MODULO 5 - Estatística Multivariada - CCA - Análise de Correlação/Correspondência Canônica
Leonardo Reffatti
16 de junho de 2019
Aula 5.29
CCA - Análise de Correlação Canônica matrizes de distância de dois conjunto de dados pelo método qui-quadrado, sendo uma com variáveis de Presença/Aunsência de espécies e outra com variáveis fisico-químicas do solo
Objetivo: Desenvolver uma CCA da matriz de distâncias pelo método qui-quadrado de um conjunto de dados de composição de espécies “varespec” para entender qual a relação com o conjunto de dados de variáveis fisico-químicas do solo “varechem”.
Este material está disponível em: http://rpubs.com/leonardoreffatti.
CCA de um conjunto de dados de composição de espécies (Presença/Ausência + Abundância) com varespec através da matriz de distâncias pelo método qui-quadrado. Conjunto de dados fisico-químicos do solo com varechem. Desenvolver a cca através da função cca() do pacote vegan, plotagem da CCA, avaliar como o conjunto de dados de espécies se corresponde com os resultados fisico-químicos através da CCA e CA+envfit.
library(permute)
library(lattice)
library(vegan)## This is vegan 2.5-2#Carregando um primeiro conjunto de dados do pacote vegan
data("varespec")
data("varechem")
resultado.cca <- cca(varespec, varechem)
summary(resultado.cca)##
## Call:
## cca(X = varespec, Y = varechem)
##
## Partitioning of scaled Chi-square:
## Inertia Proportion
## Total 2.0832 1.000
## Constrained 1.4415 0.692
## Unconstrained 0.6417 0.308
##
## Eigenvalues, and their contribution to the scaled Chi-square
##
## Importance of components:
## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6
## Eigenvalue 0.4389 0.2918 0.16285 0.14213 0.11795 0.08903
## Proportion Explained 0.2107 0.1401 0.07817 0.06823 0.05662 0.04274
## Cumulative Proportion 0.2107 0.3507 0.42890 0.49713 0.55375 0.59649
## CCA7 CCA8 CCA9 CCA10 CCA11 CCA12
## Eigenvalue 0.07029 0.05836 0.03114 0.013294 0.008364 0.006538
## Proportion Explained 0.03374 0.02801 0.01495 0.006382 0.004015 0.003139
## Cumulative Proportion 0.63023 0.65825 0.67319 0.679576 0.683592 0.686730
## CCA13 CCA14 CA1 CA2 CA3 CA4
## Eigenvalue 0.006156 0.004733 0.19776 0.14193 0.10117 0.07079
## Proportion Explained 0.002955 0.002272 0.09493 0.06813 0.04857 0.03398
## Cumulative Proportion 0.689685 0.691958 0.78689 0.85502 0.90359 0.93757
## CA5 CA6 CA7 CA8 CA9
## Eigenvalue 0.05330 0.03330 0.018868 0.015104 0.009488
## Proportion Explained 0.02559 0.01598 0.009057 0.007251 0.004554
## Cumulative Proportion 0.96315 0.97914 0.988195 0.995446 1.000000
##
## Accumulated constrained eigenvalues
## Importance of components:
## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6 CCA7
