Estimation of an oblique structure via penalized likelihood factor analysis

Kei Hirose, Michio Yamamoto

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)


The problem of sparse estimation via a lasso-type penalized likelihood procedure in a factor analysis model is considered. Typically, model estimation assumes that the common factors are orthogonal (i.e., uncorrelated). However, if the common factors are correlated, the lasso-type penalization method based on the orthogonal model frequently estimates an erroneous model. To overcome this problem, factor correlations are incorporated into the model. Together with parameters in the orthogonal model, these correlations are estimated by a maximum penalized likelihood procedure. Entire solutions are computed by the EM algorithm with a coordinate descent, enabling the application of a wide variety of convex and nonconvex penalties. The proposed method is applicable even when the number of variables exceeds that of observations. The effectiveness of the proposed strategy is evaluated by Monte Carlo simulations, and its utility is demonstrated through real data analysis.

Original languageEnglish
Pages (from-to)120-132
Number of pages13
JournalComputational Statistics and Data Analysis
Publication statusPublished - Nov 2014
Externally publishedYes


  • Nonconvex penalty
  • Oblique structure
  • Penalized likelihood factor analysis
  • Rotation technique

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics


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