| tags: [ PCA Ocular Biometry R ] categories: [Coding Experiments ]
PCA of Phenotypic Data
# required packages
require(tidyverse)
require(broom)
require(missMDA)
require(FactoMineR)
require(moments)
require(Hmisc)
require(corrplot)Introduction
The results of the Pearson correlations between the phenotypic variables, indicate that there were several correlated variables, that were not due to being left and right values of the same variable. For example, the keratometry measurements were negatively correlated with axial length. These relationships suggest that there is an underlying component, or a latent phenotype, that may better explain these variables. Performing a principal component analysis on these variables would reduce the dimensions that need to be considered in subsequent analyses, without excluding any variables, by identifying principal components. https://towardsdatascience.com/a-one-stop-shop-for-principal-component-analysis-5582fb7e0a9c
Methods and Results
1. Load and generate initial data (incl. subsetting and mipca)
phen.data.uvaf <- read.csv('C:/Users/Martha/Documents/Honours/Project/honours.project/Data/NIES_master_database_120815_data_dictionary-2.csv')
summary.uvaf <- summary(phen.data.uvaf)
quant.data_uvaf <- c("R.Logmar.VA", "RVA.with.PH", "L.Logmar.VA", "LVA.with.PH",
"R.Sph..pre.dilate.", "R.Cyl..pre.dilate.", "R.Axis..pre.dilate.", "L.Sph..pre.dilate.", "L.Cyl..pre.dilate.","L.Axis..pre.dilate.", "R.K.value.H", "R.K.Value.H.Axis", "R.K.value.V", "R.K.value.V.Axis", "L.K.value.H","L.K.value.H.Axis", "L.K.value.V", "L.K.value.V.Axis", "R.Pachimetry", "L.Pachimetry", "R.Axial.Length","L.Axial.Length", "R.AC.Depth", "L.AC.Depth", "R.IOP.mmHg", "L.IOP.mmHg", "R.CDR", "L.CDR", "totaluvafmm")
quant.data.subset_uvaf <- phen.data.uvaf[quant.data_uvaf]
phen.data.adults_uvaf<-phen.data.uvaf[phen.data.uvaf$Age.excel>17,]
quant.variables_uvaf<- c("R.Logmar.VA", "L.Logmar.VA","R.Sph..pre.dilate.", "R.Cyl..pre.dilate.", "R.Axis..pre.dilate.", "L.Sph..pre.dilate.", "L.Cyl..pre.dilate.","L.Axis..pre.dilate.", "R.K.value.H", "R.K.Value.H.Axis", "R.K.value.V", "R.K.value.V.Axis", "L.K.value.H", "L.K.value.H.Axis", "L.K.value.V", "L.K.value.V.Axis", "R.Pachimetry", "L.Pachimetry", "R.Axial.Length","L.Axial.Length", "R.AC.Depth", "L.AC.Depth", "R.IOP.mmHg", "L.IOP.mmHg", "R.CDR", "L.CDR", "totaluvafmm")
quant.data.adults_uvaf<- phen.data.adults_uvaf[quant.variables_uvaf]
ocular_data_uvaf <- read.csv('quant.data.adults_uvaf.csv', head = T, as.is = T, row.names = 1)
ocular_data_uvaf <- as.matrix(ocular_data_uvaf)
nbdim = estim_ncpPCA(ocular_data_uvaf, method = 'EM', method.cv="Kfold")##
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|=================================================================| 100%nbdim## $ncp
## [1] 5
##
## $criterion
## 0 1 2 3 4 5
## 827407.7 829593.9 824966.6 826207.3 817653.0 798909.9res.comp = MIPCA(ocular_data_uvaf, ncp = nbdim$ncp, nboot = 1000)
imputed_phen_data_uvaf<-res.comp$res.imputePCA2. Force data into data frame
