On Estimation of Sparse Factor Loadings using Distribution-free Approach
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Date
2020
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Abstract
Sparse Factor Analysis (SFA) is often used for the analysis of high dimensional data, providing
simpler pattern of factor loadings by constraining insigni cant loadings to be zero. However,
existing SFA approaches require the assumption of normality of data since sparse factor loadings
are obtained through a likelihood function with additional constraint or penalty function.
This work proposes a method for obtaining sparse factor loadings without requiring any
distributional assumption. In this method, the orthogonal sparse eigenvectors were computed
based on Procrustes reformulation, and thereafter, an iterative procedure was provided to
nd sparse factor loadings corresponding to the orthogonal sparse eigenvectors. In the end,
the proposed method was compared with penalized likelihood factor analysis via nonconvex
penalties using simulated data. Results show that sparse factor loadings from both methods
provide simpler structure of factor loadings than the structure obtained from standard Exploratory
Factor Analysis. In addition, the new method out-performs the penalized likelihood factor
analysis via nonconvex penalties as it provides smaller values of MSE even when the two
methods have the same level of sparsity.
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Keywords
Exploratory factor analysis, Factor loadings, Sparsity, Sparse eigenvectors, Regularized maximum likelihood.