© Ricardo Solar/UFMG - compartilhamento e utilização não-comercial livres. Não reproduzir sem autorização > DOI: http://doi.org/10.5281/zenodo.7392285
Até agora, o que trabalhamos foram análises onde uma variável Y era confrontada contra variáveis (uma ou mais) X. A isso, damos o nome de análises univariadas. Nessa aula, mudaremos o foco, para análises onde temos muitas variáveis Y e ter ou não variáveis X. A essas, damos o nome de análises multivariadas.
São várias possibilidades, Análises de Componentes Principais, Análises de Redundância, Componentes Canônicos, e por aí vai. Aqui irei passar por algumas dessas, mas certamente sem cobrir todas. A principal referência para análises multivariadas é o livro Numerical Ecology de Legendre & Legendre. Caso vá utilizar algumas dessas análises, não deixe de consultar a referência.
1 Análise de Componentes Principais (PCA)
Para essa análise, iremos usar dados de uma série de características coletadas da expressão gênica de microorganismos de dois grupos, quero entender como isso se agrupa.
1.1 Carregamento dos dados
setwd("~/Dropbox/UFMG/Disciplinas/R UFAC/Aulas/Multivar/")
dados <- read.table("dados_EC.txt", h=T, row.names = 1)Agora vamos carregar os pacotes
library(vegan)
library(ggplot2)
library(factoextra)
library(ade4)
library(FactoMineR)1.2 Montagem do modelo de PCA
res.PCA <- FactoMineR::PCA(dados, scale.unit = T, graph = F, ncp=nrow(dados))
summary(res.PCA)##
## Call:
## FactoMineR::PCA(X = dados, scale.unit = T, ncp = nrow(dados),
## graph = F)
##
##
## Eigenvalues
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6 Dim.7
## Variance 520.916 113.068 71.792 55.646 35.515 30.692 25.686
## % of var. 55.240 11.990 7.613 5.901 3.766 3.255 2.724
## Cumulative % of var. 55.240 67.231 74.844 80.745 84.511 87.766 90.489
## Dim.8 Dim.9 Dim.10 Dim.11 Dim.12 Dim.13
## Variance 22.194 19.125 15.059 12.359 11.684 9.262
## % of var. 2.354 2.028 1.597 1.311 1.239 0.982
## Cumulative % of var. 92.843 94.871 96.468 97.779 99.018 100.000
##
## Individuals (the 10 first)
## Dist Dim.1 ctr cos2 Dim.2 ctr cos2
## For0 | 41.442 | -34.327 16.157 0.686 | -7.958 4.001 0.037 |
## For24 | 25.450 | -16.809 3.874 0.436 | -6.467 2.642 0.065 |
## For48 | 21.533 | -12.391 2.105 0.331 | -8.568 4.638 0.158 |
## For72 | 24.558 | 12.489 2.139 0.259 | -10.217 6.595 0.173 |
## For96 | 27.522 | 8.165 0.914 0.088 | -16.403 16.997 0.355 |
## For120 | 31.481 | 27.109 10.077 0.742 | 4.179 1.103 0.018 |
## For144 | 41.651 | 29.874 12.238 0.514 | 20.534 26.636 0.243 |
## Mix0 | 44.611 | -38.573 20.402 0.748 | 14.513 13.306 0.106 |
## Mix24 | 34.171 | -23.077 7.302 0.456 | 14.787 13.812 0.187 |
## Mix48 | 23.964 | -19.690 5.316 0.675 | 4.037 1.030 0.028 |
## Dim.3 ctr cos2
## For0 -17.053 28.934 0.169 |
## For24 -5.064 2.551 0.040 |
## For48 -6.888 4.720 0.102 |
## For72 7.920 6.241 0.104 |
## For96 8.227 6.734 0.089 |
## For120 -3.918 1.528 0.015 |
## For144 -14.133 19.874 0.115 |
## Mix0 5.414 2.917 0.015 |
## Mix24 15.020 22.446 0.193 |
## Mix48 1.556 0.241 0.004 |
##
## Variables (the 10 first)
## Dim.1 ctr cos2 Dim.2 ctr cos2 Dim.3 ctr
## X1.1.1.1 | 0.943 0.171 0.889 | 0.209 0.039 0.044 | 0.146 0.029
## X1.1.1.100 | 0.925 0.164 0.856 | 0.086 0.007 0.007 | 0.230 0.074
## X1.1.1.103 | -0.882 0.149 0.778 | 0.377 0.126 0.142 | 0.180 0.045
## X1.1.1.127 | -0.726 0.101 0.527 | 0.137 0.017 0.019 | 0.308 0.132
## X1.1.1.130 | -0.547 0.057 0.299 | 0.506 0.226 0.256 | 0.476 0.315
## X1.1.1.169 | 0.784 0.118 0.614 | 0.568 0.286 0.323 | 0.019 0.001
## X1.1.1.17 | 0.821 0.129 0.674 | 0.367 0.119 0.135 | 0.400 0.223
## X1.1.1.18 | -0.869 0.145 0.755 | 0.448 0.178 0.201 | 0.123 0.021
## X1.1.1.193 | 0.924 0.164 0.854 | 0.241 0.052 0.058 | 0.103 0.015
## X1.1.1.205 | 0.771 0.114 0.594 | 0.261 0.060 0.068 | 0.106 0.016
## cos2
## X1.1.1.1 0.021 |
## X1.1.1.100 0.053 |
## X1.1.1.103 0.033 |
## X1.1.1.127 0.095 |
## X1.1.1.130 0.226 |
## X1.1.1.169 0.000 |
## X1.1.1.17 0.160 |
## X1.1.1.18 0.015 |
## X1.1.1.193 0.011 |
## X1.1.1.205 0.011 |1.3 Eixos da PCA
Uma das utilizações da PCA é resumir muitas variáveis em seu primeiro eixo, e aí usar esse eixo como variável em análises univariadas. Como capturar esse eixo?
res.PCA$ind$coord[,1]## For0 For24 For48 For72 For96 For120 For144
## -34.326732 -16.809292 -12.391342 12.489109 8.165240 27.108870 29.874279
## Mix0 Mix24 Mix48 Mix72 Mix96 Mix120 Mix144
## -38.573113 -23.076539 -19.689819 11.037095 6.297256 22.295580 27.5994081.4 Correlação entre as variáveis e todos os eixos do PCA
dimdesc(res.PCA, 1:13, proba = 0.01)## $Dim.1
##
## Link between the variable and the continuous variables (R-square)
## =================================================================================
## correlation p.value
## X1.4.3.19 0.9863575 9.039070e-11
## X3.5.1.108 0.9850327 1.571746e-10
## X2.5.1.17 0.9837283 2.587644e-10
## X5.4.2.12 0.9830167 3.340097e-10
## X3.5.2.3 0.9809213 6.682965e-10
## X2.3.1.31 0.9765573 2.278362e-09
## X4.1.1.5 0.9747535 3.540667e-09
## X3.5.4.19 0.9735744 4.644346e-09
## X5.4.99.17 0.9725616 5.807264e-09
## X4.2.1.129 0.9725616 5.807264e-09
## X6.6.1.1 0.9720957 6.418057e-09
## X4.2.1.126 0.9705460 8.846871e-09
## X2.3.1.274 0.9686795 1.273900e-08
## X2.7.4.1 0.9662036 2.000104e-08
## X1.1.1.85 0.9659194 2.101863e-08
## X2.4.2.17 0.9657686 2.157583e-08
## X1.2.1.88 0.9639960 2.909724e-08
## X4.1.99.17 0.9635202 3.144961e-08
## X5.1.3.2 0.9632563 3.282062e-08
## X2.7.7.70 0.9629873 3.426907e-08
## X2.7.1.167 0.9629873 3.426907e-08
## X2.3.1.117 0.9629261 3.460551e-08
## X5.4.99.18 0.9628141 3.522885e-08
## X2.1.1.195 0.9625565 3.669828e-08
## X2.7.8.5 0.9624881 3.709666e-08
## X4.2.1.109 0.9620053 4.001338e-08
## X6.3.3.1 0.9619209 4.054213e-08
## X2.1.1.13 0.9612362 4.505021e-08
## X1.2.1.41 0.9593829 5.938012e-08
## X2.8.1.10 0.9591115 6.176473e-08
## X6.2.1.1 0.9585278 6.716150e-08
## X2.7.2.8 0.9582712 6.965540e-08
## X2.1.3.2 