Aggiunta di ellissi a un grafico di analisi del componente principale (PCA)

Question

Ho difficoltà ad aggiungere il gruppo di ellissi variabili sopra un singolo grafico di fattore PCA del sito che include anche frecce di fattore variabile PCA.

Il mio codice:

prin_comp<-rda(data[,2:9], scale=TRUE) 
pca_scores<-scores(prin_comp) 

#sites=individual site PC1 & PC2 scores, Waterbody=Row Grouping Variable. 
#site scores in the PCA plot are stratified by Waterbody type. 

plot(pca_scores$sites[,1], 
    pca_scores$sites[,2], 
    pch=21, 
    bg=point_colors[data$Waterbody], 
    xlim=c(-2,2), 
    ylim=c(-2,2), 
    xlab=x_axis_text, 
    ylab=y_axis_text) 

#species=column PCA1 & PCA2 Response variables 
arrows(0,0,pca_scores$species[,1],pca_scores$species[,2],lwd=1,length=0.2) 

#I want to draw 'Waterbody' Grouping Variable ellipses that encompass completely, 
# their appropriate individual site scores (this is to visualise total error/variance). 

Ho tentato di utilizzare sia dataellipse, plotellipses & funzioni ellisse, ma senza alcun risultato. L'ignoranza sta vincendo su questo. Se non ho fornito informazioni sufficienti per favore fatemelo sapere.

dati (log10 trasformata):

dput(data) 

