2.04683860 1.19578076 -1.28101528 2.082455972 0.304215542 1.419810759
## 11 0.32744222 0.40605949 1.19459227 -0.004675656 -2.303209465 0.498169660
## 12 0.55280697 0.46270515 0.77330108 -0.511759680 0.702626571 -0.451476645
## 13 0.27702903 -1.38785022 -0.74741777 1.021680734 -0.299753063 0.748810014
## 14 0.31414081 0.11121727 1.61907264 -1.438493422 0.738061864 -0.255291543
## 15 0.54283889 -1.48535908 -0.45377015 0.490119181 -0.238455659 0.628443581
## 16 1.00426659 -1.56905041 -1.54176199 -1.041637276 1.243989865 -0.211600190
## 17 2.15846186 1.48479626 1.07442137 0.688707000 1.041556562 -0.933809430
## 18 0.24001129 -0.25465497 1.07599213 -0.672144442 -1.252887633 -0.291354668
## 19 1.38329395 0.33509395 0.73498471 1.220967271 -0.339273685 1.358192378
## 20 0.90252773 0.19536142 0.30451080 -0.198288495 1.333730422 -0.404274152
## 21 -0.66915749 1.63788570 0.22632545 -0.440373397 0.856724454 0.767761540
## 22 -0.49453085 0.81651854 -0.56594679 0.999285261 -0.044901496 -1.133143966
## 23 -1.43527457 -1.33479821 -0.38540012 0.993991374 0.552325720 -0.444186770
## 24 -1.23233440 0.46149144 1.19540470 1.332933590 -0.908094898 -1.456761287
## 25 -1.10542312 -0.05993872 -1.06367375 0.498697704 -0.113392579 -0.948971591
## 26 -0.49769459 1.12841464 0.42758334 0.866568189 -1.786036052 -0.300979693
## 27 -0.95034745 0.87881227 0.09141902 -1.654412098 1.835482622 1.062324126
## 28 -0.67377660 0.77856752 -1.66965981 0.450016485 0.248784679 0.505274042
## 29 -0.99776124 0.24385229 0.50677994 0.533525171 0.240479825 -1.353577313
## 30 -0.13442897 1.17818334 -2.37560714 -1.190837873 -1.290275684 -0.488381809
## 31 0.08772510 1.75257614 -0.42198148 -0.738391486 1.132333783 -0.496853392
## 32 -0.72266800 -1.40065764 1.54059849 -0.459125834 0.007735647 3.501405663
## 33 -1.00624670 0.56082261 -0.04200532 0.375557837 -0.430404896 0.158617826
## 34 -0.56906710 -0.75616376 -0.33557170 0.319778720 1.052769825 -1.117698422
## 35 -1.33456761 0.31440243 0.62109474 0.510224971 0.523564880 -0.451885771
## 36 -0.09377257 0.92462323 -0.85076020 1.234934748 -0.163257827 2.430910315
## 37 -0.81471603 0.02243947 -1.11368552 0.280096661 -1.155206125 -0.014212074
## 38 -1.43904844 -0.72972576 1.30751487 0.398687569 1.128624628 0.710687121
## 39 -1.13492533 0.75766199 -1.58638763 -2.419972029 -0.506626616 0.838195625
## 40 -1.68838770 -1.01962808 0.56803400 0.849425009 1.109489080 -0.288042483
## [,7] [,8] [,9] [,10]
## 1 -1.53995973 0.15447820 0.42664839 -0.989221222
## 2 2.45703607 1.49023079 -0.49889539 0.618975240
## 3 1.32250182 0.73809880 -0.41114858 1.140893454
## 4 -0.93132184 0.17076608 -0.61436782 -0.114434529
## 5 0.67643110 0.39499161 -0.66330901 -0.793839151