## Eigenvalue 0.4389 0.2918 0.1628 0.1421 0.11795 0.08903 0.07029
## Proportion Explained 0.3045 0.2024 0.1130 0.0986 0.08183 0.06176 0.04877
## Cumulative Proportion 0.3045 0.5069 0.6198 0.7184 0.80027 0.86203 0.91080
## CCA8 CCA9 CCA10 CCA11 CCA12 CCA13
## Eigenvalue 0.05836 0.03114 0.013294 0.008364 0.006538 0.006156
## Proportion Explained 0.04049 0.02160 0.009223 0.005803 0.004536 0.004271
## Cumulative Proportion 0.95128 0.97288 0.982107 0.987910 0.992446 0.996716
## CCA14
## Eigenvalue 0.004733
## Proportion Explained 0.003284
## Cumulative Proportion 1.000000
##
## Scaling 2 for species and site scores
## * Species are scaled proportional to eigenvalues
## * Sites are unscaled: weighted dispersion equal on all dimensions
##
##
## Species scores
##
## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6
## Callvulg 0.075347 -0.93581 1.677742 0.695507 1.077518 -0.345001
## Empenigr -0.181340 0.07610 0.036462 -0.427727 -0.138153 0.010517
## Rhodtome -1.053549 -0.06026 0.077428 -0.938897 -0.213938 -0.518031
## Vaccmyrt -1.277428 0.30759 0.303704 -0.092088 -0.568820 -0.613023
## Vaccviti -0.152563 0.12054 -0.053031 -0.362279 0.083942 0.008938
## Pinusylv 0.242956 0.26432 0.223265 -0.273806 0.292102 -0.063335
## Descflex -1.443872 0.27019 -0.162082 0.606576 -0.476067 0.382590
## Betupube -0.711004 -0.22681 -0.083007 -2.408417 -0.216212 -1.671857
## Vacculig 0.513817 -1.18831 -0.377748 0.177035 -0.958084 0.311138
## Diphcomp 0.099310 -0.89289 -0.419273 -0.532348 -0.270745 0.622270
## Dicrsp -0.849964 0.23153 -1.751924 0.260810 1.522412 0.390210
## Dicrfusc -0.499460 -0.41539 0.824743 -0.258156 0.112149 0.638702
## Dicrpoly -0.527090 0.08050 -0.812083 -1.201383 0.768689 -1.025365
## Hylosple -1.828026 0.79385 0.049816 1.358093 -0.916528 -0.223338
## Pleuschr -0.924978 0.33684 -0.009146 0.308091 -0.065518 0.018741
## Polypili 0.144172 -0.45586 -0.515356 -0.281796 -0.052660 0.050659
## Polyjuni -0.606869 0.21021 -0.352109 -0.336004 -0.612858 0.351629
## Polycomm -0.894165 0.32063 -0.234919 -1.076106 -0.408823 -0.776736
## Pohlnuta -0.009508 0.25268 -0.140571 -0.351201 0.424031 -0.096811
## Ptilcili -0.576115 -0.12234 -0.058593 -2.109265 -0.166198 -1.507591
## Barbhatc -0.694092 -0.22970 -0.118360 -2.574980 -0.172821 -2.054320
## Cladarbu 0.211517 -0.71201 -0.026366 0.052216 -0.040564 -0.078262
## Cladrang 0.381030 -0.61678 -0.243893 0.105921 -0.163536 0.032637
## Cladstel 0.906486 0.70213 0.082949 0.067771 -0.016579 0.027407
## Cladunci -0.230671 0.06372 -0.013810 -0.391170 0.910527 -0.146092
## Cladcocc 0.219419 -0.13619 0.128350 -0.077450 0.033754 0.125028
## Cladcorn -0.225404 0.07008 -0.090524 -0.258643 -0.109501 0.170706
## Cladgrac -0.108836 -0.18599 -0.159664 -0.201023 0.241156 -0.021594
## Cladfimb 0.020022 -0.09179 0.192626 -0.262413 -0.035959 -0.034780
## Cladcris -0.137056 0.01609 0.422960 -0.423861 0.138016 -0.129810
## Cladchlo 0.443621 0.55305 -0.278345 -0.576292 0.169030 -0.224882
## Cladbotr -0.680481 -0.19013 0.195105 -1.330144 0.218169 -1.262258
## Cladamau -0.015996 -1.16331 -0.728763 -0.498887 -0.350481 0.714608
## Cladsp 0.686166 0.39137 0.307091 0.279524 0.604150 0.124850
## Cetreric 0.064619 -0.03889 -0.427516 0.118844 0.945590 -0.173838
## Cetrisla 0.159171 0.35076 -0.049161 -0.884501 0.166607 -0.689545
## Flavniva 0.872373 -0.64645 -0.465365 1.961193 0.368671 -2.332045
## Nepharct -0.762768 0.19877 -0.558560 -0.057976 -1.137069 0.744096
## Stersp 0.121697 -1.28229 -0.963619 -0.003712 -0.369284 0.417103
## Peltapht -0.397796 0.16843 0.049634 -0.338986 -0.263955 0.194009
## Icmaeric 0.172805 -1.53313 -0.429975 -0.154452 -0.413750 0.319003
## Cladcerv 0.708032 -0.05882 -0.316283 1.225539 0.004871 -1.044377
## Claddefo -0.301412 -0.02090 0.243431 -0.564576 0.292677 -0.188788
## Cladphyl 1.002262 1.12620 0.016613 -0.101195 0.094379 0.145598
##
##
## Site scores (weighted averages of species scores)
##
## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6
## 18 0.1785 -1.05988 -0.408835 -0.60721 -0.56492 0.24175
## 15 -0.9702 -0.19714 0.421046 0.30324 0.15171 0.80394
## 24 -1.2798 0.47645 -2.946863 0.39292 3.95433 0.76592
## 27 -1.5009 0.65216 0.085837 0.76207 -1.23251 -0.09756
## 23 -0.5981 -0.18404 -0.135611 -1.16425 -0.30249 0.07033
## 19 -0.1103 0.71431 0.016591 -0.07773 -0.55210 -0.08258
## 22 -1.0921 -0.49026 2.120668 -0.43014 0.26010 1.87287
## 16 -0.7558 -0.78712 1.652152 -0.15892 0.47523 1.73677
## 28 -2.2421 1.15075 0.248921 1.88204 -1.80814 -1.19935
## 13 0.4035 -1.46904 2.240249 1.21956 1.85549 -0.91541
## 14 -0.4563 -0.69333 1.089571 -1.04519 2.70161 0.15628
## 20 -0.5583 -0.25296 -0.336340 -0.36433 0.27453 0.10923
## 25 -1.2922 0.25087 -1.456542 -0.02698 0.96227 2.19508
## 7 0.5576 -2.01700 -0.923568 0.14954 -1.34406 0.19237
## 5 0.6651 -2.24847 -1.631533 0.44110 -1.23074 0.53544
## 6 0.5920 -1.29165 -0.470112 -0.08331 -0.28830 -0.18265
## 3 1.3379 0.39399 -0.212551 0.26020 -0.61477 0.30075
## 4 1.1675 -0.55997 -0.207980 2.14490 0.35776 -3.17436
## 2 1.4091 1.12669 0.011297 0.04175 -0.40173 0.27311
## 9 1.3130 1.69016 0.238808 -0.13429 0.00160 0.04923
## 12 1.0115 1.08413 0.085287 -0.24485 -0.12365 0.18392
## 10 1.4105 1.54744 0.232569 -0.16699 -0.15736 0.16768
## 11 0.4651 0.05411 -0.146473 0.25902 -0.08197 -0.03886
## 21 -0.7191 0.42952 0.009702 -3.83149 -0.83861 -4.06109
##
##
## Site constraints (linear combinations of constraining variables)
##
## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6
## 18 -0.42308 -1.32466 -0.49215 -0.94489 -0.048464 0.9398
## 15 -0.19026 0.49687 0.45454 -0.52951 -0.076603 -0.7899
## 24 -0.86328 0.25213 -2.76035 0.56993 3.292710 0.2629
## 27 -1.69805 0.48669 -0.56351 1.07358 -0.614147 0.4988
## 23 -0.79557 0.10723 0.25751 -0.90419 -0.287557 0.4387
## 19 -0.67702 1.00130 0.03344 -1.00351 -0.141279 -0.9383
## 22 -0.81881 -0.67147 1.51674 -0.05858 0.566703 2.2159
## 16 -0.14877 -1.16222 1.02373 -0.44751 -0.154699 -0.2515
## 28 -2.07190 1.09778 0.49758 1.88707 -1.394002 -0.6375
## 13 0.16534 -1.35508 2.60193 1.25142 1.760111 -0.5461
## 14 -0.14069 0.20118 0.77762 -0.87922 0.676806 -0.3838
## 20 -0.68566 0.08107 -0.20421 -1.11529 1.112185 -0.7635
## 25 -0.90562 0.29517 -0.55183 -0.07379 -1.131782 0.8128
## 7 1.38453 -1.92877 -0.80045 0.36440 -1.653585 -0.1187
## 5 0.09709 -2.02095 -1.57794 0.03999 -0.441247 0.9902
## 6 0.41866 -0.56908 -0.32436 0.06603 -0.058116 0.3371
## 3 0.95649 