PCA and Hotelling's T^2 for confidence intervall in R

Question

I made a principal component analysis and took the 2 first principal components. I made a chart of my points based on the score of the 2 PC. I would like to add on this grap

Answer 1

The pcaMethods package has a function simpleEllipse(x, y, alpha, len) that will do this. Given two uncorrelated data vectors it will return an ellipse, where the axes are scaled based on the variance of each score, and the F statistic.

Answer 2

We can plot the confidence ellipse for PCA with vegan or ggbiplot as below:

set.seed(1)
data <- matrix(rnorm(500), ncol=5) # some random data
data <- setNames(as.data.frame(rbind(data, matrix(runif(25, 5, 10), ncol=5))), LETTERS[1:5]) # add some outliers
class <- sample(c(0,3,6,8), 105, replace=TRUE) # 4 groups

library(vegan)
PC <- rda(data, scale=TRUE)
pca_scores <- scores(PC, choices=c(1,2))
plot(pca_scores$sites[,1], pca_scores$sites[,2],
     pch=class, col=class, xlim=c(-2,2), ylim=c(-2,2))
arrows(0,0,pca_scores$species[,1],pca_scores$species[,2],lwd=1,length=0.2)
ordiellipse(PC,class,conf=0.95)

library(ggbiplot)
PC <- prcomp(data, scale = TRUE)
ggbiplot(PC, obs.scale = 1, var.scale = 1, groups = as.factor(class), ellipse = TRUE, 
                                                    ellipse.prob = 0.95)