data.imputed.phen<-as.data.frame(imputed_phen_data_uvaf)
data("data.imputed.phen")## Warning in data("data.imputed.phen"): data set 'data.imputed.phen' not
## found3. Perform PCA
res.pca.phen<-PCA(imputed_phen_data_uvaf, ncp = 9, graph = FALSE)4. Extract eigenvalues and variable contribution values
eig.val.phen<-res.pca.phen$eig
eig.val.phen## eigenvalue percentage of variance
## comp 1 4.46445605 16.5350224
## comp 2 3.03462767 11.2393617
## comp 3 2.70591009 10.0218892
## comp 4 2.29083212 8.4845634
## comp 5 1.99631740 7.3937681
## comp 6 1.73902134 6.4408198
## comp 7 1.33361314 4.9393079
## comp 8 1.14042049 4.2237796
## comp 9 1.03413600 3.8301334
## comp 10 0.95617736 3.5413976
## comp 11 0.90422198 3.3489703
## comp 12 0.82071526 3.0396861
## comp 13 0.76532587 2.8345402
## comp 14 0.69691037 2.5811495
## comp 15 0.62562435 2.3171272
## comp 16 0.56537477 2.0939806
## comp 17 0.43981044 1.6289276
## comp 18 0.37185411 1.3772374
## comp 19 0.23882002 0.8845186
## comp 20 0.20310730 0.7522492
## comp 21 0.19345131 0.7164863
## comp 22 0.15046332 0.5572715
## comp 23 0.10063631 0.3727271
## comp 24 0.09238358 0.3421614
## comp 25 0.05514221 0.2042304
## comp 26 0.04775727 0.1768788
## comp 27 0.03288987 0.1218143
## cumulative percentage of variance
## comp 1 16.53502
## comp 2 27.77438
## comp 3 37.79627
## comp 4 46.28084
## comp 5 53.67460
## comp 6 60.11542
## comp 7 65.05473
## comp 8 69.27851
## comp 9 73.10865
## comp 10 76.65004
## comp 11 79.99901
## comp 12 83.03870
## comp 13 85.87324
## comp 14 88.45439
## comp 15 90.77152
## comp 16 92.86550
## comp 17 94.49442
## comp 18 95.87166
## comp 19 96.75618
## comp 20 97.50843
## comp 21 98.22492
## comp 22 98.78219
## comp 23 99.15492
## comp 24 99.49708
## comp 25 99.70131
## comp 26 99.87819
## comp 27 100.000005. Produce screeplot
barplot(eig.val.phen[, 2],
names.arg = 1:nrow(eig.val.phen),
main = "Variances Explained by PCs (%)",
xlab = "Principal Components",
ylab = "Percentage of variances",
col ="steelblue")
lines(x = 1:nrow(eig.val.phen), eig.val.phen[, 2],
type = "b", pch = 19, col = "red")
6. View variable results from PCA
head(res.pca.phen$var)## $coord
## Dim.1 Dim.2 Dim.3 Dim.4
## R.Logmar.VA 0.0544464200 -0.114937900 0.540407138 0.183366000
## L.Logmar.VA 0.0025023044 -0.161163535 0.545612781 0.215880315
## R.Sph..pre.dilate. 0.2222981329 -0.749667932 -0.074503133 -0.099498700
## R.Cyl..pre.dilate. -0.0389650618 -0.007827815 -0.677201661 -0.182137588
## R.Axis..pre.dilate. 0.0744110543 -0.036495457 0.180273031 0.116551594
## L.Sph..pre.dilate. 