0.12458 -0.51056 0.15157 -1.065096 -0.1616
## 4 0.85641 -0.79366 -0.46982 2.32495 0.468453 -2.8417
## 2 1.53650 0.92994 0.09664 0.25941 -0.009995 0.7130
## 9 1.53381 1.60412 -0.01520 -0.11658 0.698700 0.6643
## 12 0.44751 0.23990 0.93887 -0.28191 0.128819 0.3828
## 10 1.11107 1.59354 -0.04164 0.11005 -0.461130 0.2664
## 11 0.59050 0.36592 -0.04552 -0.14145 -0.070919 -0.3881
## 21 -0.68681 -0.23299 -0.17348 -2.78317 -0.205599 -2.1817
##
##
## Biplot scores for constraining variables
##
## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6
## N -0.22290 -0.52891 0.006729 0.17735 -0.253216 0.102014
## P -0.31866 0.57886 -0.162001 0.47947 0.184099 -0.121835
## K -0.36612 0.30794 0.359824 0.47942 0.325444 -0.196637
## Ca -0.44764 0.42176 -0.037765 0.09827 0.307969 0.043545
## Mg -0.43499 0.34051 -0.142169 0.10790 0.497841 -0.005758
## S -0.02406 0.41570 0.148384 0.44446 0.597063 -0.166296
## Al 0.76978 -0.04747 0.037610 0.39098 0.160905 -0.336554
## Fe 0.64909 -0.08811 -0.042067 0.26297 -0.069806 -0.111345
## Mn -0.72232 0.22460 0.113052 0.29152 -0.138680 0.180471
## Zn -0.35810 0.33493 -0.277916 0.34572 0.619191 -0.001195
## Mo 0.20413 -0.10334 -0.157007 0.32424 0.516439 -0.313525
## Baresoil -0.53675 -0.25477 0.136910 -0.52055 0.166621 -0.352409
## Humdepth -0.69673 0.20163 0.271625 -0.13574 -0.003252 -0.051350
## pH 0.49716 0.07509 -0.326341 0.02092 -0.145569 -0.059091#Os primeiros resultados mostram apenas os valores referentes ao conjunto de dados varespec.
#Na sequencia, "constrained" integra-se os resultados de varechem nos valores apresentados para identificar o quanto a adição da matriz de varechem auxilia na interpretação do conjunto total de resultados da análise de correlação canônica.
plot(resultado.cca)
#Comparação da CCA com CA + Envfit
resultado.ca<-cca(varespec)
resultado.envfit<-envfit(resultado.ca, varechem)
#resultado de permutação de cada variável do varechem
resultado.envfit##
## ***VECTORS
##
## CA1 CA2 r2 Pr(>r)
## N 0.47470 -0.88015 0.2196 0.077 .
## P 0.44827 0.89390 0.3054 0.028 *
## K 0.73616 0.67680 0.1773 0.157
## Ca 0.69724 0.71684 0.3064 0.017 *
## Mg 0.77318 0.63419 0.2466 0.062 .
## S 0.05137 0.99868 0.0902 0.381
## Al -0.97491 -0.22260 0.4995 0.001 ***
## Fe -0.96390 -0.26627 0.3682 0.009 **
## Mn 0.91444 0.40473 0.4750 0.005 **
## Zn 0.77039 0.63758 0.1766 0.160
## Mo -0.63809 -0.76997 0.0539 0.613
## Baresoil 0.97947 -0.20161 0.2533 0.065 .
## Humdepth 0.91602 0.40112 0.4524 0.006 **
## pH -0.99831 0.05818 0.2187 0.088 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Permutation: free
## Number of permutations: 999#Comparação de Gráficos CCA com CA + Envfit
par(mfrow=c(1,2))
plot(resultado.cca, main="CCA")
plot(resultado.ca, main="CA + Envfit")
plot(resultado.envfit)
#Existem diferenças na construção estatística dos gráficos, porém em termos conceituais são a mesma coisa.
#Praticamente nada da interpretação dos resultados vai mudar. Na situação com envfit, temos o resultado de significância para cada variável fisico-química.