[Varimax rotated PCA in R] #R

varimax-pca.R

library(tidyverse)
library(FactoMineR)

iris %>%
  select(-Species) %>%
  PCA(graph = FALSE) -> res

# FactoMineR does not return the loadings but the coordinates of the variables
# You can divide the results of PCA by the square root of the eigenvalue of each dimension to recover the loadings

# rotation - method 0
# In ugly base code
t(apply(res$var$coord, 1, function(x) {x/sqrt(res$eig[,1])}))

# wrapped in a function
rotate_varimax <- function(x){
  
  mini <- function(y){
    y / sqrt(x$eig[,1])
  }
  
  x %>%
    .$var %>%
    .$coord %>% # coordinates of variables to create a scatter plot
    apply(1, mini) %>%
    t()
}

res %>% rotate_varimax() # returns loadings?

# return loadings
sweep(res$var$coord, 2, sqrt(res$eig[,1]),'/') 

## method 2
## same result
iris %>%
  select(-Species) %>%
  prcomp(scale = TRUE) %>%
  .$rotation

iris %>%
  select(-Species) %>%
  prcomp(scale = TRUE) -> p

p$x

iris %>%
  select(-Species) %>%
  psych::principal(nfactors = 3, rotate = "varimax")