Single and multiple-group penalized factor analysis: a trust-region algorithm approach with integrated automatic multiple tuning parameter selection

Geminiani, Elena, Marra, Giampiero and Moustaki, Irini ORCID: 0000-0001-8371-1251 (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. ISSN 0033-3123

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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.

Item Type:	Article
Official URL:	https://www.springer.com/journal/11336
Additional Information:	© 2021 The Authors
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics Q Science > QA Mathematics
Date Deposited:	19 Feb 2021 10:15
Last Modified:	16 Nov 2024 02:48
URI:	http://eprints.lse.ac.uk/id/eprint/108873

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