In arleyc/PCAtest: Statistical significance of PCA

knitr::opts_chunk$set(echo = TRUE)

PCA of uncorrelated variables is not significant

library(testthat)
library(PCAtest)

data("ex0")
PCAout<-PCAtest(ex0, 100, 100, 0.05, indload=F, varcorr=FALSE, counter=F, plot=F)
test_that("PCA of uncorrelated variables is not significant",{
    expect_gt(max(PCAout$`Null Psi`),PCAout$`Empirical Psi`)
    expect_gt(max(PCAout$`Null Phi`),PCAout$`Empirical Phi`)
  })

PCA of two fully-correlated variables has only PC1 significant

v1<-seq(0,1,0.01)
v2<-seq(0,1,0.01)
x<-cbind(v1,v2)
PCAout<-PCAtest(x, 100, 100, 0.05, indload=F, varcorr=FALSE, counter=F, plot=F)
test_that("PCA of two fully-correlated variables has Psi=2, Phi=1,
  and only PC1 is significant",{
  expect_equal(PCAout$`Empirical Psi`,2.0000)
  expect_equal(PCAout$`Empirical Phi`,1.0000)
  expect_equal(PCAout$`Percentage of variation of empirical PC's`[1],100)
})