0.9580515 7.185026e-08
## X2.7.4.22 0.9572369 8.049581e-08
## X6.3.2.4 0.9570904 8.213856e-08
## X3.1.2.6 0.9562881 9.163436e-08
## X1.3.1.98 0.9558768 9.684358e-08
## X2.1.1.64 0.9551197 1.070748e-07
## X2.1.1.222 0.9551197 1.070748e-07
## X2.10.1.1 0.9539667 1.243634e-07
## X1.13.11.79 0.9538863 1.256500e-07
## X2.7.6.1 0.9533010 1.353559e-07
## X2.8.1.12 0.9528910 1.425160e-07
## X3.6.1.31 0.9527146 1.456918e-07
## X2.4.2.21 0.9516603 1.659185e-07
## X2.4.99.12 0.9510407 1.788533e-07
## X2.4.2.10 0.9503859 1.934172e-07
## X6.1.1.21 0.9503112 1.951403e-07
## X3.1.3.77 0.9501860 1.980538e-07
## X1.13.11.54 0.9498564 2.058986e-07
## X2.4.2.18 0.9495249 2.140480e-07
## X2.3.1.275 0.9489849 2.278919e-07
## X2.2.1.7 0.9483879 2.440488e-07
## X2.7.1.148 0.9478218 2.602352e-07
## X1.4.9.1 0.9473229 2.752250e-07
## X4.2.3.5 0.9469346 2.873802e-07
## X2.6.1.9 0.9468467 2.901925e-07
## X2.5.1.15 0.9465235 3.007275e-07
## X2.4.1.83 0.9465167 3.009540e-07
## X4.1.99.22 0.9464605 3.028187e-07
## X1.17.7.4 0.9459168 3.213599e-07
## X2.7.4.8 0.9456460 3.309406e-07
## X2.7.8.26 0.9450216 3.539327e-07
## X4.1.1.65 0.9441894 3.866120e-07
## X4.3.2.1 0.9441683 3.874723e-07
## X4.2.1.75 0.9441526 3.881149e-07
## X2.7.7.38 0.9439931 3.946731e-07
## X1.1.1.1 0.9429306 4.407574e-07
## X6.1.1.16 0.9428211 4.457482e-07
## X2.7.1.39 0.9425783 4.569833e-07
## X2.3.1.51 0.9415839 5.054649e-07
## X2.8.1.6 0.9410899 5.310856e-07
## X3.4.11.1 0.9410846 5.313645e-07
## X2.7.1.23 0.9409567 5.381750e-07
## X3.5.1.18 0.9409415 5.389857e-07
## X4.2.1.51 0.9408433 5.442724e-07
## X5.1.3.20 0.9407129 5.513488e-07
## X4.1.1.20 0.9406342 5.556623e-07
## X6.3.2.17 0.9396848 6.098814e-07
## X2.5.1.47 0.9391692 6.411156e-07
## X2.7.7.62 0.9386521 6.737495e-07
## X2.7.1.156 0.9386521 6.737495e-07
## X5.3.1.24 0.9373675 7.608108e-07
## X1.3.3.3 0.9372635 7.682411e-07
## X6.1.1.1 0.9371159 7.788991e-07
## X2.4.1.80 0.9357849 8.806184e-07
## X4.2.1.46 0.9355459 8.999974e-07
## X2.7.7.24 0.9345196 9.872467e-07
## X4.1.1.81 0.9344830 9.904836e-07
## X2.7.8.13 0.9341930 1.016438e-06
## X2.5.1.39 0.9336000 1.071241e-06
## X1.5.5.2 0.9332974 1.100136e-06
## X3.6.1.66 0.9319316 1.238676e-06
## X6.1.1.11 0.9318515 1.247226e-06
## X1.3.1.9 0.9310701 1.333239e-06
## X4.99.1.1 0.9307553 1.369239e-06
## X6.3.2.1 0.9298165 1.481394e-06
## X2.7.4.16 0.9290898 1.573320e-06
## X4.1.1.50 0.9285482 1.644858e-06
## X4.3.99.3 0.9281831 1.694566e-06
## X2.3.1.35 0.9279610 1.725402e-06
## X2.4.1.288 0.9276511 1.769219e-06
## X2.7.4.9 0.9273505 1.812577e-06
## X2.4.1.227 0.9270798 1.852374e-06
## X3.1.3.18 0.9269836 1.866696e-06
## X2.4.2.7 0.9267736 1.898258e-06
## X1.1.1.100 0.9250796 2.169328e-06
## X1.3.5.2 0.9250098 2.181148e-06
## X4.1.1.12 0.9248706 2.204874e-06
## X2.5.1.3 0.9248548 2.207580e-06
## X3.5.4.26 0.9238557 2.384388e-06
## X1.1.1.193 0.9238557 2.384388e-06
## X2.7.7.18 0.9236305 2.425798e-06
## X6.1.1.3 0.9230171 2.541638e-06
## X2.8.1.7 0.9227502 2.593425e-06
## X3.5.4.16 0.9223070 2.681372e-06
## X5.1.3.1 0.9221570 2.711688e-06
## X6.1.1.4 0.9220557 2.732303e-06
## X2.5.1.75 0.9218015 2.784657e-06
## X3.1.3.25 0.9213125 2.887651e-06
## X2.7.7.41 0.9211321 2.926445e-06
## X2.6.1.42 0.9211121 2.930760e-06
## X2.7.2.11 0.9209867 2.958004e-06
## X5.3.1.16 0.9209861 2.958140e-06
## X4.3.3.7 0.9202354 3.125632e-06
## X5.1.1.7 0.9196859 3.253102e-06
## X2.7.1.24 0.9196330 3.265611e-06
## X6.1.1.17 0.9190576 3.404094e-06
## X2.7.4.3 0.9187295 3.485186e-06
## X3.6.1.9 0.9181769 3.625382e-06
## X2.7.4.25 0.9180519 3.657721e-06
## X2.3.1.180 0.9169352 3.957353e-06
## X4.3.1.19 0.9160282 4.215340e-06
## X2.4.2.14 0.9159650 4.233806e-06
## X5.4.2.10 0.9156426 4.329118e-06
## X1.18.1.2 0.9154230 4.395043e-06
## X3.5.4.10 0.9147085 4.615257e-06
## X2.1.2.3 0.9145609 4.661864e-06
## X6.1.1.7 0.9140000 4.842515e-06
## X2.7.1.130 0.9138856 4.880031e-06
## X2.4.1.129 0.9127861 5.253217e-06
## X6.3.2.5 0.9123996 5.389815e-06
## X6.1.1.19 0.9122264 5.451970e-06
## X4.3.2.2 0.9120567 5.513434e-06
## X2.5.1.19 0.9118760 5.579539e-06
## X4.1.1.97 0.9117401 5.629671e-06
## X2.3.1.39 0.9115824 5.688279e-06
## X7.1.1.8 0.9108138 5.981287e-06
## X1.1.1.94 0.9106965 6.027085e-06
## X2.1.1.148 0.9106410 6.048821e-06
## X2.4.1.182 0.9105127 6.099401e-06
## X6.1.1.10 0.9102863 6.189465e-06
## X6.3.2.6 0.9096967 6.429147e-06
## X2.5.1.141 0.9092807 6.602780e-06
## X1.1.1.42 0.9088959 6.766824e-06
## X1.5.1.2 0.9064491 7.890137e-06
## X2.1.2.10 0.9064447 7.892303e-06
## X2.7.6.3 0.9057532 8.236162e-06
## X4.3.2.10 0.9052902 8.473193e-06
## X5.4.99.9 0.9047627 8.750033e-06
## X3.1.4.3 0.9039586 9.186293e-06
## X3.5.2.17 0.9034366 9.478958e-06
## X1.1.1.22 0.9032993 9.557197e-06
## X2.7.7.9 0.9031109 9.665363e-06
## X2.7.7.23 0.9019088 1.037974e-05
## X2.3.1.157 0.9019088 1.037974e-05
## X3.4.11.5 0.9011824 1.083200e-05
## X1.17.3.2 0.9007740 1.109330e-05
## X3.2.1.52 0.8998112 1.172981e-05
## X4.1.3.27 0.8988437 1.239924e-05
## X2.6.99.2 0.8982147 1.285107e-05
## X6.3.4.20 0.8978936 1.308687e-05
## X2.1.1.67 0.8972337 1.358257e-05
## X6.1.1.5 0.8967932 1.392197e-05
## X1.11.1.15 0.8948693 1.548680e-05
## X2.7.4.6 0.8942450 1.602446e-05
## X1.17.1.8 0.8942174 1.604863e-05
## X6.3.2.8 0.8940269 1.621591e-05
## X4.2.1.24 0.8939668 1.626897e-05
## X2.7.7.3 0.8931189 1.703298e-05
## X1.8.4.8 0.8927013 1.741996e-05
## X2.7.9.1 0.8905010 1.957956e-05
## X2.5.1.61 0.8892910 2.085748e-05
## X4.1.1.31 0.8877515 2.258143e-05
## X4.1.1.48 0.8873222 2.308229e-05
## X2.3.1.30 0.8868618 2.362961e-05
## X2.6.1.52 0.8863443 2.425741e-05
## X5.3.1.6 0.8862894 2.432483e-05
## X3.5.1.2 0.8860194 2.465850e-05
## X5.1.1.1 0.8852860 2.558377e-05
## X1.1.1.44 0.8838397 2.749176e-05
## X2.2.1.6 0.8825700 2.926124e-05
## X2.4.2.9 0.8804887 3.236241e-05
## X3.6.1.1 0.8800728 3.301322e-05
## X1.1.1.3 0.8797355 3.354877e-05
## X2.7.1.49 0.8791729 3.445786e-05
## X4.2.1.59 0.8784750 3.561349e-05
