Andrews Loadings: Project FPCA Eigenfunctions to Original Variables

Given FPCA results on Andrews-transformed data, projects each eigenfunction back onto the Fourier basis to obtain loadings in the original variable space. This reveals which variables contribute most to each principal component.

Usage

andrews_loadings(fpca, fd_andrews, ncomp = NULL)

Arguments

fpca

Result from fdata2pc() (class "fdata2pc").

fd_andrews

The fdata object returned by andrews_transform() (must carry the "andrews_basis" attribute).

ncomp

Number of principal components to project (default: all available in fpca).

Value

A data.frame of class "andrews_loadings" with columns:

Variable

Original variable name.

Loading

Inner-product loading value.

PC

Principal component label ("PC1", "PC2", ...).

See also

andrews_transform(), fdata2pc()

Examples

X <- scale(iris[, 1:4])
fd <- andrews_transform(X)
fpca <- fdata2pc(fd, ncomp = 3)
loadings <- andrews_loadings(fpca, fd)
head(loadings)
#>       Variable     Loading  PC
#> 1 Sepal.Length -0.16355095 PC1
#> 2  Sepal.Width  0.08487338 PC1
#> 3 Petal.Length -0.18343483 PC1
#> 4  Petal.Width -0.17786725 PC1
#> 5 Sepal.Length  0.11957088 PC2
#> 6  Sepal.Width  0.29061451 PC2