## 6 1.84062569 0.99570897 2.07516951 -1.948210453
## 7 -1.10329625 0.80461144 1.25912076 -0.588117887
## 8 -1.31200982 -0.12510422 1.25568830 0.514658493
## 9 -0.26683427 0.10962038 0.15659950 -0.994577099
## 10 -0.07436346 0.10952466 0.06384920 1.564622615
## 11 -1.98995133 -1.43212645 -0.95598770 0.495052022
## 12 0.18765230 -0.81679340 -0.79669689 0.009818485
## 13 0.62287374 0.15434827 -1.94721017 1.654336546
## 14 0.24801123 -0.17790617 1.22170432 0.812373848
## 15 0.96173354 -0.47258478 -1.29849749 0.540818850
## 16 -1.12302957 -0.35685053 -0.18758320 -1.047094938
## 17 0.25601954 -0.59891309 0.71694452 1.143173451
## 18 -1.01703551 1.34259430 -0.47124638 0.149464300
## 19 0.09133063 -1.52363165 0.84402066 -0.895361390
## 20 0.28219400 -1.62824466 -2.43105501 -0.365901160
## 21 -0.37044147 1.28021579 -0.12399324 -0.655271306
## 22 0.35792277 1.56837825 -2.10069915 -0.640192274
## 23 -0.29976778 -0.49358893 0.72876475 -1.051584715
## 24 0.82858941 -1.22385904 0.45339907 0.317290482
## 25 -1.52307846 -0.25528586 -0.77821060 -0.542905923
## 26 -0.46059180 0.65220095 0.93336063 1.408425820
## 27 -0.96638009 0.14739104 0.21048762 2.104123051
## 28 -0.66449907 0.32083544 1.17597507 -0.658512402
## 29 1.21075203 0.04886203 -0.35570970 -1.504634983
## 30 1.47158730 -2.45512369 0.10367470 -0.985966024
## 31 -0.50986091 1.60377757 -0.70230133 -0.431190278
## 32 0.53338267 -0.21063788 0.65253718 -1.022298432
## 33 0.17469937 1.83394305 -0.24353470 0.472252366
## 34 -0.53473490 -0.57317125 1.44959477 1.771938109
## 35 0.21316512 -1.60846701 -0.37960842 -0.150912894
## 36 -0.53915966 0.09518024 -0.55588883 -1.316877971
## 37 0.83191812 1.13994023 1.03934633 0.311853803
## 38 -0.98209275 0.34986333 -0.32841456 -0.081982986
## 39 1.32825743 -0.96437878 1.11551179 1.147346897
## 40 0.31172478 -0.58889406 -0.03803886 0.601670184
##
## $corr.X.xscores
## [,1] [,2] [,3] [,4] [,5] [,6]
## X36b4 -0.004147031 0.08031376 0.353255619 -0.18064944 -0.451029389 0.5042562
## ACAT1 -0.110978348 0.03510453 -0.210524357 0.18082040 -0.377085546 0.4004143
## ACAT2 0.182625401 0.58092100 0.557951872 -0.27536350 0.253264714 0.1545253
## ACBP 0.659884074 -0.25288482 0.522813743 0.17044864 -0.136178641 0.3123814
## ACC1 0.064321033 0.01285737 0.123007814 0.25110857 -0.574330101 0.4549204
## ACC2 0.341290505 0.33996445 0.073881720 0.35872252 -0.002544151 0.6266599
## ACOTH -0.477384718 0.38623899 -0.351440855 -0.03660321 -0.419783843 0.4037806
## ADISP -0.253999692 -0.09055100 -0.133074374 -0.09811440 -0.088339865 0.7337710
## ADSS1 -0.162858311 0.15997475 -0.042335605 0.04736904 -0.353223326 0.7949483
## ALDH3 0.763922125 -0.30656876 -0.007984654 -0.20486051 -0.418491770 