## X3.6.1.54 0.8783186 3.587688e-05
## X4.2.1.2 0.8756429 4.063270e-05
## X4.1.2.25 0.8755219 4.085953e-05
## X1.17.1.4 0.8721144 4.767932e-05
## X3.5.4.9 0.8719009 4.813566e-05
## X1.5.1.5 0.8719009 4.813566e-05
## X2.1.1.107 0.8703975 5.145141e-05
## X1.3.1.76 0.8701910 5.192103e-05
## X4.99.1.4 0.8701447 5.202673e-05
## X2.7.1.26 0.8690665 5.454012e-05
## X3.1.3.7 0.8686039 5.564851e-05
## X5.4.99.15 0.8676965 5.787579e-05
## X2.7.7.4 0.8670069 5.961640e-05
## X2.8.1.8 0.8669268 5.982137e-05
## X3.6.1.40 0.8666102 6.063695e-05
## X2.3.1.61 0.8661109 6.194163e-05
## X3.6.1.27 0.8659624 6.233420e-05
## X2.5.1.9 0.8657187 6.298250e-05
## X2.1.3.3 0.8642144 6.710761e-05
## X2.7.1.12 0.8640445 6.758684e-05
## X2.5.1.16 0.8639107 6.796639e-05
## X1.14.14.18 0.8631231 7.023551e-05
## X3.2.1.141 0.8617774 7.425538e-05
## X3.1.3.27 0.8615823 7.485341e-05
## X2.5.1.54 0.8609719 7.674950e-05
## X4.1.1.23 0.8607497 7.744942e-05
## X1.8.1.4 0.8592307 8.237484e-05
## X1.1.1.284 0.8589122 8.343908e-05
## X4.1.3.30 0.8579562 8.670124e-05
## X4.4.1.13 0.8567243 9.105695e-05
## X3.4.19.13 0.8559801 9.377321e-05
## X2.3.2.2 0.8559801 9.377321e-05
## X3.5.4.25 0.8550695 9.718627e-05
## X4.6.1.17 0.8546352 9.884927e-05
## X2.6.1.16 0.8537568 1.022832e-04
## X6.3.5.3 0.8535066 1.032789e-04
## X5.3.1.23 0.8518771 1.099584e-04
## X1.4.4.2 0.8498350 1.188201e-04
## X2.7.7.13 0.8490590 1.223359e-04
## X6.6.1.2 0.8466571 1.337569e-04
## X6.3.4.2 0.8466145 1.339670e-04
## X2.1.1.163 0.8465560 1.342560e-04
## X1.8.1.2 0.8462481 1.357852e-04
## X1.4.3.5 0.8450183 1.420345e-04
## X2.7.2.3 0.8421560 1.574868e-04
## X6.3.2.9 0.8400684 1.695938e-04
## X3.5.2.9 0.8394292 1.734483e-04
## X2.4.1.18 0.8393215 1.741044e-04
## X6.3.2.10 0.8390618 1.756955e-04
## X2.4.1.21 0.8377318 1.840287e-04
## X1.2.4.2 0.8374694 1.857099e-04
## X1.1.5.12 0.8370181 1.886307e-04
## X2.3.1.1 0.8367858 1.901479e-04
## X1.1.1.49 0.8361659 1.942471e-04
## X2.7.7.60 0.8359193 1.958974e-04
## X6.3.2.3 0.8303825 2.360462e-04
## X1.1.1.219 0.8301221 2.380869e-04
## X6.1.1.9 0.8300494 2.386586e-04
## X2.5.1.78 0.8292773 2.448044e-04
## X3.1.2.12 0.8288890 2.479428e-04
## X3.5.4.3 0.8288620 2.481630e-04
## X3.2.1.28 0.8283167 2.526282e-04
## X6.3.5.2 0.8269163 2.643957e-04
## X3.5.1.5 0.8257071 2.749086e-04
## X2.5.1.6 0.8238401 2.918019e-04
## X1.1.1.17 0.8208639 3.204570e-04
## X3.3.1.1 0.8192451 3.369703e-04
## X1.7.1.13 0.8191252 3.382199e-04
## X1.2.1.27 0.8184618 3.452026e-04
## X3.5.1.25 0.8175194 3.553221e-04
## X4.2.1.20 0.8164324 3.672900e-04
## X4.2.1.11 0.8164208 3.674199e-04
## X1.3.98.3 0.8157022 3.755105e-04
## X4.2.1.1 0.8149017 3.846924e-04
## X2.6.1.1 0.8147887 3.860036e-04
## X6.3.4.4 0.8128812 4.086739e-04
## X1.17.7.3 0.8106442 4.366137e-04
## X4.2.1.19 0.8105017 4.384452e-04
## X3.5.1.1 0.8099954 4.449996e-04
## X4.2.1.9 0.8098411 4.470122e-04
## X4.1.1.8 0.8093887 4.529563e-04
## X2.7.7.77 0.8093272 4.537695e-04
## X2.7.1.33 0.8089194 4.591896e-04
## X5.4.99.5 0.8086283 4.630913e-04
## X2.3.1.8 0.8066902 4.897505e-04
## X2.3.1.181 0.8064897 4.925761e-04
## X1.1.1.267 0.8036879 5.334709e-04
## X2.7.2.1 0.7999985 5.914362e-04
## X5.3.1.9 0.7988435 6.105868e-04
## X6.3.4.21 0.7984571 6.171035e-04
## X2.5.1.7 0.7984464 6.172854e-04
## X2.7.1.40 0.7962304 6.557531e-04
## X6.1.1.2 0.7957277 6.647405e-04
## X6.1.1.15 0.7936327 7.032702e-04
## X3.5.1.10 0.7922359 7.299405e-04
## X2.5.1.55 0.7889917 7.950148e-04
## X3.6.1.23 0.7873746 8.291417e-04
## X1.1.1.169 0.7836964 9.111448e-04
## X1.5.1.20 0.7827247 9.338540e-04
## X1.1.1.23 0.7816203 9.602148e-04
## X3.1.3.11 0.7812522 9.691306e-04
## X6.3.5.4 0.7793645 1.015904e-03
## X2.3.1.129 0.7782954 1.043182e-03
## X2.7.2.4 0.7762802 1.096190e-03
## X6.3.5.5 0.7747885 1.136795e-03
## X4.1.1.37 0.7732832 1.178979e-03
## X2.3.1.37 0.7729228 1.189260e-03
## X2.6.1.62 0.7725882 1.198871e-03
## X4.4.1.5 0.7715501 1.229081e-03
## X5.2.1.1 0.7709838 1.245815e-03
## X1.1.1.205 0.7708348 1.250247e-03
## X6.3.2.2 0.7675656 1.350720e-03
## X1.1.1.262 0.7619818 1.537117e-03
## X2.3.1.12 0.7593016 1.633566e-03
## X1.13.11.53 0.7575164 1.700428e-03
## X4.3.1.7 0.7563655 1.744676e-03
## X1.1.5.3 0.7547051 1.810118e-03
## X1.2.4.1 0.7543424 1.824666e-03
## X6.1.1.6 0.7333488 2.839085e-03
## X1.3.5.1 0.7327526 2.873289e-03
## X6.3.1.2 0.7279176 3.162846e-03
## X3.4.16.4 0.7244912 3.381602e-03
## X2.7.8.7 0.7218074 3.561126e-03
## X2.1.2.1 0.7205702 3.646358e-03
## X6.3.3.3 0.7169965 3.901603e-03
## X6.3.5.7 0.7165649 3.933356e-03
## X4.2.1.33 0.7131785 4.189583e-03
## X1.2.1.38 0.7050123 4.861429e-03
## X1.11.1.6 0.7023126 5.101132e-03
## X3.1.3.2 0.7016365 5.162587e-03
## X4.1.1.36 0.6943398 5.863294e-03
## X6.1.1.14 0.6874159 6.594705e-03
## X1.1.5.4 0.6832041 7.073121e-03
## X6.3.4.5 0.6807649 7.362261e-03
## X5.4.99.16 0.6776411 7.745844e-03
## X1.2.1.12 0.6743739 8.163436e-03
## X3.1.1.31 0.6701714 8.725952e-03
## X6.1.1.20 0.6695099 8.817155e-03
## X6.3.4.13 0.6683897 8.973276e-03
## X2.7.1.158 -0.6617301 9.946029e-03
## X2.4.2.22 -0.6693914 8.833569e-03
## X2.7.1.58 -0.6711147 8.597154e-03
## X1.1.1.350 -0.6800192 7.452461e-03
## X2.4.1.25 -0.6826380 7.139426e-03
## X3.4.11.23 -0.6854617 6.813445e-03
## X6.4.1.1 -0.6861312 6.737884e-03
## X2.4.1.12 -0.6866282 6.682209e-03
## X5.1.3.3 -0.6891285 6.407528e-03
## X4.1.99.19 -0.6899289 6.321486e-03
## X4.1.2.4 -0.6962187 5.676173e-03
## X1.14.11.8 -0.6971664 5.583579e-03
## X4.1.3.34 -0.6974513 5.555969e-03
## X2.7.1.6 -0.6985504 5.450468e-03
## X1.6.99.3 -0.7009672 5.223989e-03
## X2.7.7.12 -0.7050957 4.854166e-03
## X7.6.2.7 -0.7061177 4.765859e-03
## X1.17.1.9 -0.7080089 4.605777e-03
## X5.1.3.9 -0.7094652 4.485395e-03
## X1.5.99.12 -0.7098228 4.456216e-03
## X4.3.1.3 -0.7126710 4.229083e-03
## X2.1.2.13 -0.7132561 4.183571e-03
## X1.1.1.305 -0.7132561 4.183571e-03
## X3.6.1.29 -0.7139266 4.131885e-03
## X1.1.1.330 -0.7142998 4.103335e-03
