Statistics and Its Interface

Volume 3 (2010)

Number 4

A penalized maximum likelihood approach to sparse factor analysis

Pages: 429 – 436

DOI: http://dx.doi.org/10.4310/SII.2010.v3.n4.a1

Authors

Jang Choi (School of Statistics, University of Minnesota, Minneapolis, Minn., U.S.A.)

Gary Oehlert (School of Statistics, University of Minnesota, Minneapolis, Minn., U.S.A.)

Hui Zou (School of Statistics, University of Minnesota, Minneapolis, Minn., U.S.A.)

Abstract

Factor analysis is a popular multivariate analysis method which is used to describe observed variables as linear combinations of hidden factors. In applications one usually needs to rotate the estimated factor loading matrix in order to obtain a more understandable model. In this article, an $\ell_1$ penalization method is introduced for performing sparse factor analysis in which factor loadings naturally adopt a sparse representation, greatly facilitating the interpretation of the fitted factor model. A generalized expectation–maximization algorithm is developed for computing the $\ell_1$ penalized estimator. Efficacy of the proposed methodology and algorithm is demonstrated by simulated and real data.

Keywords

adaptive lasso, EM algorithm, factor analysis, lasso, sparse factor loadings

2010 Mathematics Subject Classification

Primary 62H25. Secondary 62J07.

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