0.2157730734 -0.741563320 -0.028337763 -0.099630446
## L.Cyl..pre.dilate. -0.0353192404 0.015101176 -0.659967624 -0.129377482
## L.Axis..pre.dilate. -0.0663972718 -0.094991703 0.150404068 -0.006797582
## R.K.value.H 0.8477612821 0.362041934 0.008288281 0.006889421
## R.K.Value.H.Axis 0.0148145126 0.108818430 -0.039062580 0.076872515
## R.K.value.V 0.8529066416 0.331382329 0.239749496 0.054567761
## R.K.value.V.Axis 0.0293931928 -0.117603074 0.041566255 -0.081364253
## L.K.value.H 0.8067098352 0.390929801 -0.066829148 0.024529945
## L.K.value.H.Axis 0.0025602251 -0.160882634 0.146649344 -0.117936268
## L.K.value.V 0.8377724869 0.355676325 0.253603322 0.047540429
## L.K.value.V.Axis -0.0004256266 0.085964553 -0.050067628 0.150582886
## R.Pachimetry -0.0403711404 0.073509124 -0.432580223 0.602275884
## L.Pachimetry -0.0418685404 0.054815570 -0.431089452 0.614955798
## R.Axial.Length -0.8163529851 0.364141160 0.148322854 0.097480184
## L.Axial.Length -0.7689956145 0.353186716 0.154045266 0.091400848
## R.AC.Depth -0.3054051944 0.640632645 0.190011182 -0.106126466
## L.AC.Depth -0.3456434183 0.606894505 0.198229281 -0.109559431
## R.IOP.mmHg 0.0772203412 0.058119319 -0.232760509 0.666948632
## L.IOP.mmHg 0.0603489198 0.040067981 -0.210765096 0.689190117
## R.CDR -0.1224100323 -0.341268728 0.447955677 0.408191925
## L.CDR -0.1315457636 -0.349791812 0.416555582 0.398488175
## totaluvafmm -0.1926461484 -0.073715297 -0.200184007 -0.212104536
## Dim.5 Dim.6 Dim.7 Dim.8
## R.Logmar.VA -0.073819981 -0.17834950 -0.1312467114 -0.308213628
## L.Logmar.VA -0.105400976 -0.13068434 -0.1710628815 -0.227924588
## R.Sph..pre.dilate. -0.025395355 -0.18664028 0.0001315208 0.310829034
## R.Cyl..pre.dilate. 0.119434081 0.34824026 0.1208151556 -0.105037911
## R.Axis..pre.dilate. 0.425202489 -0.33587579 -0.1227933562 -0.008471504
## L.Sph..pre.dilate. -0.002422289 -0.24385470 0.0403430289 0.386978856
## L.Cyl..pre.dilate. 0.204580195 0.34719734 0.0887889825 -0.188682860
## L.Axis..pre.dilate. -0.491021665 0.08584972 -0.1082354042 0.168292466
## R.K.value.H 0.009406417 0.15586390 0.0933216959 -0.024477674
## R.K.Value.H.Axis 0.527260543 -0.31399070 -0.1179732223 -0.017239604
## R.K.value.V -0.030477293 -0.00885822 0.0470011390 0.024836880
## R.K.value.V.Axis -0.519474330 0.24669856 0.1236579264 0.048218530
## L.K.value.H 0.072463954 0.17272134 0.0872749408 -0.054932589
## L.K.value.H.Axis -0.491642347 0.29019459 -0.1559239020 0.027673280
## L.K.value.V -0.050871910 -0.01063553 0.0170994501 0.032418519
## L.K.value.V.Axis 0.504744985 -0.18514359 0.0199852529 0.155000435
## R.Pachimetry -0.321465517 -0.39788161 0.3608643272 -0.031907007
## L.Pachimetry -0.324539655 -0.38778394 0.3553319230 -0.036362185
## R.Axial.Length 0.008961286 0.03963525 -0.0579100072 -0.138021188
## L.Axial.Length -0.064433440 0.02754427 -0.0423815190 -0.131798512
## R.AC.Depth -0.040846644 -0.04253352 0.1464267126 0.473757436
## L.AC.Depth -0.019516425 -0.01395826 0.1730881647 0.495157379
## R.IOP.mmHg 0.005568590 0.25749142 -0.4959447285 0.227385004
## L.IOP.mmHg 0.007289724 0.29788009 -0.4775788627 0.197351855
## R.CDR 0.289681991 0.45939849 0.4156534736 0.047170638
## L.CDR 0.316173256 0.46543030 0.4218965815 0.055180782
## totaluvafmm 0.221325266 0.07647918 -0.1601102389 0.187275915
## Dim.9
## R.Logmar.VA 0.185538848
## L.Logmar.VA 0.152998709
## R.Sph..pre.dilate. 