0.2802920
## [,7] [,8] [,9] [,10]
## X36b4 0.20656867 -0.42360261 0.38961482 0.06706312
## ACAT1 -0.51578663 0.07432948 0.44212367 0.37399967
## ACAT2 -0.34755735 0.02003586 -0.16458395 -0.07574233
## ACBP -0.16453026 -0.03018004 -0.13804019 -0.18722291
## ACC1 0.12241104 0.41997845 0.42118219 -0.10928220
## ACC2 0.32954402 0.22838644 0.27394109 0.07274718
## ACOTH -0.28747785 0.01294899 0.20498554 -0.18435097
## ADISP -0.18332076 0.23377890 0.49165156 0.15409523
## ADSS1 0.16877345 0.33776826 -0.09817094 0.18689607
## ALDH3 0.04790734 0.09475924 0.07911627 0.09578203
##
## $corr.Y.xscores
## [,1] [,2] [,3] [,4] [,5]
## C14.0 0.05333084 0.45305154 -0.001487133 0.12555031 0.17853070
## C16.0 0.67338005 -0.26028283 0.383532693 0.04492735 -0.04507824
## C18.0 0.39533047 -0.59181698 0.095708619 -0.23807581 0.04170962
## C16.1n.9 -0.33973442 0.42624031 0.013866519 0.27160247 0.03230013
## C16.1n.7 0.13377548 0.47673007 -0.070499634 0.08424460 0.13797394
## C18.1n.9 -0.02997286 0.59288769 0.081682899 0.26280024 0.05125117
## C18.1n.7 0.21661212 0.30971789 0.124824225 0.22777070 0.14756562
## C20.1n.9 -0.33928472 0.16011564 -0.256950319 0.23800696 0.48181573
## C20.3n.9 0.59729064 0.29574709 0.159416112 0.36005168 0.14810355
## C18.2n.6 -0.69041443 -0.15563794 -0.067368871 0.01649435 0.01358603
## C18.3n.6 0.33266085 0.21596205 0.171662122 0.17215492 0.20383610
## C20.2n.6 -0.52364179 -0.26055738 -0.085677821 0.24618542 0.12480741
## C20.3n.6 0.42919631 -0.44070812 0.227383638 -0.14168614 0.02050834
## C20.4n.6 0.23616279 -0.44214807 0.116208264 -0.06443796 0.15338564
## C22.4n.6 -0.17755786 -0.43255539 -0.113938305 0.10044344 0.16729927
## C22.5n.6 0.02899953 -0.46462426 -0.080688616 0.17290098 0.09541784
## C18.3n.3 -0.13349184 0.10450305 -0.608932687 -0.21429905 -0.16430534
## C20.3n.3 0.02428397 -0.08706868 -0.613952709 -0.13623160 -0.11348915
## C20.5n.3 0.14139317 -0.32126411 -0.290622047 -0.21266570 -0.11272433
## C22.5n.3 0.15442043 -0.02937458 0.017963314 -0.03496373 -0.08657896
## C22.6n.3 0.04207631 -0.18013533 0.337283537 -0.23128859 -0.25101632
## [,6] [,7] [,8] [,9] [,10]
## C14.0 0.34662255 0.02200318 0.1503402847 0.04424750 -0.094411045
## C16.0 0.05666512 -0.10146443 0.1018933886 -0.01843506 -0.011849787
## C18.0 -0.16377993 -0.06412795 -0.0564436825 -0.07831380 0.011654204
## C16.1n.9 0.32250420 0.10693734 0.1470819666 -0.01660255 -0.025045609
## C16.1n.7 0.33146341 0.01434930 0.1321177019 0.05057969 -0.095232819
## C18.1n.9 0.31841098 0.07289152 0.1182043511 0.02349495 0.021107156
## C18.1n.7 0.44190883 0.07705318 0.1154821096 0.04032313 -0.058896136
## C20.1n.9 -0.12295179 0.05717429 0.0560752366 0.08552798 0.005236849