## X4.2.1.104 -0.7150217 4.048545e-03
## X5.5.1.19 -0.7168853 3.909764e-03
## X2.4.1.16 -0.7170493 3.897735e-03
## X2.1.1.22 -0.7182100 3.813411e-03
## X1.1.1.127 -0.7261702 3.272968e-03
## X2.7.1.137 -0.7300981 3.029551e-03
## X3.7.1.12 -0.7315975 2.940484e-03
## X2.4.1.255 -0.7392540 2.517340e-03
## X5.3.2.3 -0.7394074 2.509386e-03
## X4.1.1.68 -0.7394721 2.506034e-03
## X3.2.2.5 -0.7434019 2.309119e-03
## X3.1.3.99 -0.7465959 2.158265e-03
## X4.3.3.6 -0.7470914 2.135581e-03
## X3.2.1.23 -0.7497281 2.018016e-03
## X4.4.1.21 -0.7518611 1.926721e-03
## X3.5.4.6 -0.7539130 1.842011e-03
## X1.1.1.336 -0.7565415 1.737850e-03
## X4.2.1.17 -0.7566341 1.734269e-03
## X1.1.1.35 -0.7566341 1.734269e-03
## X2.7.1.48 -0.7599762 1.608848e-03
## X1.1.1.93 -0.7616576 1.548538e-03
## X1.1.1.83 -0.7616576 1.548538e-03
## X1.13.11.1 -0.7619233 1.539174e-03
## X4.2.1.42 -0.7620773 1.533768e-03
## X2.7.1.198 -0.7622985 1.526028e-03
## X2.1.1.14 -0.7637617 1.475609e-03
## X1.3.1.12 -0.7641182 1.463530e-03
## X3.2.2.9 -0.7644533 1.452246e-03
## X4.2.1.48 -0.7658521 1.405890e-03
## X3.5.1.54 -0.7663452 1.389833e-03
## X4.2.1.147 -0.7672295 1.361405e-03
## X4.1.2.43 -0.7672295 1.361405e-03
## X5.5.1.4 -0.7674151 1.355498e-03
## X6.1.1.22 -0.7675854 1.350094e-03
## X5.3.1.8 -0.7681970 1.330833e-03
## X5.3.1.26 -0.7721951 1.210242e-03
## X4.1.2.13 -0.7725220 1.200779e-03
## X2.4.1.256 -0.7742137 1.152759e-03
## X1.3.8.8 -0.7744308 1.146708e-03
## X1.3.8.7 -0.7744308 1.146708e-03
## X1.13.11.15 -0.7755360 1.116299e-03
## X3.7.1.22 -0.7763224 1.095059e-03
## X2.8.1.4 -0.7773662 1.067365e-03
## X4.1.99.1 -0.7793964 1.015100e-03
## X4.2.1.70 -0.7802344 9.941307e-04
## X3.1.4.16 -0.7843889 8.952297e-04
## X3.1.3.6 -0.7843889 8.952297e-04
## X1.13.11.11 -0.7850804 8.795609e-04
## X2.7.1.208 -0.7858557 8.622556e-04
## X1.13.11.20 -0.7863032 8.523911e-04
## X4.1.1.22 -0.7864148 8.499468e-04
## X3.5.2.7 -0.7869195 8.389564e-04
## X2.7.1.21 -0.7879369 8.171445e-04
## X1.1.98.6 -0.7895945 7.825856e-04
## X1.5.1.7 -0.7904803 7.646026e-04
## X2.7.7.53 -0.7906355 7.614855e-04
## X2.7.7.5 -0.7906355 7.614855e-04
## X6.4.1.2 -0.7938017 7.000983e-04
## X4.2.1.68 -0.7940013 6.963645e-04
## X1.2.1.50 -0.7943792 6.893414e-04
## X6.2.1.20 -0.7952892 6.726616e-04
## X2.3.1.40 -0.7952892 6.726616e-04
## X2.7.1.17 -0.7953057 6.723631e-04
## X2.7.1.16 -0.7970763 6.408491e-04
## X4.2.1.44 -0.7977676 6.288707e-04
## X2.6.1.85 -0.7995484 5.988421e-04
## X3.5.99.7 -0.8032069 5.407578e-04
## X1.13.11.3 -0.8042388 5.252217e-04
## X2.3.1.199 -0.8085463 4.641946e-04
## X1.4.1.21 -0.8102480 4.417189e-04
## X1.11.1.9 -0.8108850 4.335353e-04
## X3.1.3.4 -0.8111591 4.300505e-04
## X1.5.1.36 -0.8114309 4.266183e-04
## X2.6.1.19 -0.8118645 4.211882e-04
## X5.3.1.30 -0.8136581 3.993144e-04
## X5.3.1.14 -0.8137632 3.980622e-04
## X5.3.3.4 -0.8141149 3.938928e-04
## X4.2.1.22 -0.8142150 3.927123e-04
## X4.1.3.17 -0.8145779 3.884573e-04
## X2.7.1.107 -0.8146015 3.881818e-04
## X4.4.1.17 -0.8150889 3.825298e-04
## X2.7.9.3 -0.8153774 3.792145e-04
## X4.3.1.17 -0.8182488 3.474702e-04
## X1.7.99.1 -0.8197815 3.314242e-04
## X2.7.1.197 -0.8208583 3.205126e-04
## X2.7.1.100 -0.8210390 3.187105e-04
## X2.7.1.166 -0.8213398 3.157284e-04
## X4.1.1.74 -0.8221591 3.077198e-04
## X3.1.2.14 -0.8233739 2.961485e-04
## X4.1.2.20 -0.8240258 2.900853e-04
## X2.3.1.16 -0.8249856 2.813409e-04
## X4.7.1.1 -0.8253468 2.781057e-04
## X5.3.3.14 -0.8269569 2.640481e-04
## X2.7.9.2 -0.8289650 2.473261e-04
## X1.14.13.9 -0.8292607 2.449376e-04
## X5.3.3.2 -0.8304928 2.351863e-04
## X2.3.1.5 -0.8310005 2.312600e-04
## X1.5.1.3 -0.8313708 2.284303e-04
## X3.2.1.1 -0.8315473 2.270920e-04
## X1.14.14.17 -0.8318461 2.248395e-04
## X3.2.1.39 -0.8319266 2.242355e-04
## X1.1.1.261 -0.8332954 2.141705e-04
## X2.7.1.29 -0.8333523 2.137598e-04
## X2.7.1.28 -0.8333523 2.137598e-04
## X2.6.1.13 -0.8334391 2.131351e-04
## X3.2.1.55 -0.8352060 2.007351e-04
## X5.1.3.14 -0.8361111 1.946127e-04
## X4.1.1.15 -0.8368779 1.895454e-04
## X1.1.1.38 -0.8370789 1.882347e-04
## X4.3.2.3 -0.8379229 1.828118e-04
## X1.13.11.63 -0.8379237 1.828070e-04
## X2.7.1.201 -0.8390383 1.758401e-04
## X2.6.1.82 -0.8394842 1.731139e-04
## X2.7.8.8 -0.8396468 1.721280e-04
## X3.1.3.89 -0.8406019 1.664307e-04
## X7.1.2.1 -0.8407890 1.653326e-04
## X3.5.4.5 -0.8411960 1.629639e-04
## X2.7.1.56 -0.8412299 1.627683e-04
## X2.7.11.24 -0.8421313 1.576255e-04
## X3.11.1.1 -0.8425604 1.552243e-04
## X1.14.99.46 -0.8427193 1.543426e-04
## X2.1.1.45 -0.8431840 1.517875e-04
## X2.6.1.87 -0.8435988 1.495359e-04
## X5.1.3.4 -0.8445103 1.446832e-04
## X3.5.3.26 -0.8456434 1.388296e-04
## X4.3.1.1 -0.8457100 1.384916e-04
## X2.7.4.24 -0.8459458 1.373005e-04
## X2.7.4.21 -0.8459458 1.373005e-04
## X4.3.1.18 -0.8467532 1.332841e-04
## X3.1.3.70 -0.8467672 1.332150e-04
## X4.2.1.84 -0.8499151 1.184619e-04
## X1.8.1.7 -0.8502411 1.170131e-04
## X1.13.11.57 -0.8514878 1.116048e-04
## X3.5.3.1 -0.8529220 1.056362e-04
## X1.4.1.14 -0.8544773 9.945960e-05
## X2.3.1.242 -0.8550199 9.737483e-05
## X4.2.1.49 -0.8558198 9.436686e-05
## X5.1.3.22 -0.8566551 9.130679e-05
## X4.1.1.21 -0.8575964 8.795543e-05
## X2.7.1.20 -0.8601551 7.934805e-05
## X1.5.1.42 -0.8604469 7.841181e-05
## X4.1.1.11 -0.8608277 7.720338e-05
## X1.2.1.72 -0.8613501 7.557025e-05
## X5.4.2.7 -0.8625262 7.199615e-05
## X3.2.1.3 -0.8625839 7.182442e-05
## X5.3.1.15 -0.8641127 6.739418e-05
## X5.4.3.8 -0.8662627 6.154263e-05
## X1.6.5.2 -0.8675909 5.813960e-05
## X4.4.1.15 -0.8676446 5.800524e-05
## X2.7.1.202 -0.8682829 5.642836e-05
## X2.4.1.109 -0.8689385 5.484505e-05
## X1.1.1.18 -0.8691518 5.433791e-05
## X2.4.2.3 -0.8697130 5.302147e-05
## X1.9.6.1 -0.8711758 4.971244e-05
## X3.6.1.63 -0.8715761 4.883686e-05
## X3.5.2.6 -0.8723160 4.725155e-05
## X2.7.1.1 -0.8726526 4.654433e-05
## X2.7.1.92 -0.8735598 4.468129e-05
## X2.3.1.29 -0.8738055 4.418736e-05
## X3.5.1.110 -0.8746675 4.248941e-05
## X4.2.1.8 -0.8750691 4.171674e-05
## X7.3.2.3 -0.8768778 3.837772e-05
## X3.5.4.4 -0.8772238 3.776445e-05
## X1.6.1.1 -0.8774378 3.738921e-05
## X1.2.1.71 -0.8775371 3.721624e-05
## X4.99.1.7 -0.8784222 3.570229e-05
## X3.5.3.11 -0.8784977 3.557552e-05
## X2.7.4.29 -0.8800374 3.306909e-05
## X4.1.1.17 -0.8806349 3.213617e-05
## X2.6.1.76 -0.8817077 3.051521e-05
## X1.1.1.103 -0.8822311 2.974900e-05
## X1.1.1.60 -0.8822750 2.968548e-05
## X4.2.3.3 -0.8827751 2.896934e-05
## X2.4.2.4 -0.8830053 2.864439e-05
## X1.2.1.95 -0.8833329 2.818721e-05
## X1.2.1.31 -0.8833329 2.818721e-05
## X1.1.99.3 -0.8842388 2.695398e-05
## X2.7.1.19 -0.8842525 2.693577e-05
## X2.7.8.11 -0.8844877 2.662306e-05
## X2.4.2.43 -0.8850090 2.594061e-05
## X2.7.4.23 -0.8854416 2.538513e-05
## X2.4.1.198 -0.8861383 2.451110e-05
## X3.1.1.11 -0.8867398 2.377642e-05
## X2.7.7.27 -0.8867790 2.372911e-05
## X2.7.7.1 -0.8881429 2.213240e-05
## X2.7.1.22 -0.8881429 2.213240e-05
## X1.7.2.3 -0.8883355 2.191424e-05
## X2.3.1.54 -0.8896905 2.042824e-05
## X3.5.3.4 -0.8899325 2.017172e-05
## X3.1.4.53 -0.8902392 1.985046e-05
## X5.3.3.1 -0.8906841 1.939188e-05
## X3.1.3.46 -0.8908371 1.923622e-05
## X2.7.1.105 -0.8908371 1.923622e-05
## X3.8.1.2 -0.8923829 1.771982e-05
## X2.9.1.1 -0.8929608 1.717860e-05
## X2.4.2.53 -0.8935473 1.664337e-05
## X2.3.1.251 -0.8946424 1.568050e-05
## X3.2.2.4 -0.8948889 1.547016e-05
## X2.7.1.89 -0.8953526 1.508079e-05
## X3.1.1.85 -0.8954936 1.496396e-05
## X4.6.1.1 -0.8967347 1.396755e-05
## X6.3.4.6 -0.8983249 1.277092e-05
## X2.3.1.243 -0.8993262 1.206163e-05
## X2.4.2.2 -0.9000059 1.159874e-05
## X2.4.2.15 -0.9000059 1.159874e-05
## X3.1.1.32 -0.9005049 1.126826e-05
## X4.2.2.3 -0.9005109 1.126434e-05
## X1.7.5.1 -0.9010476 1.091773e-05
## X2.3.1.15 -0.9019682 1.034344e-05
## X2.7.1.2 -0.9019802 1.033613e-05
## X3.6.1.22 -0.9025548 9.990637e-06
## X2.4.1.34 -0.9028335 9.826550e-06
## X2.5.1.48 -0.9029978 9.730814e-06
## X3.1.1.4 -0.9035061 9.439567e-06
## X3.1.3.1 -0.9045624 8.857068e-06
## X3.7.1.3 -0.9052040 8.517922e-06
## X2.2.1.2 -0.9060046 8.109711e-06
## X2.8.1.1 -0.9065047 7.863024e-06
## X1.1.1.290 -0.9067262 7.755730e-06
## X5.3.1.28 -0.9068371 7.702433e-06
## X3.5.1.16 -0.9068514 7.695599e-06
## X2.7.8.37 -0.9076892 7.303142e-06
## X2.7.1.35 -0.9102183 6.216718e-06
## X5.1.3.15 -0.9111817 5.839521e-06
## X3.1.3.71 -0.9112642 5.808132e-06
## X5.4.4.2 -0.9114366 5.742932e-06
## X4.1.1.19 -0.9123339 5.413316e-06
## X6.1.1.18 -0.9123574 5.404918e-06
## X4.1.3.38 -0.9130573 5.159057e-06
## X3.5.3.23 -0.9132711 5.085817e-06
## X1.5.1.38 -0.9145425 4.667698e-06
## X3.5.1.96 -0.9153562 4.415239e-06
## X3.1.5.1 -0.9160586 4.206475e-06
## X3.6.1.26 -0.9162346 4.155448e-06
## X3.1.3.45 -0.9162954 4.137948e-06
## X3.2.2.10 -0.9174975 3.804056e-06
## X4.1.3.40 -0.9181999 3.619457e-06
## X4.1.1.2 -0.9184328 3.559895e-06
## X4.3.2.7 -0.9204756 3.071209e-06
## X3.6.1.41 -0.9220872 2.725873e-06
## X2.4.2.1 -0.9225231 2.638190e-06
## X2.3.1.47 -0.9238985 2.376576e-06
## X3.1.4.14 -0.9251878 2.151108e-06
## X3.1.4.55 -0.9271104 1.847840e-06
## X3.6.1.67 -0.9272548 1.826571e-06
## X1.2.1.19 -0.9286100 1.636565e-06
## X2.1.1.197 -0.9287655 1.615834e-06
## X3.1.3.3 -0.9289288 1.594313e-06
## X3.2.1.18 -0.9329080 1.138267e-06
## X1.14.14.35 -0.9332053 1.109060e-06
## X2.7.1.11 -0.9346699 9.740528e-07
## X2.3.1.109 -0.9372952 7.659730e-07
## X1.11.1.21 -0.9382670 6.989357e-07
## X5.3.1.17 -0.9403603 5.708796e-07
## X6.2.1.5 -0.9433201 4.233742e-07
## X4.4.1.22 -0.9437024 4.068679e-07
## X4.1.3.1 -0.9450001 3.547460e-07
## X4.1.1.49 -0.9471148 2.816840e-07
## X4.1.1.98 -0.9506061 1.884139e-07
## X3.2.1.14 -0.9507492 1.852211e-07
## X3.1.3.5 -0.9521933 1.554210e-07
## X3.1.3.16 -0.9532668 1.359408e-07
## X1.2.1.70 -0.9537002 1.286710e-07
## X2.7.11.1 -0.9569792 8.340344e-08
## X2.3.3.9 -0.9656985 2.183893e-08
## X2.4.1.1 -0.9721372 6.361569e-09
## X1.1.1.37 -0.9819205 4.849743e-10
##
## $Dim.2
##
## Link between the variable and the continuous variables (R-square)
## =================================================================================
## correlation p.value
## X3.5.3.6 0.8601962 7.921576e-05
## X1.7.1.7 0.8535198 1.032265e-04
## X5.3.1.5 0.7895116 7.842840e-04
## X4.2.1.40 0.7893065 7.885040e-04
## X4.2.1.79 0.7824831 9.395713e-04
## X2.4.2.8 0.7714821 1.231080e-03
## X1.14.14.9 0.7691478 1.301324e-03
## X2.2.1.9 0.7670449 1.367299e-03
## X4.1.2.40 0.7575038 1.700910e-03
## X2.7.1.121 0.7374315 2.613396e-03
## X5.4.2.11 0.7174603 3.867707e-03
## X5.3.1.12 0.7070682 4.684872e-03
## X6.3.1.20 0.7048206 4.878155e-03
## X4.2.99.20 0.7025096 5.083333e-03
## X5.3.1.4 0.6999280 5.320455e-03
## X5.1.2.1 0.6997837 5.333960e-03
## X2.7.1.5 0.6981454 5.489162e-03
## X4.1.2.4 0.6906993 6.239508e-03
## X2.3.3.10 0.6853644 6.824483e-03
## X6.3.1.1 0.6812364 7.305674e-03
## X4.2.1.28 0.6803264 7.415197e-03
## X4.1.3.34 0.6785723 7.629915e-03
## X6.2.1.26 0.6782364 7.671588e-03
## X4.1.3.36 0.6766450 7.871369e-03
## X3.2.1.93 0.6745025 8.146676e-03
## X4.2.1.82 0.6694270 8.828636e-03
## X2.7.1.6 0.6658784 9.331047e-03
##
## $Dim.3
##
## Link between the variable and the continuous variables (R-square)
## =================================================================================
## correlation p.value
## X1.4.3.16 0.8129398 0.0004079614
## X3.5.1.9 0.7319602 0.0029192503
## X1.14.14.5 0.7213816 0.0035902819
## X1.7.3.3 -0.6715300 0.0085409128
## X4.1.1.33 -0.6808482 0.0073522390
## X3.5.2.5 -0.7009573 0.0052248979
## X2.7.1.36 -0.7012513 0.0051978551
## X2.7.4.2 -0.7036652 0.0049799129
## X1.1.1.34 -0.7584431 0.0016654531
## X1.3.3.4 -0.8287927 0.0002487262
##
## $Dim.4
##
## Link between the variable and the continuous variables (R-square)
## =================================================================================
## correlation p.value
## X1.2.1.10 0.8768865 