0.082132646
## R.Cyl..pre.dilate. 0.221927042
## R.Axis..pre.dilate. 0.264464151
## L.Sph..pre.dilate. 0.069133562
## L.Cyl..pre.dilate. 0.291446581
## L.Axis..pre.dilate. 0.091481866
## R.K.value.H 0.033853766
## R.K.Value.H.Axis 0.291256580
## R.K.value.V -0.087703772
## R.K.value.V.Axis -0.369750439
## L.K.value.H 0.080505625
## L.K.value.H.Axis 0.414703648
## L.K.value.V -0.080150872
## L.K.value.V.Axis -0.409785778
## R.Pachimetry 0.046031988
## L.Pachimetry 0.051015281
## R.Axial.Length -0.073753233
## L.Axial.Length -0.089216780
## R.AC.Depth 0.216547427
## L.AC.Depth 0.223984465
## R.IOP.mmHg -0.002536463
## L.IOP.mmHg -0.013793992
## R.CDR 0.045244378
## L.CDR 0.022572131
## totaluvafmm -0.226155208
##
## $cor
## Dim.1 Dim.2 Dim.3 Dim.4
## R.Logmar.VA 0.0544464200 -0.114937900 0.540407138 0.183366000
## L.Logmar.VA 0.0025023044 -0.161163535 0.545612781 0.215880315
## R.Sph..pre.dilate. 0.2222981329 -0.749667932 -0.074503133 -0.099498700
## R.Cyl..pre.dilate. -0.0389650618 -0.007827815 -0.677201661 -0.182137588
## R.Axis..pre.dilate. 0.0744110543 -0.036495457 0.180273031 0.116551594
## L.Sph..pre.dilate. 0.2157730734 -0.741563320 -0.028337763 -0.099630446
## L.Cyl..pre.dilate. -0.0353192404 0.015101176 -0.659967624 -0.129377482
## L.Axis..pre.dilate. -0.0663972718 -0.094991703 0.150404068 -0.006797582
## R.K.value.H 0.8477612821 0.362041934 0.008288281 0.006889421
## R.K.Value.H.Axis 0.0148145126 0.108818430 -0.039062580 0.076872515
## R.K.value.V 0.8529066416 0.331382329 0.239749496 0.054567761
## R.K.value.V.Axis 0.0293931928 -0.117603074 0.041566255 -0.081364253
## L.K.value.H 0.8067098352 0.390929801 -0.066829148 0.024529945
## L.K.value.H.Axis 0.0025602251 -0.160882634 0.146649344 -0.117936268
## L.K.value.V 0.8377724869 0.355676325 0.253603322 0.047540429
## L.K.value.V.Axis -0.0004256266 0.085964553 -0.050067628 0.150582886
## R.Pachimetry -0.0403711404 0.073509124 -0.432580223 0.602275884
## L.Pachimetry -0.0418685404 0.054815570 -0.431089452 0.614955798
## R.Axial.Length -0.8163529851 0.364141160 0.148322854 0.097480184
## L.Axial.Length -0.7689956145 0.353186716 0.154045266 0.091400848
## R.AC.Depth -0.3054051944 0.640632645 0.190011182 -0.106126466
## L.AC.Depth -0.3456434183 0.606894505 0.198229281 -0.109559431
## R.IOP.mmHg 0.0772203412 0.058119319 -0.232760509 0.666948632
## L.IOP.mmHg 0.0603489198 0.040067981 -0.210765096 0.689190117
## R.CDR -0.1224100323 -0.341268728 0.447955677 0.408191925
## L.CDR -0.1315457636 -0.349791812 0.416555582 0.398488175
## totaluvafmm -0.1926461484 -0.073715297 -0.200184007 -0.212104536
## Dim.5 Dim.6 Dim.7 Dim.8
## R.Logmar.VA -0.073819981 -0.17834950 -0.1312467114 -0.308213628
## L.Logmar.VA -0.105400976 -0.13068434 -0.1710628815 -0.227924588
## R.Sph..pre.dilate. -0.025395355 -0.18664028 0.0001315208 0.310829034
## R.Cyl..pre.dilate. 0.119434081 0.34824026 0.1208151556 -0.105037911
## R.Axis..pre.dilate. 0.425202489 -0.33587579 -0.1227933562 -0.008471504
## L.Sph..pre.dilate. -0.002422289 -0.24385470 0.0403430289 0.386978856
## L.Cyl..pre.dilate. 