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>.
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