3.836207e-05
## X4.1.3.39 0.8226401 3.030952e-04
## X3.5.1.53 0.7652214 1.426644e-03
## X3.1.3.8 0.7541918 1.830735e-03
## X3.4.24.84 0.7532285 1.869936e-03
## X4.1.1.96 0.7323790 2.894887e-03
## X3.5.3.12 0.7306520 2.996403e-03
## X2.3.1.222 0.6921813 6.084153e-03
## X5.5.1.6 0.6694845 8.820669e-03
## X7.2.4.2 0.6693768 8.835587e-03
## X2.7.1.168 0.6654312 9.395892e-03
## X2.4.1.131 -0.7939307 6.976837e-04
##
## $Dim.5
##
## Link between the variable and the continuous variables (R-square)
## =================================================================================
## correlation p.value
## X1.1.1.304 0.7941401 0.0006937783
## X6.2.1.30 0.7922376 0.0007299072
## X2.7.2.2 0.7623588 0.0015239238
## X5.3.3.18 0.7546109 0.0018138865
## X1.14.13.149 0.7284427 0.0031303363
## X2.3.1.184 0.7233703 0.0034556960
## X3.3.2.12 0.7221321 0.0035390130
## X1.2.1.91 0.7221321 0.0035390130
## X7.1.1.2 0.7066539 0.0047200418
## X2.1.1.152 0.6975600 0.0055454690
## X3.5.4.44 0.6901872 0.0062939083
## X3.5.1.125 0.6901872 0.0062939083
## X1.1.1.271 -0.6711547 0.0085917231
##
## $Dim.6
##
## Link between the variable and the continuous variables (R-square)
## =================================================================================
## correlation p.value
## X2.4.1.11 0.7699630 0.001276440
## X3.1.4.4 0.7554848 0.001779147
## X3.2.1.31 0.6671284 0.009151613
## X1.14.18.1 0.6618508 0.009927715
##
## $Dim.7
##
## $Dim.8
##
## Link between the variable and the continuous variables (R-square)
## =================================================================================
## correlation p.value
## X2.3.1.41 -0.7042035 0.004932296
## X2.7.7.81 -0.7113610 0.004332393
##
## $Dim.9
##
## Link between the variable and the continuous variables (R-square)
## =================================================================================
## correlation p.value
## X1.7.2.4 -0.8117398 4.227441e-04
## X3.5.99.6 -0.8632770 6.978751e-05
##
## $Dim.10
##
## $Dim.11
##
## $Dim.12
##
## Link between the variable and the continuous variables (R-square)
## =================================================================================
## correlation p.value
## X5.4.4.4 0.7680254 0.001336213
## X4.2.1.127 0.7680254 0.001336213
##
## $Dim.13fviz_eig(res.PCA)
##Biplot - visualizando os padrões gerais
1.4.1 Gráfico de variáveis. Variáveis correlacionadas positivas apontam para o mesmo lado do gráfico. Variáveis correlacionadas negativas apontam para lados opostos do gráfico
fviz_pca_biplot(res.PCA,
col.var = "#4C9900", # Variables color
alpha.var=.1,
col.ind = "#696969", # Individuals color
label = "ind"
)
1.4.2 Gráfico de indivíduos. Indivíduos com perfil semelhante são agrupados
fviz_pca_var(res.PCA,
col.var = "contrib", # Color by contributions to the PC
alpha.var = .5,
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
label="none",
repel = TRUE # Avoid text overlapping
)
varieties <- rownames(dados)
varieties[grep(pattern = "For", x = varieties)] <- "Forastero"
varieties[grep(pattern = "Mix", x = varieties)] <- "Hybrid"
varieties <- as.factor(varieties)
fviz_pca_ind(res.PCA,
col.ind = varieties, # color by groups
palette = c("#FF3333", "#4C9900"),
addEllipses = TRUE, # Concentration ellipses
ellipse.type = "confidence",
legend.title = "Groups",
repel = TRUE
)
2 NMDS e PERMANOVA - tentando identificar os grupos existentes
2.1 Padronização dos dados - transformação de Hellinger
dados2 <- decostand(dados, method = "hel")2.2 Construção do modelo
NMDS <- metaMDS(dados2, k=2, trymax = 10000, trace = F)
NMDS##
## Call:
## metaMDS(comm = dados2, k = 2, trymax = 10000, trace = F)
##
## global Multidimensional Scaling using monoMDS
##
## Data: dados2
## Distance: bray
##
## Dimensions: 2
## Stress: 0.03089656
## Stress type 1, weak ties
## Best solution was repeated 1 time in 20 tries
## The best solution was from try 20 (random start)
## Scaling: centring, PC rotation, halfchange scaling
## Species: expanded scores based on 'dados2'2.3 Plot
library(data.table)
df <- data.table(mds1=NMDS$points[,1], mds2=NMDS$points[,2], groups=varieties)
hulls <- df[,.SD[chull(mds1, mds2)], by=groups]
ggplot(df, aes(x=mds1, y=mds2))+
geom_polygon(data=hulls, aes(colour=groups), linetype=3, linewidth=2, alpha=0)+
geom_point(shape=21, aes(fill=groups), alpha=.9, size=4)+
scale_fill_manual(values=c("#FF3333", "#4C9900"))+
scale_colour_manual(values=c("#FF3333", "#4C9900"))+
theme_classic()+
theme(legend.position="bottom", legend.title=element_blank())+
scale_x_continuous("NMDS1")+
scale_y_continuous("NMDS2")+
theme(text = element_text(size=20),axis.text.x = element_text(vjust=1, colour="black"), axis.text.y=element_text(colour="black"))
2.4 PERMANOVA - tentando avaliar a significância entre os grupos
permanova <- adonis2(dados2~varieties, permutations = 999)
permanova3 Análise de Redundância (RDA)
Para essa análise, vamos seguir o exemplo contido no link: https://r.qcbs.ca/workshop10/book-en/redundancy-analysis.html
3.1 Preparar os dados
3.1.1 Carregar os dados de espécies
setwd("~/Dropbox/UFMG/Disciplinas/R UFAC/Aulas/Multivar/")
spe <- read.csv("data_spe.csv", row.names = 1)
(remove <- which(rowSums(spe)==0)) ## a linha 8 possui 0 indivuduos## 8
## 8which(colSums(spe)==0)## named integer(0)spe <- spe[-remove, ] #cuidado, esse comando só pode ser rodado uma vez3.1.2 Carregar os dados de variáveis ambientais
env <- read.csv("data_env.csv", row.names = 1)
env <- env[-remove, ] # remover a linha equivlente que tinha 0 indivíduos. #cuidado, esse comando só pode ser rodado uma vez3.1.3 Avaliar e padronizar os dados
Os dados de espécies possuem muitos zeros (e isso é bem comum!), portanto precisamos padronizar isso. É recomendado usar a transformação de Hellinger
spe.hel <- decostand(spe, method = "hellinger")Os dados ambientais possuem muitas variáveis, precisamos conferir a correlação entre elas antes de simplemente colocar no modelo.
