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Mixtures of factor analyzers with covariates for modeling multiply censored dependent variables

Author

Listed:
  • Wan-Lun Wang

    (Feng Chia University)

  • Luis M. Castro

    (Pontificia Universidad Católica de Chile
    Millennium Nucleus Center for the Discovery of Structures in Complex Data
    Pontificia Universidad Católica de Chile)

  • Wan-Chen Hsieh

    (National Chung Hsing University)

  • Tsung-I Lin

    (National Chung Hsing University
    China Medical University)

Abstract

Censored data arise frequently in diverse applications in which observations to be measured may be subject to some upper and lower detection limits due to the restriction of experimental apparatus such that they are not exactly quantifiable. Mixtures of factor analyzers with censored data (MFAC) have been recently proposed for model-based density estimation and clustering of high-dimensional data in the presence of censored observations. In this paper, we consider an extended version of MFAC by considering regression equations to describe the relationship between covariates and multiply censored dependent variables. Two analytically feasible EM-type algorithms are developed for computing maximum likelihood estimates of model parameters with closed-form expressions. Moreover, we provide an information-based method to compute asymptotic standard errors of mixing proportions and regression coefficients. The utility and performance of our proposed methodology are illustrated through a simulation study and two real data examples.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:5:d:10.1007_s00362-020-01177-1
    DOI: 10.1007/s00362-020-01177-1
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    References listed on IDEAS

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    1. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard, 2003. "Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 561-575, January.
    2. Antonio Punzo & Paul. D. McNicholas, 2017. "Robust Clustering in Regression Analysis via the Contaminated Gaussian Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 34(2), pages 249-293, July.
    3. Vaida, Florin & Fitzgerald, Anthony P. & DeGruttola, Victor, 2007. "Efficient hybrid EM for linear and nonlinear mixed effects models with censored response," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5718-5730, August.
    4. Xiao‐Li Meng & David Van Dyk, 1997. "The EM Algorithm—an Old Folk‐song Sung to a Fast New Tune," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(3), pages 511-567.
    5. 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.
    6. Karlis, Dimitris & Xekalaki, Evdokia, 2003. "Choosing initial values for the EM algorithm for finite mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 577-590, January.
    7. Cosslett, Stephen R. & Lee, Lung-Fei, 1985. "Serial correlation in latent discrete variable models," Journal of Econometrics, Elsevier, vol. 27(1), pages 79-97, January.
    8. Utkarsh J. Dang & Antonio Punzo & Paul D. McNicholas & Salvatore Ingrassia & Ryan P. Browne, 2017. "Multivariate Response and Parsimony for Gaussian Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 34(1), pages 4-34, April.
    9. Maria Karlsson & Thomas Laitila, 2014. "Finite mixture modeling of censored regression models," Statistical Papers, Springer, vol. 55(3), pages 627-642, August.
    10. Melnykov, Volodymyr & Melnykov, Igor, 2012. "Initializing the EM algorithm in Gaussian mixture models with an unknown number of components," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1381-1395.
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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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