0.204580195 0.34719734 0.0887889825 -0.188682860
## L.Axis..pre.dilate. -0.491021665 0.08584972 -0.1082354042 0.168292466
## R.K.value.H 0.009406417 0.15586390 0.0933216959 -0.024477674
## R.K.Value.H.Axis 0.527260543 -0.31399070 -0.1179732223 -0.017239604
## R.K.value.V -0.030477293 -0.00885822 0.0470011390 0.024836880
## R.K.value.V.Axis -0.519474330 0.24669856 0.1236579264 0.048218530
## L.K.value.H 0.072463954 0.17272134 0.0872749408 -0.054932589
## L.K.value.H.Axis -0.491642347 0.29019459 -0.1559239020 0.027673280
## L.K.value.V -0.050871910 -0.01063553 0.0170994501 0.032418519
## L.K.value.V.Axis 0.504744985 -0.18514359 0.0199852529 0.155000435
## R.Pachimetry -0.321465517 -0.39788161 0.3608643272 -0.031907007
## L.Pachimetry -0.324539655 -0.38778394 0.3553319230 -0.036362185
## R.Axial.Length 0.008961286 0.03963525 -0.0579100072 -0.138021188
## L.Axial.Length -0.064433440 0.02754427 -0.0423815190 -0.131798512
## R.AC.Depth -0.040846644 -0.04253352 0.1464267126 0.473757436
## L.AC.Depth -0.019516425 -0.01395826 0.1730881647 0.495157379
## R.IOP.mmHg 0.005568590 0.25749142 -0.4959447285 0.227385004
## L.IOP.mmHg 0.007289724 0.29788009 -0.4775788627 0.197351855
## R.CDR 0.289681991 0.45939849 0.4156534736 0.047170638
## L.CDR 0.316173256 0.46543030 0.4218965815 0.055180782
## totaluvafmm 0.221325266 0.07647918 -0.1601102389 0.187275915
## Dim.9
## R.Logmar.VA 0.185538848
## L.Logmar.VA 0.152998709
## R.Sph..pre.dilate. 0.082132646
## R.Cyl..pre.dilate. 0.221927042
## R.Axis..pre.dilate. 0.264464151
## L.Sph..pre.dilate. 0.069133562
## L.Cyl..pre.dilate. 0.291446581
## L.Axis..pre.dilate. 0.091481866
## R.K.value.H 0.033853766
## R.K.Value.H.Axis 0.291256580
## R.K.value.V -0.087703772
## R.K.value.V.Axis -0.369750439
## L.K.value.H 0.080505625
## L.K.value.H.Axis 0.414703648
## L.K.value.V -0.080150872
## L.K.value.V.Axis -0.409785778
## R.Pachimetry 0.046031988
## L.Pachimetry 0.051015281
## R.Axial.Length -0.073753233
## L.Axial.Length -0.089216780
## R.AC.Depth 0.216547427
## L.AC.Depth 0.223984465
## R.IOP.mmHg -0.002536463
## L.IOP.mmHg -0.013793992
## R.CDR 0.045244378
## L.CDR 0.022572131
## totaluvafmm -0.226155208
##
## $cos2
## Dim.1 Dim.2 Dim.3 Dim.4
## R.Logmar.VA 2.964413e-03 1.321072e-02 0.2920398743 3.362309e-02
## L.Logmar.VA 6.261527e-06 2.597369e-02 0.2976933064 4.660431e-02
## R.Sph..pre.dilate. 4.941646e-02 5.620020e-01 0.0055507169 9.899991e-03
## R.Cyl..pre.dilate. 1.518276e-03 6.127469e-05 0.4586020895 3.317410e-02
## R.Axis..pre.dilate. 5.537005e-03 1.331918e-03 0.0324983658 1.358427e-02
## L.Sph..pre.dilate. 4.655802e-02 5.499162e-01 0.0008030288 9.926226e-03
## L.Cyl..pre.dilate. 1.247449e-03 2.280455e-04 0.4355572644 1.673853e-02
## L.Axis..pre.dilate. 