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Model-based clustering of censored data via mixtures of factor analyzers

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  • Wang, Wan-Lun
  • Castro, Luis M.
  • Lachos, Victor H.
  • Lin, Tsung-I

Abstract

Mixtures of factor analyzers (MFA) provide a promising tool for modeling and clustering high-dimensional data that contain an overwhelmingly large number of attributes measured on individuals arisen from a heterogeneous population. Due to the restriction of experimental apparatus, measurements can be limited to some lower and/or upper detection bounds and thus the data are possibly censored. In this paper, we extend the MFA to accommodate censored data, and the new model is called the MFA with censoring (MFAC). A computationally feasible alternating expectation conditional maximization (AECM) algorithm is developed to carry out maximum likelihood estimation of the MFAC model. Practical issues related to model-based clustering and recovery of censored data are also discussed. Simulation studies are conducted to examine the effect of censoring in classification, estimation and cluster validation. We also present an application of the proposed approach to two real data examples in which a certain number of left-censored observations are present.

Suggested Citation

  • Wang, Wan-Lun & Castro, Luis M. & Lachos, Victor H. & Lin, Tsung-I, 2019. "Model-based clustering of censored data via mixtures of factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 140(C), pages 104-121.
    • Handle: RePEc:eee:csdana:v:140:y:2019:i:c:p:104-121
    DOI: 10.1016/j.csda.2019.06.001
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    Citations

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    Cited by:

    1. 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).
    2. 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).
    3. 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.
    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. Christian E. Galarza & Tsung-I Lin & Wan-Lun Wang & Víctor H. Lachos, 2021. "On moments of folded and truncated multivariate Student-t distributions based on recurrence relations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(6), pages 825-850, August.
    6. Wan-Lun Wang & Luis M. Castro & Wan-Chen Hsieh & Tsung-I Lin, 2021. "Mixtures of factor analyzers with covariates for modeling multiply censored dependent variables," Statistical Papers, Springer, vol. 62(5), pages 2119-2145, October.
    7. Wan-Lun Wang & Tsung-I Lin, 2022. "Robust clustering of multiply censored data via mixtures of t factor analyzers," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 22-53, March.
    8. Francisco H. C. Alencar & Christian E. Galarza & Larissa A. Matos & Victor H. Lachos, 2022. "Finite mixture modeling of censored and missing data using the multivariate skew-normal distribution," 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 521-557, September.

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