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A robust factor analysis model based on the canonical fundamental skew-t distribution

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Abstract

The traditional factor analysis rested on the assumption of multivariate normality has been extended by considering the restricted multivariate skew-t (rMST) distribution for the unobserved factors and errors jointly. However, the rMST distribution has limited use for characterising skewness that concentrates in a single direction. This paper is devoted to introducing a more flexible robust factor analysis model based on the broader canonical fundamental skew-t (CFUST) distribution, called the CFUSTFA model. The proposed new model can account for more complex features of skewness toward multiple directions. An efficient alternating expectation conditional maximization algorithm fabricated under several reduced complete-data spaces is developed to estimate parameters under the maximum likelihood (ML) perspective. To assess the variability of parameter estimates, we present an information-based approach to approximating the asymptotic covariance matrix of the ML estimators. The effectiveness and applicability of the proposed techniques are demonstrated through the analysis of simulated and real datasets.

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Acknowledgements

The authors are grateful to the Co-Editors, the Associate Editor and two anonymous referees for their valuable comments and constructive suggestions which had improved the content of this paper greatly. This project was partially supported by the Ministry of Science and Technology of Taiwan under Grant Nos. 109-2118-M-005-005-MY3 and 110-2118-M-006-006-MY3.

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Authors and Affiliations

  1. Department of Statistics and Institute of Data Science, National Cheng Kung University, Tainan, 701, Taiwan

    Wan-Lun Wang

  2. Institute of Statistics, National Chung Hsing University, Taichung, 402, Taiwan

    Tsung-I Lin & I-An Chen

  3. Department of Public Health, China Medical University, Taichung, 404, Taiwan

    Tsung-I Lin

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  1. Tsung-I Lin
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  2. I-An Chen
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  3. Wan-Lun Wang
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Correspondence to Wan-Lun Wang.

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Lin, TI., Chen, IA. & Wang, WL. A robust factor analysis model based on the canonical fundamental skew-t distribution. Stat Papers 64, 367–393 (2023). https://doi.org/10.1007/s00362-022-01318-8

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