4.408598e-03 9.023424e-03 0.0226213836 4.620712e-05
## R.K.value.H 7.186992e-01 1.310744e-01 0.0000686956 4.746413e-05
## R.K.Value.H.Axis 2.194698e-04 1.184145e-02 0.0015258852 5.909384e-03
## R.K.value.V 7.274497e-01 1.098142e-01 0.0574798209 2.977640e-03
## R.K.value.V.Axis 8.639598e-04 1.383048e-02 0.0017277536 6.620142e-03
## L.K.value.H 6.507808e-01 1.528261e-01 0.0044661351 6.017182e-04
## L.K.value.H.Axis 6.554753e-06 2.588322e-02 0.0215060300 1.390896e-02
## L.K.value.V 7.018627e-01 1.265056e-01 0.0643146447 2.260092e-03
## L.K.value.V.Axis 1.811580e-07 7.389904e-03 0.0025067674 2.267521e-02
## R.Pachimetry 1.629829e-03 5.403591e-03 0.1871256489 3.627362e-01
## L.Pachimetry 1.752975e-03 3.004747e-03 0.1858381156 3.781706e-01
## R.Axial.Length 6.664322e-01 1.325988e-01 0.0219996690 9.502386e-03
## L.Axial.Length 5.913543e-01 1.247409e-01 0.0237299439 8.354115e-03
## R.AC.Depth 9.327233e-02 4.104102e-01 0.0361042494 1.126283e-02
## L.AC.Depth 1.194694e-01 3.683209e-01 0.0392948476 1.200327e-02
## R.IOP.mmHg 5.962981e-03 3.377855e-03 0.0541774544 4.448205e-01
## L.IOP.mmHg 3.641992e-03 1.605443e-03 0.0444219259 4.749830e-01
## R.CDR 1.498422e-02 1.164643e-01 0.2006642887 1.666206e-01
## L.CDR 1.730429e-02 1.223543e-01 0.1735185526 1.587928e-01
## totaluvafmm 3.711254e-02 5.433945e-03 0.0400736365 4.498833e-02
## Dim.5 Dim.6 Dim.7 Dim.8
## R.Logmar.VA 5.449390e-03 3.180854e-02 1.722570e-02 9.499564e-02
## L.Logmar.VA 1.110937e-02 1.707840e-02 2.926251e-02 5.194962e-02
## R.Sph..pre.dilate. 6.449240e-04 3.483459e-02 1.729771e-08 9.661469e-02
## R.Cyl..pre.dilate. 1.426450e-02 1.212713e-01 1.459630e-02 1.103296e-02
## R.Axis..pre.dilate. 1.807972e-01 1.128125e-01 1.507821e-02 7.176638e-05
## L.Sph..pre.dilate. 5.867484e-06 5.946511e-02 1.627560e-03 1.497526e-01
## L.Cyl..pre.dilate. 4.185306e-02 1.205460e-01 7.883483e-03 3.560122e-02
## L.Axis..pre.dilate. 2.411023e-01 7.370174e-03 1.171490e-02 2.832235e-02
## R.K.value.H 8.848068e-05 2.429356e-02 8.708939e-03 5.991565e-04
## R.K.Value.H.Axis 2.780037e-01 9.859016e-02 1.391768e-02 2.972040e-04
## R.K.value.V 9.288654e-04 7.846807e-05 2.209107e-03 6.168706e-04
## R.K.value.V.Axis 2.698536e-01 6.086018e-02 1.529128e-02 2.325027e-03
## L.K.value.H 5.251025e-03 2.983266e-02 7.616915e-03 3.017589e-03
## L.K.value.H.Axis 2.417122e-01 8.421290e-02 2.431226e-02 7.658104e-04
## L.K.value.V 2.587951e-03 1.131146e-04 2.923912e-04 1.050960e-03
## L.K.value.V.Axis 2.547675e-01 3.427815e-02 3.994103e-04 2.402513e-02
## R.Pachimetry 1.033401e-01 1.583098e-01 1.302231e-01 1.018057e-03
## L.Pachimetry 1.053260e-01 1.503764e-01 1.262608e-01 1.322208e-03
## R.Axial.Length 8.030465e-05 1.570953e-03 3.353569e-03 1.904985e-02
## L.Axial.Length 4.151668e-03 7.586866e-04 1.796193e-03 1.737085e-02
## R.AC.Depth 1.668448e-03 1.809100e-03 2.144078e-02 2.244461e-01
## L.AC.Depth 3.808908e-04 1.948330e-04 2.995951e-02 2.451808e-01
## R.IOP.mmHg 3.100919e-05 6.630183e-02 2.459612e-01 5.170394e-02
## L.IOP.mmHg 5.314007e-05 8.873255e-02 2.280816e-01 3.894775e-02
## R.CDR 8.391566e-02 2.110470e-01 1.727678e-01 2.225069e-03
## L.CDR 9.996553e-02 2.166254e-01 1.779967e-01 3.044919e-03
## totaluvafmm 4.898487e-02 5.849065e-03 2.563529e-02 3.507227e-02
## Dim.9
## R.Logmar.VA 3.442466e-02
## L.Logmar.VA 2.340860e-02
## R.Sph..pre.dilate. 