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A robust factor analysis model using the restricted skew- $$t$$ t distribution

Author

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  • Tsung-I Lin
  • Pal Wu
  • Geoffrey McLachlan
  • Sharon Lee

Abstract

Factor analysis is a classical data-reduction technique that seeks a potentially lower number of unobserved variables that can account for the correlations among the observed variables. This paper presents an extension of the factor analysis model, called the skew- $$t$$ t factor analysis model, constructed by assuming a restricted version of the multivariate skew- $$t$$ t distribution for the latent factors and a symmetric $$t$$ t -distribution for the unobservable errors jointly. The proposed model shows robustness to violations of normality assumptions of the underlying latent factors and provides flexibility in capturing extra skewness as well as heavier tails of the observed data. A computationally feasible expectation conditional maximization algorithm is developed for computing maximum likelihood estimates of model parameters. The usefulness of the proposed methodology is illustrated using both simulated and real data. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • Tsung-I Lin & Pal Wu & Geoffrey McLachlan & Sharon Lee, 2015. "A robust factor analysis model using the restricted skew- $$t$$ t distribution," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 510-531, September.
    • Handle: RePEc:spr:testjl:v:24:y:2015:i:3:p:510-531
    DOI: 10.1007/s11749-014-0422-2
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    Cited by:

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    3. Trang Quynh Nguyen & Elizabeth A. Stuart, 2020. "Propensity Score Analysis With Latent Covariates: Measurement Error Bias Correction Using the Covariate’s Posterior Mean, aka the Inclusive Factor Score," Journal of Educational and Behavioral Statistics, , vol. 45(5), pages 598-636, October.
    4. Hashemi, Farzane & Naderi, Mehrdad & Jamalizadeh, Ahad & Bekker, Andriette, 2021. "A flexible factor analysis based on the class of mean-mixture of normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    5. 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.
    6. 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.
    7. Wan-Lun Wang & Min Liu & Tsung-I Lin, 2017. "Robust skew-t factor analysis models for handling missing data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 649-672, November.
    8. Kim, Hea-Jung, 2018. "Bayesian hierarchical robust factor analysis models for partially observed sample-selection data," Journal of Multivariate Analysis, Elsevier, vol. 164(C), pages 65-82.
    9. Stegeman, Alwin, 2016. "A new method for simultaneous estimation of the factor model parameters, factor scores, and unique parts," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 189-203.
    10. Abbas Mahdavi & Narayanaswamy Balakrishnan & Ahad Jamalizadeh, 2024. "Robust Classification via Finite Mixtures of Matrix Variate Skew- t Distributions," Mathematics, MDPI, vol. 12(20), pages 1-17, October.
    11. Lee, Sharon X. & McLachlan, Geoffrey J., 2021. "On formulations of skew factor models: Skew factors and/or skew errors," Statistics & Probability Letters, Elsevier, vol. 168(C).
    12. Ma, Xuan & Zhao, Jianhua & Wang, Yue & Shang, Changchun & Jiang, Fen, 2023. "Robust factored principal component analysis for matrix-valued outlier accommodation and detection," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).

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