How to add multiple confidence ellipses to PCA plot in R? - r

Question

I am very very new to R and stats in general, and am having trouble adding multiple confidence ellipses to a PCA plot.
My interest is in highlighting potential groupings/clusters in the PCA plot with 95% confidence ellipses. I have tried using the dataEllipse function in R, however I cannot figure out how to add multiple ellipses with different centers to the PCA plot (the centers would be at various points that appear to contain a cluster, in this case lithic sources and lithic tools likely made from that source).
Thanks for any help with this!
{
lithic_final <- LITHIC.DATASHEET.FOR.R.COMPLETE.FORMAT
lithic_final
pca1 <- princomp(lithic_final); pca1
lithic_source <- c("A1", "A1", "A1", "A1", "A2","A2", "A2", "A3","A3","A3","B","B","B","B","B","B","C","C","C","C","C","C","C","D","D","D","D","D","D","D","D","E","E","E","E","E","E","E","E","F","F","G","G","G","G","H","H","H","H","H","H","H","I1","I1","I1","I2","I2","I2","I2","I2","J1","J1","J2","J2","J2","J2","J2","J2","J2","J2","J2","K","K","K","K","K","K","K","L","L","L","L","L","L","L","L","L","L","L","L","L","L","BB1","BB1","BB1","FC","FC","FC","JRPP","JRPP","JRPP","BB2","BB2","BB2","BB2","MWP","MWP","MWP","MWP","RPO","RPO","RPO")
lithic_source
summary(pca1)
plot(pca1)
#Plotting the scores with the Lithic Source Info
round(pca1$scores[,1:2], 2)
pca_scores <-round(pca1$scores[,1:2], 2)
plot(pca1$scores[,1], pca1$scores[,2], type="n")
text(pca1$scores[,1], pca1$scores[,2],labels=abbreviate(lithic_source, minlength=3), cex=.45)
#Plotting PCA Scores of EACH SAMPLE for PCA 2 and 3 with Lithic Source Info
round(pca1$scores[,2:3], 2)
pca2_3_scores <-round(pca1$scores[,2:3], 2)
plot(pca1$scores[,2], pca1$scores[,3], type="n")
text(pca1$scores[,2], pca1$scores[,3], labels=abbreviate(lithic_source, minlength=3), cex=.45)
#Plotting PCA Scores of EACH SAMPLE for PCA 3 and 4 with Lithic Source Info
round(pca1$scores[,3:4], 2)
pca3_4_scores <-round(pca1$scores[,3:4], 2)
plot(pca1$scores[,3], pca1$scores[,4], type="n")
text(pca1$scores[,3], pca1$scores[,4], labels=abbreviate(lithic_source, minlength=3), cex=.45)
#Plotting PCA Scores of EACH SAMPLE for PCA 1 and 3 with Lithic Source Info
round(pca1$scores[,1:3], 2)
pca1_3_scores <-round(pca1$scores[,1:3], 2)
plot(pca1$scores[,1], pca1$scores[,3], type="n")
text(pca1$scores[,1], pca1$scores[,3], labels=abbreviate(lithic_source, minlength=3), cex=.45)
#Plotting PCA Scores of EACH SAMPLE for PCA 1 and 4 with Lithic Source Info
round(pca1$scores[,1:4], 2)
pca1_4_scores <-round(pca1$scores[,1:4], 2)
plot(pca1$scores[,1], pca1$scores[,4], type="n")
text(pca1$scores[,1], pca1$scores[,4], labels=abbreviate(lithic_source, minlength=3), cex=.45)
#TRYING TO GET ELLIPSES ADDED TO PCA 1 and 4 scores
dataEllipse(pca1$scores[,1], pca1$scores[,4],centers=12,add=TRUE,levels=0.9, plot.points=FALSE)
structure(list(Ca.K12 = c(418L, 392L, 341L, 251L, 297L, 238L,
258L, 5L, 2L, 37L), Cr.K12 = c(1L, 12L, 15L, 6L, 9L, 6L, 35L,
7L, 45L, 32L), Cu.K12 = c(89L, 96L, 81L, 63L, 88L, 103L, 104L,
118L, 121L, 90L), Fe.K12 = c(18627L, 18849L, 18413L, 12893L,
17757L, 17270L, 16198L, 2750L, 4026L, 3373L), K.K12 = c(20L,
23L, 28L, 0L, 34L, 17L, 45L, 102L, 150L, 147L), Mn.K12 = c(205L,
212L, 235L, 120L, 216L, 212L, 246L, 121L, 155L, 115L), Nb.K12 = c(139L,
119L, 154L, 91L, 122L, 137L, 137L, 428L, 414L, 428L), Rb.K12 = c(99L,
42L, 79L, 49L, 210L, 243L, 168L, 689L, 767L, 705L), Sr.K12 = c(3509L,
3766L, 3481L, 2715L, 2851L, 2668L, 2695L, 202L, 220L, 217L),
Ti.K12 = c(444L, 520L, 431L, 293L, 542L, 622L, 531L, 82L,
129L, 84L), Y.K12 = c(135L, 121L, 105L, 74L, 144L, 79L, 85L,
301L, 326L, 379L), Zn.K12 = c(131L, 133L, 108L, 78L, 124L,
111L, 114L, 81L, 78L, 59L), Zr.K12 = c(1348L, 1479L, 1333L,
964L, 1506L, 1257L, 1296L, 3967L, 4697L, 4427L)), .Names = c("Ca.K12",
"Cr.K12", "Cu.K12", "Fe.K12", "K.K12", "Mn.K12", "Nb.K12", "Rb.K12",
"Sr.K12", "Ti.K12", "Y.K12", "Zn.K12", "Zr.K12"), row.names = c(NA,
10L), class = "data.frame")