col<- colorRampPalette(c("blue", "white", "red"))(20)
heatmap(x = cor(env), col = col, symm = TRUE)
Outra opção pra visualizar é
psych::pairs.panels(env)
library(corrplot)## corrplot 0.92 loadedcorrelacao <- cor(env)
corrplot(correlacao, type = "upper", method="color", tl.col = "black", tl.srt = 45)
ou ainda
col <- colorRampPalette(c("#BB4444", "#EE9988", "#FFFFFF", "#77AADD", "#4477AA"))
corrplot(correlacao, method="color", col=col(200),
type="upper", order="hclust",
addCoef.col = "black", # Add coefficient of correlation
tl.col="black", tl.srt=45, #Text label color and rotation
# Combine with significance
#p.mat = p.mat, sig.level = 0.01, insig = "blank",
# hide correlation coefficient on the principal diagonal
diag=FALSE
)
Há mesmo muitas correlações, principalmente da variável das.
Como as variáveis foram medidas em escalas diferentes, vamos também usar a função decostand, na opção standardize. Isso colocará todos os dados com média 0 e 1 unidade de desvio padrão.
env.z <- decostand(env, method = "standardize")Nossos dados estão prontos agora! Podemos ir para as análises.
A primeira coisa que faremos é remover a variável das do conjunto de ambientais, pois ela era muito correlacionada.
env.z <- subset(env.z, select = -das)3.1.4 Rodando a RDA
Agora podemos rodar a RDA
spe.rda <- vegan::rda(spe.hel ~ ., data = env.z)
summary(spe.rda)##
## Call:
## rda(formula = spe.hel ~ alt + pen + deb + pH + dur + pho + nit + amm + oxy + dbo, data = env.z)
##
## Partitioning of variance:
## Inertia Proportion
## Total 0.5025 1.0000
## Constrained 0.3689 0.7341
## Unconstrained 0.1336 0.2659
##
## Eigenvalues, and their contribution to the variance
##
## Importance of components:
## RDA1 RDA2 RDA3 RDA4 RDA5 RDA6 RDA7
## Eigenvalue 0.2280 0.05442 0.03382 0.03008 0.007487 0.005662 0.004429
## Proportion Explained 0.4538 0.10829 0.06730 0.05986 0.014898 0.011268 0.008814
## Cumulative Proportion 0.4538 0.56208 0.62938 0.68924 0.704136 0.715404 0.724218
## RDA8 RDA9 RDA10 PC1 PC2 PC3
## Eigenvalue 0.002811 0.001381 0.0007926 0.04642 0.02072 0.01746
## Proportion Explained 0.005595 0.002747 0.0015773 0.09238 0.04123 0.03474
## Cumulative Proportion 0.729812 0.732560 0.7341370 0.82652 0.86775 0.90249
## PC4 PC5 PC6 PC7 PC8 PC9
## Eigenvalue 0.01325 0.009738 0.005882 0.005122 0.003998 0.003030
## Proportion Explained 0.02637 0.019379 0.011705 0.010192 0.007956 0.006031
## Cumulative Proportion 0.92886 0.948235 0.959940 0.970132 0.978088 0.984118
## PC10 PC11 PC12 PC13 PC14 PC15
## Eigenvalue 0.003004 0.001809 0.001111 0.0007554 0.0005616 0.0003469
## Proportion Explained 0.005979 0.003601 0.002211 0.0015033 0.0011177 0.0006904
## Cumulative Proportion 0.990097 0.993698 0.995909 0.9974126 0.9985302 0.9992206
## PC16 PC17 PC18
## Eigenvalue 0.0002483 0.0001113 3.200e-05
## Proportion Explained 0.0004942 0.0002216 6.367e-05
## Cumulative Proportion 0.9997148 0.9999363 1.000e+00
##
## Accumulated constrained eigenvalues
## Importance of components:
## RDA1 RDA2 RDA3 RDA4 RDA5 RDA6 RDA7
## Eigenvalue 0.2280 0.05442 0.03382 0.03008 0.007487 0.005662 0.004429
## Proportion Explained 0.6181 0.14751 0.09167 0.08154 0.020294 0.015348 0.012006
## Cumulative Proportion 0.6181 0.76563 0.85730 0.93884 0.959135 0.974483 0.986489
## RDA8 RDA9 RDA10
## Eigenvalue 0.002811 0.001381 0.0007926
## Proportion Explained 0.007621 0.003742 0.0021485
## Cumulative Proportion 0.994109 0.997851 1.0000000
##
## Scaling 2 for species and site scores
## * Species are scaled proportional to eigenvalues
## * Sites are unscaled: weighted dispersion equal on all dimensions
## * General scaling constant of scores: 1.93676
##
##
## Species scores
##
## RDA1 RDA2 RDA3 RDA4 RDA5 RDA6
## CHA 0.13165 0.103011 -0.0172558 -0.235893 0.0185193 0.0221025
## TRU 0.61829 -0.009587 0.2863218 0.077981 -0.0002929 -0.0131230
## VAI 0.49901 0.142765 -0.1999345 0.007029 -0.0636477 -0.0078160
## LOC 0.38975 0.147620 -0.2235978 0.083310 -0.0225081 -0.0273493
## OMB 0.13328 0.096119 0.0001608 -0.235474 0.0128430 0.0517589
## BLA 0.06656 0.109572 -0.0033336 -0.197116 0.0177164 0.0144250
## HOT -0.17138 0.072625 0.0081007 -0.008591 0.0210074 -0.0642826
## TOX -0.12546 0.160816 0.0106627 -0.036292 -0.0339079 -0.0913475
## VAN -0.08405 0.049425 -0.0640432 0.010129 -0.0167668 0.0175047
## CHE -0.09596 -0.131741 -0.1808882 -0.055352 0.0899699 0.0234751
## BAR -0.17993 0.209024 0.0358096 -0.070651 0.0008568 -0.0277178
## SPI -0.15536 0.157851 0.0244009 -0.011114 -0.0325750 -0.0354818
## GOU -0.20180 0.040027 -0.0448392 -0.008890 -0.0611972 0.0341513
## BRO -0.10105 0.049146 -0.0458356 0.088503 -0.0871574 0.0677310
## PER -0.08819 0.121087 -0.0470900 0.078629 0.0029062 -0.0046711
## BOU -0.20490 0.161262 0.0451044 0.018169 -0.0156914 -0.0015366
## PSO -0.22974 0.109603 0.0186218 0.011661 0.0353251 -0.0343478
## ROT -0.16703 0.004211 0.0067925 0.036803 -0.0579586 0.0680597
## CAR -0.17610 0.143517 0.0343842 0.011121 0.0032877 -0.0023979
## TAN -0.13246 0.127994 -0.0721057 0.109027 0.0556198 0.0135747
## BCO -0.18787 0.117043 0.0487394 0.036248 0.0208310 0.0313117
## PCH -0.15067 0.080058 0.0486948 0.043339 0.0352494 0.0689095
## GRE -0.31191 0.014095 0.0221539 0.022690 -0.0243663 0.0367353
## GAR -0.31230 -0.147197 -0.1318943 0.039348 0.0484994 -0.0380365
## BBO -0.24208 0.087370 0.0391560 0.034379 0.0541665 -0.0004277
## ABL -0.42821 -0.222422 0.0093609 -0.129619 -0.1121364 -0.0448125
## ANG -0.19192 0.140604 0.0437442 0.026061 -0.0061464 0.0152905
##
##
## Site scores (weighted sums of species scores)
##
## RDA1 RDA2 RDA3 RDA4 RDA5 RDA6
## 1 0.37844 -0.442557 1.59911 0.30334 0.46115 -0.25749
## 2 0.53342 -0.049571 0.29691 0.38382 -0.39592 -0.57773
## 3 0.49530 -0.002279 0.11568 0.47364 -0.78826 -0.18505
## 4 0.33905 0.068384 -0.22978 0.57718 -0.42387 0.33957
## 5 0.02915 -0.139350 -0.42917 0.59397 -0.10125 0.90793
## 6 0.24982 -0.039579 -0.48199 0.55767 0.13076 0.20562
## 7 0.46641 -0.103929 -0.03475 0.32290 -0.00367 -0.33237
## 9 0.04700 -0.460097 -0.94060 0.21229 1.66756 -0.35924
## 10 0.31973 -0.093408 -0.54293 0.17722 -0.15664 0.10771
## 11 