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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 (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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Identification Number: 10.1007/s11336-021-09751-8

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: 20 Jul 2021 03:02
URI: http://eprints.lse.ac.uk/id/eprint/108873

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