structure(list(Waterbody = structure(c(4L, 4L, 4L, 4L, 4L, 4L, 
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
5L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L), .Label = c("Ditch", "Garden Pond", 
"Peri-Urban Ponds", "River", "Stream"), class = "factor"), Catchment_Size = c(9.73045926, 
9.73045926, 9.73045926, 9.73045926, 9.73045926, 9.73045926, 9.73045926, 
9.73045926, 9.73045926, 9.73045926, 9.73045926, 9.73045926, 9.73045926, 
9.73045926, 9.73045926, 9.73045926, 9.73045926, 9.73045926, 9.73045926, 
9.73045926, 8.602059991, 8.602059991, 8.602059991, 8.602059991, 
8.602059991, 8.602059991, 8.602059991, 8.602059991, 8.602059991, 
8.602059991, 8.602059991, 8.602059991, 8.602059991, 8.602059991, 
8.602059991, 8.602059991, 8.602059991, 8.602059991, 8.602059991, 
8.602059991, 5.230525555, 5.271197816, 5.310342762, 5.674064357, 
5.745077916, 5.733059168, 5.90789752, 5.969640923, 0, 0, 0.419955748, 
0, 0.079181246, 0, 0.274157849, 0, 0.301029996, 1, 0.62838893, 
0.243038049, 0, 0, 0, 1.183269844, 0, 1.105510185, 0, 0.698970004, 
2, 1.079181246, 2.954242509, 1.84509804, 1.477121255, 2.477121255, 
3.662757832, 1.397940009, 1.84509804, 0), pH = c(0.888740961, 
0.891537458, 0.890421019, 0.904715545, 0.886490725, 0.88592634, 
0.892651034, 0.891537458, 0.895422546, 0.8876173, 0.881384657, 
0.888179494, 0.876794976, 0.898725182, 0.894316063, 0.882524538, 
0.881384657, 0.916980047, 0.890979597, 0.886490725, 0.88592634, 
0.903089987, 0.889301703, 0.897627091, 0.896526217, 0.890979597, 
0.927370363, 0.904174368, 0.907948522, 0.890979597, 0.910090546, 
0.892094603, 0.896526217, 0.891537458, 0.894869657, 0.894316063, 
0.898725182, 0.914343157, 0.923244019, 0.905256049, 0.870988814, 
0.868644438, 0.872156273, 0.874481818, 0.88422877, 0.876217841, 
0.874481818, 0.8876173, 0.859138297, 0.887054378, 0.856124444, 
0.856124444, 0.860936621, 0.903089987, 0.860338007, 0.8876173, 
0.860338007, 0.906335042, 0.922206277, 0.851869601, 0.862131379, 
0.868056362, 0.869818208, 0.861534411, 0.875061263, 0.852479994, 
0.868644438, 0.898725182, 0.870403905, 0.88422877, 0.867467488, 
0.905256049, 0.88536122, 0.8876173, 0.876794976, 0.914871818, 
0.899820502, 0.946943271), Conductivity = c(2.818885415, 2.824125834, 
2.824776462, 2.829303773, 2.824125834, 2.82672252, 2.829303773, 
2.82672252, 2.824776462, 2.829946696, 2.846337112, 2.862727528, 
2.845718018, 2.848804701, 2.86923172, 2.85308953, 2.867467488, 
2.847572659, 2.86569606, 2.849419414, 2.504606771, 2.506775537, 
2.691346764, 2.628797486, 2.505963518, 2.48756256, 2.501470072, 
2.488973525, 2.457124626, 2.778295991, 2.237040791, 2.429267666, 
2.3287872, 2.461198289, 2.384174139, 2.386320574, 2.410608543, 
2.404320467, 2.426836454, 2.448397103, 2.768704683, 2.76718556, 
2.771602178, 2.775289978, 2.90579588, 2.909020854, 3.007747778, 
3.017867719, 2.287129621, 2.099680641, 2.169674434, 1.980457892, 
2.741781696, 2.597804842, 2.607669437, 2.419129308, 2.786751422, 
2.639884742, 2.19893187, 2.683497318, 2.585235063, 2.393048466, 
2.562411833, 2.785329835, 2.726808683, 2.824776462, 2.699056855, 
2.585122186, 2.84260924, 2.94792362, 2.877371346, 2.352568386, 
2.202760687, 2.819543936, 2.822168079, 2.426348574, 2.495683068, 
2.731266349), NO3 = c(1.366236124, 1.366236124, 1.376029182, 
1.385606274, 1.376029182, 1.385606274, 1.385606274, 1.385606274, 
1.376029182, 1.385606274, 1.458637849, 1.489114369, 1.482158695, 
1.496098992, 1.502290528, 1.50174373, 1.500785173, 1.499549626, 
1.485721426, 1.490520309, 0.693726949, 0.693726949, 1.246005904, 
1.159266331, 0.652246341, 0.652246341, 0.883093359, 0.85672889, 
0.828659897, 1.131297797, 0.555094449, 0.85672889, 0.731588765, 
0.883093359, 0.731588765, 0.731588765, 0.693726949, 0.693726949, 
0.693726949, 0.693726949, 1.278524965, 1.210853365, 1.318480725, 
1.308777774, 1.404833717, 1.412796429, 0, 0, 0, 0, 0, 0, 1.204391332, 
0, 0, 0, 0.804820679, 0, 0, 0.021189299, 0, 0, 0.012837225, 0, 
0, 0, 0, 0.539076099, 0, 0, 1.619406411, 0, 0, 1.380753771, 0, 
0, 0, 0.931966115), NH4 = c(0.14, 0.14, 0.18, 0.19, 0.2, 0.2, 
0.15, 0.14, 0.11, 0.11, 0.04, 0.06, 0.04, 0.03, 0.07, 0.03, 0.03, 
0.04, 0.04, 0.03, 0.01, 0, 0, 0.01, 0.02, 0.02, 0.05, 0.03, 0.04, 
0.02, 0.21, 0.19, 0.2, 0.1, 0.05, 0.05, 0.08, 0.11, 0.04, 0.04, 
0.15, 2.03, 0.14, 0.09, 0.05, 0.04, 2.82, 3.18, 0.06, 0.12, 2.06, 
0.1, 0.14, 0.06, 1.06, 0.03, 0.04, 0.03, 0.03, 1.91, 0.2, 1.35, 
0.69, 0.05, 0.17, 3.18, 0.21, 0.1, 0.03, 1.18, 0.01, 0.03, 0.02, 
0.09, 0.14, 0.02, 0.07, 0.17), SRP = c(0.213348889, 0.221951667, 
0.24776, 0.228833889, 0.232275, 0.249480556, 0.259803889, 0.244318889, 
0.249480556, 0.240877778, 0.314861667, 0.292494444, 0.311420556, 
0.306258889, 0.285612222, 0.323464444, 0.316582222, 0.34067, 
0.285612222, 0.321743889, 0.074328, 0.074328, 0.120783, 0.133171, 
0.0820705, 0.080522, 0.0789735, 0.0820705, 0.080522, 0.0913615, 
0.136268, 0.1656895, 0.1223315, 0.130074, 0.1192345, 0.1285255, 
0.1873685, 0.167238, 0.15485, 0.157947, 0.1378165, 0.1966595, 
0.198208, 0.241566, 0.037164, 0.0325185, 0.455259, 0.560557, 
0.07987, 0.02119, 0.02119, 0.03912, 0.36349, 0.40098, 0.04401, 
0.07172, 0.15322, 0.92421, 0.02282, 0.17604, 0.17767, 0.66667, 
0.28688, 0.03586, 0.17278, 0.07661, 0.10432, 1.12959, 0.0170335, 
0.0975555, 0.009291, 0.0263245, 0.037164, 0.2214355, 0.0449065, 
0.068134, 0.09291, 0.545072), Zn = c(0.802630077, 1.172124009, 
0.891565332, 0.600253919, 0.583912562, 0.962473516, 0.99881711, 
0.709787074, 1.139860204, 0.953730706, 0.945832806, 0.906270378, 
0.81663232, 0.912514323, 0.935073763, 1.032328597, 1.357197063, 
1.070662063, 0.51200361, 0.987514325, 1.433709044, 1.380974206, 
1.143661074, 0.999774108, 1.449654241, 1.366165106, 1.014239038, 
0.891258617, 0.703978825, 1.086487964, 1.503432481, 1.243241499, 
0.890504851, 0.291391053, 0, 0.802855789, 0.776316103, 0.927421695, 
0.421505212, 0.952099537, 0.688802331, 0.852504392, 0.773545103, 
1.006581553, 1.028229538, 0.880619259, 0.833408503, 1.038608242, 
1.107084413, 0.973967909, 2.135781222, 1.819197019, 1.629353525, 
1.163194184, 1.343286462, 1.273614642, 1.92374902, 1.70523233, 
1.377623112, 1.119971423, 1.461175762, 1.691856516, 1.661826878, 
1.104531494, 1.449455257, 1.092376721, 1.519029523, 1.553407226, 
1.52652924, 1.332876573, 1.293079563, 0.996734891, 1.590475126, 
1.525755949, 1.180418366, 0.712624451, 0.6739512, 0.585043155 
), Mn = c(0.817367016, 0.799340549, 1.023910606, 1.012921546, 
0.821579028, 1.321888278, 1.115077717, 1.02031984, 1.135482491, 
1.073645046, 1.016866271, 1.052809328, 0.818423855, 0.836387419, 
1.151032582, 0.720490068, 1.03746634, 1.072580733, 1.041590047, 
0.979548375, 1.073168262, 1.134336511, 0.916137983, 0.641374945, 
1.083753378, 0.84441504, 0.547159121, 0.144262774, 1.084826417, 
0.674861141, 0.478566496, 1.211654401, 1.095518042, 0.387033701, 
0.647480773, 0.775828814, 0.533899101, 0.854548936, 0.755188586, 
0.714497409, 0.851808514, 0.390051496, 0.832508913, 1.222482357, 
1.477048866, 1.475147977, 2.127826941, 2.132205239, 1.639576128, 
1.155578931, 2.203783274, 1.148448404, 1.644586284, 1.122609024, 
1.577319427, 1.633417953, 1.583901241, 1.215478936, 1.135418905, 
1.612847407, 1.95593777, 1.783639208, 1.567837703, 2.251767151, 
0.992155711, 1.738923187, 0.681964459, 0.852845818, 1.77749932, 
2.465019796, 0.887729797, 0.610447221, 1.777760209, 1.034588354, 
0.303196057, 1.793371249, 1.677734668, 1.802157753)), .Names = c("Waterbody", 
"Catchment_Size", "pH", "Conductivity", "NO3", "NH4", "SRP", 
"Zn", "Mn"), class = "data.frame", row.names = c("1_1", "1_2", 
"1_3", "1_4", "1_5", "1_6", "1_7", "1_8", "1_9", "1_10", "1_11", 
"1_12", "1_13", "1_14", "1_15", "1_16", "1_17", "1_18", "1_19", 
"1_20", "2_1", "2_2", "2_3", "2_4", "2_5", "2_6", "2_7", "2_8", 
"2_9", "2_10", "2_11", "2_12", "2_13", "2_14", "2_15", "2_16", 
"2_17", "2_18", "2_19", "2_20", "3_1", "3_2", "3_3", "3_4", "3_5", 
"3_6", "3_7", "3_8", "4_1", "4_2", "4_3", "4_4", "4_5", "4_6", 
"4_7", "4_8", "4_9", "4_10", "4_11", "4_12", "4_13", "4_14", 
"4_15", "4_16", "4_17", "4_18", "4_19", "4_20", "5_1", "5_2", 
"5_3", "5_4", "5_5", "5_6", "5_7", "5_8", "5_9", "5_10")) 

