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Automated learning of factor analysis with complete and incomplete data

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  • Zhao, Jianhua
  • Shi, Lei

Abstract

In the application of the popular maximum likelihood method to factor analysis, the number of factors is commonly determined through a two-stage procedure, in which stage 1 performs parameter estimation for a set of candidate models and then stage 2 chooses the best according to certain model selection criterion. Usually, to obtain satisfactory performance, a large set of candidates is used and this procedure suffers a heavy computational burden. To overcome this problem, a novel one-stage algorithm is proposed in which parameter estimation and model selection are integrated in a single algorithm. This is obtained by maximizing the criterion with respect to model parameters and the number of factors jointly, rather than separately. The proposed algorithm is then extended to accommodate incomplete data. Experiments on a number of complete/incomplete synthetic and real data reveal that the proposed algorithm is as effective as the existing two-stage procedure while being much more computationally efficient, particularly for incomplete data.

Suggested Citation

  • Zhao, Jianhua & Shi, Lei, 2014. "Automated learning of factor analysis with complete and incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 205-218.
    • Handle: RePEc:eee:csdana:v:72:y:2014:i:c:p:205-218
    DOI: 10.1016/j.csda.2013.11.008
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Wang, Wan-Lun & Castro, Luis M. & Lin, Tsung-I, 2017. "Automated learning of t factor analysis models with complete and incomplete data," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 157-171.
    2. Nikolaos Zirogiannis & Yorghos Tripodis, 2018. "Dynamic factor analysis for short panels: estimating performance trajectories for water utilities," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 131-150, March.
    3. Wan-Lun Wang & Tsung-I Lin, 2020. "Automated learning of mixtures of factor analysis models with missing information," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 1098-1124, December.
    4. Wan-Lun Wang & Tsung-I Lin, 2022. "Robust clustering via mixtures of t factor analyzers with incomplete data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(3), pages 659-690, September.
    5. Lorenzo Finesso & Peter Spreij, 2016. "Factor analysis models via I-divergence optimization," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 702-726, September.

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