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Sparse Exploratory Factor Analysis

Trendafilov, Nickolay T.; Fontanella, Sara and Adachi, Kohei (2017). Sparse Exploratory Factor Analysis. Psychometrika, 82(3) pp. 778–794.

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Sparse principal component analysis is a very active research area in the last decade. It produces component loadings with many zero entries which facilitates their interpretation and helps avoid redundant variables. The classic factor analysis is another popular dimension reduction technique which shares similar interpretation problems and could greatly benefit from sparse solutions. Unfortunately, there are very few works considering sparse versions of the classic factor analysis. Our goal is to contribute further in this direction. We revisit the most popular procedures for exploratory factor analysis, maximum likelihood and least squares. Sparse factor loadings are obtained for them by, first, adopting a special reparameterization and, second, by introducing additional [Formula: see text]-norm penalties into the standard factor analysis problems. As a result, we propose sparse versions of the major factor analysis procedures. We illustrate the developed algorithms on well-known psychometric problems. Our sparse solutions are critically compared to ones obtained by other existing methods.

Item Type: Journal Item
Copyright Holders: 2017 The Psychometric Society
ISSN: 1860-0980
Keywords: eigenvalue reparameterization; optimization on matrix manifolds; penalties inducing sparseness
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 51865
SWORD Depositor: Jisc Publications-Router
Depositing User: Jisc Publications-Router
Date Deposited: 01 Mar 2018 14:27
Last Modified: 02 May 2019 17:40
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