sparseGFM - Sparse Generalized Factor Models with Multiple Penalty Functions
Implements sparse generalized factor models (sparseGFM)
for dimension reduction and variable selection in
high-dimensional data with automatic adaptation to weak factor
scenarios. The package supports multiple data types
(continuous, count, binary) through generalized linear model
frameworks and handles missing values automatically. It
provides 12 different penalty functions including Least
Absolute Shrinkage and Selection Operator (Lasso), adaptive
Lasso, Smoothly Clipped Absolute Deviation (SCAD), Minimax
Concave Penalty (MCP), group Lasso, and their adaptive versions
for inducing row-wise sparsity in factor loadings. Key features
include cross-validation for regularization parameter selection
using Sparsity Information Criterion (SIC), automatic
determination of the number of factors via multiple information
criteria, and specialized algorithms for row-sparse loading
structures. The methodology employs alternating minimization
with Singular Value Decomposition (SVD)-based identifiability
constraints and is particularly effective for high-dimensional
applications in genomics, economics, and social sciences where
interpretable sparse dimension reduction is crucial. For
penalty functions, see Tibshirani (1996)
<doi:10.1111/j.2517-6161.1996.tb02080.x>, Fan and Li (2001)
<doi:10.1198/016214501753382273>, and Zhang (2010)
<doi:10.1214/09-AOS729>.
