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Automated learning of mixtures of factor analysis models with missing information

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  • Wan-Lun Wang

    (Feng Chia University)

  • Tsung-I Lin

    (National Chung Hsing University
    China Medical University)

Abstract

The mixture of factor analyzers (MFA) model has emerged as a useful tool to perform dimensionality reduction and model-based clustering for heterogeneous data. In seeking the most appropriate number of factors (q) of a MFA model with the number of components (g) fixed a priori, a two-stage procedure is commonly implemented by firstly carrying out parameter estimation over a set of prespecified numbers of factors, and then selecting the best q according to certain penalized likelihood criteria. When the dimensionality of data grows higher, such a procedure can be computationally prohibitive. To overcome this obstacle, we develop an automated learning scheme, called the automated MFA (AMFA) algorithm, to effectively merge parameter estimation and selection of q into a one-stage algorithm. The proposed AMFA procedure that allows for much lower computational cost is also extended to accommodate missing values. Moreover, we explicitly derive the score vector and the empirical information matrix for calculating standard errors associated with the estimated parameters. The potential and applicability of the proposed method are demonstrated through a number of real datasets with genuine and synthetic missing values.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:29:y:2020:i:4:d:10.1007_s11749-020-00702-6
    DOI: 10.1007/s11749-020-00702-6
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    References listed on IDEAS

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    Cited by:

    1. Wan-Lun Wang & Tsung-I Lin, 2023. "Model-based clustering via mixtures of unrestricted skew normal factor analyzers with complete and incomplete data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 787-817, September.
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