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.
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