## C20.3n.9 0.11312682 0.15175008 -0.0317989765 0.15602903 -0.022040978
## C18.2n.6 -0.29813154 -0.02163425 -0.0825582766 -0.06477093 0.081078565
## C18.3n.6 -0.12381261 0.12591605 0.0009332623 0.11656948 0.022721799
## C20.2n.6 -0.21498824 0.08201372 -0.0395169927 -0.11896403 0.073224298
## C20.3n.6 -0.13869640 0.08092787 -0.0130705678 -0.23931907 0.069712209
## C20.4n.6 -0.04129411 0.23837182 -0.0109297925 -0.20934451 0.104383680
## C22.4n.6 -0.09066014 0.12492195 0.0080338731 -0.16357939 0.122251906
## C22.5n.6 -0.01713283 0.25920483 0.0510644079 -0.16325701 0.126967657
## C18.3n.3 -0.02817369 0.05135326 -0.0925313424 0.18887951 -0.041094593
## C20.3n.3 -0.07608099 -0.08464070 -0.0098514416 0.20485180 -0.060366976
## C20.5n.3 -0.16999587 -0.27836844 -0.0570984660 0.12359405 -0.096937647
## C22.5n.3 -0.28771416 -0.05127361 -0.0879868139 0.20577994 -0.098715292
## C22.6n.3 -0.20908287 -0.23098548 -0.0936791430 -0.05456911 -0.062714649
##
## $corr.X.yscores
## [,1] [,2] [,3] [,4] [,5] [,6]
## X36b4 -0.00410846 0.07909890 0.331666884 -0.16603622 -0.367577298 0.3648132
## ACAT1 -0.10994617 0.03457353 -0.197658448 0.16619336 -0.307314977 0.2896869
## ACAT2 0.18092685 0.57213372 0.523853404 -0.25308861 0.206404198 0.1117941
## ACBP 0.65374666 -0.24905956 0.490862694 0.15666059 -0.110982074 0.2259979
## ACC1 0.06372280 0.01266288 0.115490359 0.23079572 -0.468064193 0.3291203
## ACC2 0.33811625 0.33482199 0.069366540 0.32970450 -0.002073418 0.4533683
## ACOTH -0.47294469 0.38039656 -0.329963027 -0.03364228 -0.342112986 0.2921223
## ADISP -0.25163731 -0.08918129 -0.124941715 -0.09017766 -0.071994708 0.5308597
## ADSS1 -0.16134361 0.15755490 -0.039748322 0.04353724 -0.287867884 0.5751196
## ALDH3 0.75681708 -0.30193146 -0.007496683 -0.18828880 -0.341059980 0.2027823
## [,7] [,8] [,9] [,10]
## X36b4 0.13247761 -0.256598740 0.21311316 0.02419397
## ACAT1 -0.33078675 0.045025339 0.24183467 0.13492567
## ACAT2 -0.22289715 0.012136793 -0.09002483 -0.02732512
## ACBP -0.10551733 -0.018281662 -0.07550581 -0.06754331
## ACC1 0.07850524 0.254403398 0.23038002 -0.03942510
## ACC2 0.21134475 0.138345875 0.14984145 0.02624457
## ACOTH -0.18436667 0.007843896 0.11212386 -0.06650722
## ADISP -0.11756815 0.141612378 0.26892565 0.05559203
## ADSS1 0.10823860 0.204604290 -0.05369796 0.06742540
## ALDH3 0.03072416 0.057400738 0.04327535 0.03455472
##
## $corr.Y.yscores
## [,1] [,2] [,3] [,4] [,5]
## C14.0 0.05383151 0.46000986 -0.001583933 0.13660027 0.21906301
## C16.0 0.67970178 -0.26428045 0.408497458 0.04888151 -0.05531248
## C18.0 0.39904186 -0.60090657 0.101938448 -0.25902939 0.05117907
## C16.1n.9 -0.34292387 0.43278685 0.014769114 0.29550681 0.03963332
