Published:
Springer Science and Business Media LLC, 2021
Published in:
Psychometrika, 86 (2021) 1, Seite 65-95
Language:
English
DOI:
10.1007/s11336-021-09751-8
ISSN:
0033-3123;
1860-0980
Origination:
Footnote:
Description:
AbstractPenalized 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 package .