Answer 1

Dal momento che non menzionare questo nella sua interrogazione, io supporre che il pacchetto è stato utilizzato è vegan, dal momento che ha la funzione di rda() che accetta l'argomento scale=TRUE.

La chiamata iniziale plot() è stata modificata poiché alcune variabili non vengono fornite.

library(vegan) 
prin_comp<-rda(data[,2:9], scale=TRUE) 
pca_scores<-scores(prin_comp) 

plot(pca_scores$sites[,1], 
    pca_scores$sites[,2], 
    pch=21, 
    bg=as.numeric(data$Waterbody), 
    xlim=c(-2,2), 
    ylim=c(-2,2)) 
arrows(0,0,pca_scores$species[,1],pca_scores$species[,2],lwd=1,length=0.2) 

Per rendere ellissi, funzione ordiellipse() del pacchetto vegan viene utilizzato. Come argomenti, è necessario fornire gli oggetti di analisi PCA e la variabile di raggruppamento. Per controllare il numero di punti inclusi nell'ellisse, è possibile utilizzare l'argomento conf=.

ordiellipse(prin_comp,data$Waterbody,conf=0.99) 

Answer 2

Ecco una soluzione ggplot, utilizzando la bella libreria ggbiplot. Un evidente miglioramento rispetto a plot sono le etichette su questo.

library(devtools) # don't forget to install Rtools first 
install_github("ggbiplot", "vqv") 

library(ggbiplot) 
data.class <- data[,1] 
data.pca <- prcomp(data[,2:9], scale. = TRUE) 
g <- ggbiplot(data.pca, obs.scale = 1, var.scale = 1, 
       groups = data.class, ellipse = TRUE, circle = TRUE) 
g <- g + scale_color_discrete(name = '') 
g <- g + theme(legend.direction = 'horizontal', 
       legend.position = 'top') 
print(g)