Answer 1

I think you would have received a speedier reply if you had focused on your question instead of all the extraneous stuff. You gave us your commands for plotting a bunch of principal components that had nothing to do with your question. The question is, how do you plot ellipses by group? Your sample data at 10 lines and three groups is not helpful because 3 points is not enough to plot data ellipses. You are using the dataEllipse function in package car which has the simplest answer to your question:
First, a reproducible example:
set.seed(42) # so you can get the same numbers I get
source_a <- data.frame(X1=rnorm(25, 50, 5), X2=rnorm(25, 40, 5))
source_b <- data.frame(X1=rnorm(25, 20, 5), X2=rnorm(25, 40, 5))
source_c <- data.frame(X1=rnorm(25, 35, 5), X2=rnorm(25, 25, 5))
lithic_dat <- rbind(source_a, source_b, source_c)
lithic_source <- c(rep("a", 25), rep("b", 25), rep("c", 25))
Plot ellipses with scatterplot() and add text:
scatterplot(X2~X1 | lithic_source, data=lithic_dat, pch="", smooth=FALSE,
reg.line=FALSE, ellipse=TRUE, levels=.9)
text(lithic_dat$X1, lithic_dat$X2, lithic_source, cex=.75)
Scatterplot can be tweaked to do everything you want, but it is also
possible to plot the ellipses without using it:
sources <- unique(lithic_source) # vector of the different sources
plot(lithic_dat$X1, lithic_dat$X1, type="n")
text(lithic_dat$X1, lithic_dat$X2, lithic_source, cex=.75)
for (i in sources) with(lithic_dat, dataEllipse(X1[lithic_source==i],
X2[lithic_source==i], levels=.9, plot.points=FALSE))
This will work for your principal components and any other data.

Answer 2

Here is a simple solution using a package called ggbiplot (available on github) with Iris data. I hope this is what you were looking for.
library(devtools);install_github('vqv/ggbiplot')
library(ggbiplot)
pca = prcomp(iris[,1:4])
ggbiplot(pca,groups = iris$Species,ellipse = T,ellipse.prob = .95)