6.745772e-03
## R.Cyl..pre.dilate. 4.925161e-02
## R.Axis..pre.dilate. 6.994129e-02
## L.Sph..pre.dilate. 4.779449e-03
## L.Cyl..pre.dilate. 8.494111e-02
## L.Axis..pre.dilate. 8.368932e-03
## R.K.value.H 1.146077e-03
## R.K.Value.H.Axis 8.483040e-02
## R.K.value.V 7.691952e-03
## R.K.value.V.Axis 1.367154e-01
## L.K.value.H 6.481156e-03
## L.K.value.H.Axis 1.719791e-01
## L.K.value.V 6.424162e-03
## L.K.value.V.Axis 1.679244e-01
## R.Pachimetry 2.118944e-03
## L.Pachimetry 2.602559e-03
## R.Axial.Length 5.439539e-03
## L.Axial.Length 7.959634e-03
## R.AC.Depth 4.689279e-02
## L.AC.Depth 5.016904e-02
## R.IOP.mmHg 6.433646e-06
## L.IOP.mmHg 1.902742e-04
## R.CDR 2.047054e-03
## L.CDR 5.095011e-04
## totaluvafmm 5.114618e-02
##
## $contrib
## Dim.1 Dim.2 Dim.3 Dim.4
## R.Logmar.VA 6.640031e-02 0.435332513 10.792667312 1.467723882
## L.Logmar.VA 1.402529e-04 0.855910112 11.001596356 2.034383483
## R.Sph..pre.dilate. 1.106886e+00 18.519636345 0.205133086 0.432157000
## R.Cyl..pre.dilate. 3.400809e-02 0.002019183 16.948164330 1.448124495
## R.Axis..pre.dilate. 1.240242e-01 0.043890668 1.201014249 0.592984272
## L.Sph..pre.dilate. 1.042860e+00 18.121371640 0.029676847 0.433302189
## L.Cyl..pre.dilate. 2.794179e-02 0.007514777 16.096516484 0.730674795
## L.Axis..pre.dilate. 9.874882e-02 0.297348627 0.835999085 0.002017045
## R.K.value.H 1.609825e+01 4.319289748 0.002538724 0.002071916
## R.K.Value.H.Axis 4.915936e-03 0.390210995 0.056390831 0.257957950
## R.K.value.V 1.629425e+01 3.618705831 2.124232472 0.129980738
## R.K.value.V.Axis 1.935196e-02 0.455755514 0.063851107 0.288984151
## L.K.value.H 1.457693e+01 5.036074482 0.165051126 0.026266359
## L.K.value.H.Axis 1.468209e-04 0.852929085 0.794779916 0.607157686
## L.K.value.V 1.572113e+01 4.168737071 2.376821198 0.098658142
## L.K.value.V.Axis 4.057785e-06 0.243519313 0.092640454 0.989823976
## R.Pachimetry 3.650678e-02 0.178064391 6.915442213 15.834256823
## L.Pachimetry 3.926513e-02 0.099015332 6.867859947 16.508002987
## R.Axial.Length 1.492751e+01 4.369524006 0.813022912 0.414800638
## L.Axial.Length 1.324583e+01 4.110581931 0.876967196 0.364676001
## R.AC.Depth 2.089221e+00 13.524235309 1.334273800 0.491647847
## L.AC.Depth 2.676012e+00 12.137269560 1.452186003 0.523969819
## R.IOP.mmHg 1.335657e-01 0.111310369 2.002189745 19.417419319
## L.IOP.mmHg 8.157751e-02 0.052904121 1.641663038 20.734082340
## R.CDR 3.356336e-01 3.837846261 7.415778120 7.273367900
## L.CDR 3.876013e-01 4.031938178 6.412576416 6.931665771
## totaluvafmm 8.312891e-01 0.179064638 1.480967035 1.963842478
## Dim.5 Dim.6 Dim.7 Dim.8
## R.Logmar.VA 2.729721e-01 1.829105978 1.291656e+00 8.329878416
## L.Logmar.VA 5.564930e-01 0.982069436 2.194228e+00 4.555303781
## R.Sph..pre.dilate. 3.230569e-02 2.003114773 1.297056e-06 8.471847823
## R.Cyl..pre.dilate. 7.145407e-01 6.973535829 1.094493e+00 0.967446899
## R.Axis..pre.dilate. 