Single- and Multiple-Group Penalized Factor Analysis: A Trust-Region Algorithm Approach with Integrated Automatic Multiple Tuning Parameter Selection

Elena Geminiani (), Giampiero Marra and Irini Moustaki
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Elena Geminiani: University of Bologna
Giampiero Marra: University College London
Irini Moustaki: London School of Economics and Political Science

Psychometrika, 2021, vol. 86, issue 1, No 3, 65-95

Abstract: Abstract Penalized factor analysis is an efficient technique that produces a factor loading matrix with many zero elements thanks to the introduction of sparsity-inducing penalties within the estimation process. However, sparse solutions and stable model selection procedures are only possible if the employed penalty is non-differentiable, which poses certain theoretical and computational challenges. This article proposes a general penalized likelihood-based estimation approach for single- and multiple-group factor analysis models. The framework 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 that exploits second-order analytical derivative information. The proposed approach is evaluated in two simulation studies and illustrated using a real data set. All the necessary routines are integrated into the R package penfa.

Keywords: effective degrees of freedom; generalized information criterion; measurement invariance; penalized likelihood; simple structure (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11336-021-09751-8

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