Identify Loading Vectors under Sparsity in Factor Models

Simplify the loading matrix in factor models using the l1 criterion as proposed in Freyaldenhoven (2025) . Given a data matrix, find the rotation of the loading matrix with the smallest l1-norm and/or test for the presence of local factors with main function local_factors().

Overview

The l1rotation package implements the l1-rotation criterion of Freyaldenhoven (2025) to simplify the loading matrix in factor models.

Installation

# Install from CRAN
install.packages("l1rotation")

# Install latest version from GitHub
install.packages("devtools")
devtools::install_github("SimonFreyaldenhoven/l1rotation")

Usage

Find a minimal example below. For more information see the package website, documentation and vignette.

library(l1rotation)
set.seed(916) 

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

# Rerun with parallel processing
lf_lambdas <- local_factors(X = example_data, r = 2, parallel = TRUE, n_cores = 10)

# Visualize Principal Component estimate of the loadings
lf$pc_plot

# Visualize l1-rotation loadings
lf$rotated_plot

Citation

Simon Freyaldenhoven. “Identification Through Sparsity in Factor Models: the l1-rotation criterion.” Philadelphia Fed Working Paper 20-25, February 2025.

Simon Freyaldenhoven, Ryan Kobler. “l1rotation package.” Code and data repository at https://github.com/SimonFreyaldenhoven/l1rotation, March 2025.