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)
pp. 65-95.
10.1007/s11336-021-09751-8.
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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.
| Type: | Article |
|---|---|
| Title: | Single- and Multiple-Group Penalized Factor Analysis: A Trust-Region Algorithm Approach with Integrated Automatic Multiple Tuning Parameter Selection |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s11336-021-09751-8 |
| Publisher version: | https://doi.org/10.1007/s11336-021-09751-8 |
| Language: | English |
| Additional information: | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Keywords: | Effective degrees of freedom, generalized information criterion, measurement invariance, penalized likelihood, simple structure |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10126135 |
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