9.056534e+00 6.487128459 1.130628e+00 0.006292975
## L.Sph..pre.dilate. 2.939154e-04 3.419458542 1.220414e-01 13.131352514
## L.Cyl..pre.dilate. 2.096513e+00 6.931829534 5.911372e-01 3.121762724
## L.Axis..pre.dilate. 1.207735e+01 0.423811602 8.784334e-01 2.483500984
## R.K.value.H 4.432195e-03 1.396967135 6.530334e-01 0.052538210
## R.K.Value.H.Axis 1.392583e+01 5.669289690 1.043607e+00 0.026060910
## R.K.value.V 4.652894e-02 0.004512197 1.656483e-01 0.054091507
## R.K.value.V.Axis 1.351757e+01 3.499679766 1.146606e+00 0.203874509
## L.K.value.H 2.630356e-01 1.715485582 5.711488e-01 0.264603223
## L.K.value.H.Axis 1.210790e+01 4.842545401 1.823037e+00 0.067151582
## L.K.value.V 1.296363e-01 0.006504498 2.192474e-02 0.092155512
## L.K.value.V.Axis 1.276187e+01 1.971117279 2.994949e-02 2.106690919
## R.Pachimetry 5.176535e+00 9.103383291 9.764681e+00 0.089270326
## L.Pachimetry 5.276014e+00 8.647184533 9.467571e+00 0.115940435
## R.Axial.Length 4.022639e-03 0.090335448 2.514649e-01 1.670423194
## L.Axial.Length 2.079663e-01 0.043627216 1.346862e-01 1.523196754
## R.AC.Depth 8.357630e-02 0.104029798 1.607721e+00 19.680995737
## L.AC.Depth 1.907967e-02 0.011203602 2.246492e+00 21.499160380
## R.IOP.mmHg 1.553320e-03 3.812594468 1.844322e+01 4.533761073
## L.IOP.mmHg 2.661905e-03 5.102441629 1.710253e+01 3.415210020
## R.CDR 4.203523e+00 12.135962288 1.295487e+01 0.195109531
## L.CDR 5.007497e+00 12.456739686 1.334695e+01 0.266999646
## totaluvafmm 2.453762e+00 0.336342341 1.922243e+00 3.075380417
## Dim.9
## R.Logmar.VA 3.328833e+00
## L.Logmar.VA 2.263591e+00
## R.Sph..pre.dilate. 6.523099e-01
## R.Cyl..pre.dilate. 4.762586e+00
## R.Axis..pre.dilate. 6.763258e+00
## L.Sph..pre.dilate. 4.621684e-01
## L.Cyl..pre.dilate. 8.213727e+00
## L.Axis..pre.dilate. 8.092680e-01
## R.K.value.H 1.108246e-01
## R.K.Value.H.Axis 8.203021e+00
## R.K.value.V 7.438046e-01
## R.K.value.V.Axis 1.322025e+01
## L.K.value.H 6.267218e-01
## L.K.value.H.Axis 1.663022e+01
## L.K.value.V 6.212106e-01
## L.K.value.V.Axis 1.623813e+01
## R.Pachimetry 2.048999e-01
## L.Pachimetry 2.516650e-01
## R.Axial.Length 5.259985e-01
## L.Axial.Length 7.696893e-01
## R.AC.Depth 4.534489e+00
## L.AC.Depth 4.851300e+00
## R.IOP.mmHg 6.221276e-04
## L.IOP.mmHg 1.839934e-02
## R.CDR 1.979482e-01
## L.CDR 4.926829e-02
## totaluvafmm 4.945788e+007. View individual results from PCA
head(res.pca.phen$indiv)## NULLDiscussion
The PCA identified nine principal components with an eigenvalue of >1. These principal components have an additive contribution to variance of about 73%, with the first principal component contributing about 16%. These nine principal components will be carried forward to the heritability analyses (aim 2) along with the 27 phenotypic variables to determine which variables and components are highly heritable. By using principal components for the subsequent aims (heritability analysis and GWAS), important pleiotropic variants may be found.