R/penfa-package.R
penfa-package.RdThe penfa package (a short form for PENalized Factor Analysis) provides
several routines for single- and multiple-group penalized factor analysis for
continuous data. The models are estimated via a trust-region algorithm with
integrated automatic multiple tuning parameter selection. The available
penalties include lasso, adaptive lasso, scad, mcp, and ridge.
The main function of the package is penfa. To learn more about
it, start with the vignettes and tutorials at browseVignettes(package = "penfa") and
https://egeminiani.github.io/penfa/articles/.
Penalized factor analysis allows to produce parsimonious models using largely an automated procedure. In the single-group case, a typical penalty function will automatically shrink a subset of the factor loadings to zero. The use of sparsity-inducing penalty functions leads to optimally sparse factor structures supported by the data. The resulting models are less prone to instability in the estimation process and are easier to interpret and generalize than their unpenalized counterparts.
In the multiple-group scenario, penalized factor analysis can be used to automatically ascertain differences and similarities of parameter estimates across groups. Typical penalties will automatically encourage sparse loading matrices and invariant factor loadings and intercepts.
In penfa, estimation is achieved via a penalized likelihood-based
framework that builds upon differentiable approximations of
non-differentiable penalties, a theoretically founded definition of degrees
of freedom, and an algorithm with integrated automatic multiple tuning
parameter selection. The estimation is based on a trust-region algorithm
approach exploiting second-order analytical derivative information. The
standard errors for the model parameters are derived using a Bayesian
approach.
The selection of the tuning parameters is a crucial issue in penalized
estimation strategies, as the tuning parameters are responsible for the
optimal balance between goodness of fit and sparsity. In penfa, the
optimal values of the tuning parameters can be determined through the
automatic procedure or grid-searches.
In addition to the fitting function penfa, the package provides
several methods for examining the parameter estimates, monitoring
the optimization process, and inspecting the structures of the penalty
matrices through interactive visualizations.
Geminiani, E., Marra, G., & Moustaki, I. (2021). "Single- and Multiple-Group Penalized Factor Analysis: A Trust-Region Algorithm Approach with Integrated Automatic Multiple Tuning Parameter Selection." Psychometrika, 86(1), 65-95. doi: 10.1007/s11336-021-09751-8
Geminiani E. (2020), "A penalized likelihood-based framework for single and multiple-group factor analysis models" (Doctoral dissertation, University of Bologna). Available at http://amsdottorato.unibo.it/9355/.
Authors: Elena Geminiani, Giampiero Marra, Irini Moustaki
Maintainer: Elena Geminiani. Please address any query or comment to geminianielena@gmail.com.