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Mixtures of restricted skew-t factor analyzers with common factor loadings

Author

Listed:
  • Wan-Lun Wang

    (Feng Chia University)

  • Luis M. Castro

    (Pontificia Universidad Católica de Chile)

  • Yen-Ting Chang

    (National Chung Hsing University)

  • Tsung-I Lin

    (National Chung Hsing University
    China Medical University)

Abstract

Mixtures of common t factor analyzers (MCtFA) have been shown its effectiveness in robustifying mixtures of common factor analyzers (MCFA) when handling model-based clustering of the high-dimensional data with heavy tails. However, the MCtFA model may still suffer from a lack of robustness against observations whose distributions are highly asymmetric. This paper presents a further robust extension of the MCFA and MCtFA models, called the mixture of common restricted skew-t factor analyzers (MCrstFA), by assuming a restricted multivariate skew-t distribution for the common factors. The MCrstFA model can be used to accommodate severely non-normal (skewed and leptokurtic) random phenomena while preserving its parsimony in factor-analytic representation and performing graphical visualization in low-dimensional plots. A computationally feasible expectation conditional maximization either algorithm is developed to carry out maximum likelihood estimation. The numbers of factors and mixture components are simultaneously determined based on common likelihood penalized criteria. The usefulness of our proposed model is illustrated with simulated and real datasets, and experimental results signify its superiority over some existing competitors.

Suggested Citation

  • Wan-Lun Wang & Luis M. Castro & Yen-Ting Chang & Tsung-I Lin, 2019. "Mixtures of restricted skew-t factor analyzers with common factor loadings," 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. 13(2), pages 445-480, June.
    • Handle: RePEc:spr:advdac:v:13:y:2019:i:2:d:10.1007_s11634-018-0317-2
    DOI: 10.1007/s11634-018-0317-2
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    References listed on IDEAS

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    Cited by:

    1. Tsung-I Lin & I-An Chen & Wan-Lun Wang, 2023. "A robust factor analysis model based on the canonical fundamental skew-t distribution," Statistical Papers, Springer, vol. 64(2), pages 367-393, April.

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