0.48065 -0.059751 0.07611 -0.43913 0.31005 0.27861
## 12 0.49138 -0.007440 0.08033 -0.42912 0.30341 0.21058
## 13 0.49512 0.130955 0.32688 -0.77176 0.05047 0.35593
## 14 0.38259 0.195124 0.07180 -0.81039 -0.06477 0.78140
## 15 0.28843 0.209962 -0.13684 -0.71171 0.48053 0.59234
## 16 0.09251 0.402933 -0.15653 -0.29350 0.09074 -0.57845
## 17 -0.04899 0.439567 -0.10316 -0.38402 -0.31709 -1.11824
## 18 -0.13742 0.411818 -0.14279 -0.34491 -0.30152 -0.80436
## 19 -0.27608 0.338417 -0.28964 0.04886 -0.48681 -0.82121
## 20 -0.39384 0.241715 -0.10316 0.14589 -0.27614 -0.49014
## 21 -0.42776 0.287579 0.03588 0.21015 -0.21387 -0.02561
## 22 -0.46704 0.238834 0.12674 0.20246 0.19915 0.11553
## 23 -0.28260 -1.149481 -0.12838 -0.48779 0.28642 -0.86898
## 24 -0.41270 -0.776354 0.08746 -0.33354 0.28123 -0.76408
## 25 -0.35666 -0.783183 -0.06170 -0.17147 -1.30623 1.09559
## 26 -0.46994 0.089229 0.09813 0.21223 0.05933 0.43001
## 27 -0.47143 0.201319 0.13869 0.22378 0.15968 0.34418
## 28 -0.47461 0.215861 0.16878 0.23445 0.26274 0.42397
## 29 -0.37633 0.361804 0.23635 0.04817 0.02847 0.38919
## 30 -0.49359 0.273478 0.32258 0.24933 0.06437 0.60480
##
##
## Site constraints (linear combinations of constraining variables)
##
## RDA1 RDA2 RDA3 RDA4 RDA5 RDA6
## 1 0.41231 -0.45736 1.56906 0.34354 0.35943 -0.22075
## 2 0.31314 0.10276 0.01801 0.76326 -0.70324 -0.36076
## 3 0.41049 -0.06321 0.06766 0.45134 -0.25281 -0.02163
## 4 0.48360 0.09233 -0.28711 0.29452 -0.17537 0.19245
## 5 0.21275 -0.42735 -0.45514 0.38930 0.44928 0.09188
## 6 0.44590 -0.08797 -0.20162 0.39627 -0.22763 0.03749
## 7 0.53727 -0.10880 -0.23699 0.04252 0.26659 0.34671
## 9 0.00102 -0.26564 -0.62973 0.49900 0.62755 0.06921
## 10 0.16369 -0.07428 -0.10940 0.13792 0.22241 -0.27954
## 11 0.28729 0.23709 -0.09670 -0.27933 0.06708 0.37308
## 12 0.35181 0.14358 -0.02901 -0.39937 -0.17428 -0.22636
## 13 0.37325 0.09016 -0.02348 -0.62517 0.13077 -0.03310
## 14 0.40151 0.12475 -0.01469 -0.65953 0.13897 0.30526
## 15 0.22403 0.19534 0.18512 -0.55368 0.18183 0.35594
## 16 -0.03859 0.28753 -0.20130 -0.14582 0.07060 -0.27681
## 17 -0.07706 0.19775 -0.07859 -0.14387 -0.13673 -0.41621
## 18 -0.06413 0.28495 -0.08054 -0.17853 -0.19815 -0.16840
## 19 -0.02162 0.33081 0.01905 -0.24040 -0.25759 -0.01630
## 20 -0.21554 0.36432 0.05030 -0.07898 -0.43632 -0.60826
## 21 -0.34579 0.27751 -0.06366 0.05747 0.02923 -0.53057
## 22 -0.30009 0.10181 0.04606 -0.17520 0.34122 -0.46261
## 23 -0.19234 -1.01335 0.04965 -0.64236 -0.14117 -0.20203
## 24 -0.54202 -0.62155 -0.18969 -0.08445 0.56631 -0.36670
## 25 -0.41201 -0.89130 -0.08746 -0.13763 -1.12836 0.50266
## 26 -0.47949 0.03614 -0.17840 0.25266 0.15681 0.52018
## 27 -0.60917 0.15381 0.11602 0.25456 0.15037 -0.22326
## 28 -0.51332 0.39541 0.10506 0.17547 -0.03491 0.27941
## 29 -0.35142 0.33911 0.30796 0.16149 -0.11210 0.52228
## 30 -0.45546 0.25568 0.42956 0.12500 0.22022 0.81674
##
##
## Biplot scores for constraining variables
##
## RDA1 RDA2 RDA3 RDA4 RDA5 RDA6
## alt 0.8238 -0.19241 -0.01107 0.5161 0.06677 -0.06716
## pen 0.3419 -0.24900 0.76492 0.2271 0.20827 -0.12943
## deb -0.7791 0.22211 0.18513 -0.2494 -0.07930 0.38639
## pH 0.1026 0.16266 0.03127 -0.3149 0.14558 0.27883
## dur -0.5694 0.07369 -0.27232 -0.5483 0.18946 0.37711
## pho -0.4954 -0.65447 -0.07321 -0.2187 -0.42190 0.27002
## nit -0.7764 -0.20419 -0.04923 -0.2592 -0.40011 0.06754
## amm -0.4766 -0.68868 -0.08148 -0.1807 -0.47825 0.08957
## oxy 0.7630 0.53393 0.25890 -0.2119 0.04726 -0.12851
## dbo -0.5191 -0.78586 -0.13145 -0.1546 -0.17626 0.082523.1.5 Selecionando as variáveis
# Forward selection of variables:
fwd.sel <- ordiR2step(rda(spe.hel ~ 1, data = env.z), # limite inferior do modelo (modelo nulo)
scope = formula(spe.rda), # limite superior do modelo (o modelo "completo")
direction = "forward",
R2scope = TRUE, # não pode superar o R2 do modelo "completo"
pstep = 1000,
trace = TRUE) # se é TRUE, vejo o processo passo a passo## Step: R2.adj= 0
## Call: spe.hel ~ 1
##
## R2.adjusted
## <All variables> 0.58643531
## + alt 0.30317903
## + oxy 0.27664565
## + deb 0.26284719
## + nit 0.25885656
## + dbo 0.16253018
## + dur 0.14287362
## + pho 0.13366338
## + amm 0.12940835
## + pen 0.07071011
## <none> 0.00000000
## + pH -0.01877893
##
## Df AIC F Pr(>F)
## + alt 1 -28.504 13.182 0.002 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: R2.adj= 0.303179
## Call: spe.hel ~ alt
##
## R2.adjusted
## <All variables> 0.5864353
## + oxy 0.4530243
## + dbo 0.4034321
## + amm 0.3755280
## + pho 0.3708315
## + nit 0.3462991
## + pen 0.3371717
## + deb 0.3121070
## + dur 0.3116743
## <none> 0.3031790
## + pH 0.2990327
##
## Df AIC F Pr(>F)
## + oxy 1 -34.62 8.3967 0.002 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: R2.adj= 0.4530243
## Call: spe.hel ~ alt + oxy
##
## R2.adjusted
## <All variables> 0.5864353
## + dbo 0.5401552
## + pho 0.5117625
## + amm 0.5028443
## + pen 0.5006494
## + dur 0.4712537
## + deb 0.4647864
## <none> 0.4530243
## + nit 0.4476588
## + pH 0.4392323
##
## Df AIC F Pr(>F)
## + dbo 1 -38.789 5.9264 0.002 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: R2.adj= 0.5401552
## Call: spe.hel ~ alt + oxy + dbo
##
## R2.adjusted
## + pen 0.5947636
## <All variables> 0.5864353
## + dur 0.5621437
## + deb 0.5474307
## <none> 0.5401552
## + pho 0.5372307
## + amm 0.5339205
## + nit 0.5338362
## + pH 0.5296165Quais variáveis foram retidas no modelo?
fwd.sel$call## rda(formula = spe.hel ~ alt + oxy + dbo, data = env.z)Esse é o novo modelo, com as variáveis que foram retidas na seleção, temos que reescrever esse novo modelo para prosseguir
spe.rda.signif <- rda(spe.hel ~ alt + oxy + dbo, data = env.z)
# verifique o R2 ajustado (corrigido para o número de variáveis explicativas)
RsquareAdj(spe.rda.signif)## $r.squared
## [1] 0.5894243
##
## $adj.r.squared
## [1] 0.54015523.1.6 Avalianda a significância da RDA
significância do modelo
anova.cca(spe.rda.signif, step = 1000)significância dos termos
anova.cca(spe.rda.signif, step = 1000, by = "term")3.1.7 Plot dos dados
library(ggvegan)
autoplot(spe.rda.signif)