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

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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; Alma Mater Studiorum - Universitá di Bologna within the CRUI-CARE Agreement (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2021-03-26
New Economics Papers: this item is included in nep-cmp, nep-ecm and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Psychometrika, 26, March, 2021, 86(1), pp. 65 - 95. ISSN: 0033-3123

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:108873

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