local_factors: Check whether local factors are present and find the rotation...

In l1rotation: Identify Loading Vectors under Sparsity in Factor Models

Check whether local factors are present and find the rotation of the loading matrix with the smallest l1-norm.

Description

local_factors tests whether local factors are present and returns both the Principal Component estimate of the loadings and the rotation of the loadings with the smallest l1-norm. It also produces graphical illustrations of the results.

Usage

local_factors(X, r, parallel = FALSE, n_cores = NULL)

Arguments

X	A (usually standardized) t by n matrix of observations.
r	An integer denoting the number of factors in X.
parallel	A logical denoting whether the algorithm should be run in parallel.
n_cores	An integer denoting how many cores should be used, if parallel == TRUE.

Value

Returns a list with the following components:

• has_local_factors A logical equal to TRUE if local factors are present.

• initial_loadings Principal component estimate of the loading matrix.

• rotated_loadings Matrix that is the rotation of the loading matrix that produces the smallest l1-norm.

• rotation_diagnostics A list containing 3 components:

  • R Rotation matrix that when used to rotate initial_loadings produces the smallest l1-norm.

  • l1_norm Vector of length r containing the value of the l1 norm each solution generates.

  • sol_frequency Vector of length r containing the frequency in the initial grid of each solution.

• pc_plot Tile plot of the Principal Component estimate of the loading matrix.

• rotated_plot Tile plot of the l1-rotation of the loading matrix estimate.

• small_loadings_plot Plot of the number of small loadings for each column of the l1-rotation of the loading matrix estimate.

Examples

# Minimal example with 2 factors, where X is a 224 by 207 matrix
lf <- local_factors(X = example_data, r = 2)

# Visualize Principal Component estimate of the loadings
lf$pc_plot

# Visualize l1-rotation loadings
lf$pc_rotated_plot

l1rotation documentation built on June 8, 2025, 12:47 p.m.