## C16.1n.7 0.13503138 0.48405207 -0.075088570 0.09165915 0.16929855
## C18.1n.9 -0.03025424 0.60199372 0.086999772 0.28592987 0.06288686
## C18.1n.7 0.21864569 0.31447478 0.132949236 0.24781731 0.18106785
## C20.1n.9 -0.34246994 0.16257482 -0.273675632 0.25895448 0.59120368
## C20.3n.9 0.60289804 0.30028941 0.169792765 0.39174063 0.18172791
## C18.2n.6 -0.69689608 -0.15802835 -0.071754020 0.01794605 0.01667051
## C18.3n.6 0.33578389 0.21927897 0.182835888 0.18730666 0.25011358
## C20.2n.6 -0.52855777 -0.26455923 -0.091254729 0.26785275 0.15314278
## C20.3n.6 0.43322563 -0.44747686 0.242184408 -0.15415625 0.02516441
## C20.4n.6 0.23837990 -0.44893893 0.123772448 -0.07010929 0.18820920
## C22.4n.6 -0.17922479 -0.43919892 -0.121354734 0.10928369 0.20528169
## C22.5n.6 0.02927178 -0.47176032 -0.085940769 0.18811838 0.11708081
## C18.3n.3 -0.13474507 0.10610809 -0.648569103 -0.23315998 -0.20160804
## C20.3n.3 0.02451195 -0.08840595 -0.653915887 -0.14822164 -0.13925491
## C20.5n.3 0.14272058 -0.32619834 -0.309539108 -0.23138288 -0.13831645
## C22.5n.3 0.15587014 -0.02982574 0.019132575 -0.03804097 -0.10623521
## C22.6n.3 0.04247133 -0.18290199 0.359237869 -0.25164481 -0.30800525
## [,6] [,7] [,8] [,9] [,10]
## C14.0 0.47911255 0.03430895 0.248187253 0.08089356 -0.26169742
## C16.0 0.07832430 -0.15821067 0.168209341 -0.03370309 -0.03284636
## C18.0 -0.22638175 -0.09999293 -0.093179300 -0.14317379 0.03230422
## C16.1n.9 0.44577541 0.16674443 0.242808302 -0.03035289 -0.06942378
## C16.1n.7 0.45815911 0.02237446 0.218104745 0.09247011 -0.26397530
## C18.1n.9 0.44011763 0.11365772 0.195136076 0.04295362 0.05850680
## C18.1n.7 0.61082023 0.12014689 0.190642100 0.07371899 -0.16325386
## C20.1n.9 -0.16994781 0.08915028 0.092571056 0.15636278 0.01451599
## C20.3n.9 0.15636744 0.23661970 -0.052494916 0.28525326 -0.06109526
## C18.2n.6 -0.41208676 -0.03373368 -0.136290229 -0.11841463 0.22474120
## C18.3n.6 -0.17113767 0.19633741 0.001540664 0.21311306 0.06298242
## C20.2n.6 -0.29716348 0.12788172 -0.065236100 -0.21749079 0.20297000
## C20.3n.6 -0.19171051 0.12618859 -0.021577372 -0.43752463 0.19323487
## C20.4n.6 -0.05707801 0.37168657 -0.018043302 -0.38272495 0.28934051
## C22.4n.6 -0.12531328 0.19478733 0.013262612 -0.29905686 0.33886935
## C22.5n.6 -0.02368153 0.40417092 0.084298996 -0.29846749 0.35194091
## C18.3n.3 -0.03894256 0.08007371 -0.152754132 0.34531070 -0.11390986
## C20.3n.3 -0.10516153 -0.13197791 -0.016263121 0.37451134 -0.16733087
## C20.5n.3 -0.23497361 -0.43405221 -0.094260241 0.22595541 -0.26870090
## C22.5n.3 -0.39768753 -0.07994953 -0.145251858 0.37620818 -0.27362834
## C22.6n.3 -0.28900089 -0.36016926 -0.154648963 -0.09976359 -0.17383837