Sparse factor regression via penalized maximum likelihood estimation

Kei Hirose () and Miyuki Imada
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Kei Hirose: Kyushu University
Miyuki Imada: NTT Network Innovation Laboratories

Statistical Papers, 2018, vol. 59, issue 2, No 10, 633-662

Abstract: Abstract In factor regression model, the maximum likelihood estimation suffers from three disadvantages: (i) the maximum likelihood estimates are unavailable when the number of variables exceeds the number of observations, (ii) the rotation technique based on maximum likelihood estimates produces an insufficiently sparse loading matrix, and (iii) multicollinearity can occur when the estimates of unique variances (specific variances) are small because the regression coefficients are sensitive to the inverse of unique variances. To handle these problems, we propose a penalized maximum likelihood procedure. Specifically, we impose a lasso-type penalty on the factor loadings to improve the sparseness of the solution. We also introduce a penalty on unique variances, which (given the factor scores) corresponds to the ridge penalty on the regression coefficient. Theoretical properties from a prediction viewpoint of our procedure are discussed. The effectiveness of the procedure is investigated through Monte Carlo simulations. The utility of our procedure is demonstrated on real data collected by an online questionnaire.

Keywords: Coordinate descent algorithm; Lasso; Multicollinearity; Penalized maximum likelihood estimation; Rotation technique (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00362-016-0781-8

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