Manually rotate two PCs around the origin — pca_rotate

It is sometimes convenient to rotate principal components to most closely align with a sensible interpretation in terms of the original variables or to compare the results of PCA applied to two distinct datasets. This function allows for manual 2D rotations of principal components.

Usage

pca_rotate_2d(pca_obj, angle, pcs = c(1, 2))

Arguments

pca_obj: The result of a call to prcomp() or princomp(). NB It does not make sense to apply this function to the output of pca_test.
angle: A number indicating the number of degrees to rotate around the origin clockwise. Negative values will rotated counterclockwise.
pcs: A two-element vector identifying the two PCs to rotate.

Value

An object matching the class of pca_obj with loadings, scores, and variance explained by each component modified.

Details

NB: rotated components are not principal components. They no longer explain maximal variance. Rotated components should not be referred to as 'principal components'. The simplest approach is just to call them 'components' after describing the rotation. This function modifies objects of the class 'prcomp' and 'princomp', adding an additional 'note' which collects all the rotations which have been applied. This allows any plotting function which works with the outputs of prcomp() or princomp() to work. This may result in plots which incorrectly identify rotated components as principal components. Be careful not to include any such plot in a research output.

Examples

  pca_obj <- prcomp(onze_intercepts |> dplyr::select(-speaker), scale=TRUE)

  # Rotate PCs 3 and 6 by 10 degrees.
  rotated_pca <- pca_rotate_2d(pca_obj, 10, pcs = c(3,6))