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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