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Finite mixture modeling of censored and missing data using the multivariate skew-normal distribution

Author

Listed:
  • Francisco H. C. Alencar

    (Universidade Estadual de Campinas)

  • Christian E. Galarza

    (Escuela Superior Politécnica del Litoral, ESPOL)

  • Larissa A. Matos

    (Universidade Estadual de Campinas)

  • Victor H. Lachos

    (University of Connecticut)

Abstract

Finite mixture models have been widely used to model and analyze data from a heterogeneous populations. Moreover, data of this kind can be missing or subject to some upper and/or lower detection limits because of the constraints of experimental apparatuses. Another complication arises when measures of each population depart significantly from normality, such as asymmetric behavior. For such data structures, we propose a robust model for censored and/or missing data based on finite mixtures of multivariate skew-normal distributions. This approach allows us to model data with great flexibility, accommodating multimodality and skewness, simultaneously, depending on the structure of the mixture components. We develop an analytically simple, yet efficient, EM-type algorithm for conducting maximum likelihood estimation of the parameters. The algorithm has closed-form expressions at the E-step that rely on formulas for the mean and variance of the truncated multivariate skew-normal distributions. Furthermore, a general information-based method for approximating the asymptotic covariance matrix of the estimators is also presented. Results obtained from the analysis of both simulated and real datasets are reported to demonstrate the effectiveness of the proposed method. The proposed algorithm and method are implemented in the new R package CensMFM.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:advdac:v:16:y:2022:i:3:d:10.1007_s11634-021-00448-5
    DOI: 10.1007/s11634-021-00448-5
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    References listed on IDEAS

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    1. 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.
    2. Reinaldo B. Arellano-Valle & Marc G. Genton, 2010. "Multivariate extended skew-t distributions and related families," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 201-234.
    3. Prates, Marcos Oliveira & Lachos, Victor Hugo & Barbosa Cabral, Celso Rômulo, 2013. "mixsmsn: Fitting Finite Mixture of Scale Mixture of Skew-Normal Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 54(i12).
    4. Cabral, Celso Rômulo Barbosa & Lachos, Víctor Hugo & Prates, Marcos O., 2012. "Multivariate mixture modeling using skew-normal independent distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 126-142, January.
    5. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    6. 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.
    7. Lin, Tsung I. & Ho, Hsiu J. & Chen, Chiang L., 2009. "Analysis of multivariate skew normal models with incomplete data," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2337-2351, November.
    8. Victor H. Lachos & Dipankar Bandyopadhyay & Dipak K. Dey, 2011. "Linear and Nonlinear Mixed-Effects Models for Censored HIV Viral Loads Using Normal/Independent Distributions," Biometrics, The International Biometric Society, vol. 67(4), pages 1594-1604, December.
    9. Lachos, Víctor H. & Moreno, Edgar J. López & Chen, Kun & Cabral, Celso Rômulo Barbosa, 2017. "Finite mixture modeling of censored data using the multivariate Student-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 151-167.
    10. Steven Caudill, 2012. "A partially adaptive estimator for the censored regression model based on a mixture of normal distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(2), pages 121-137, June.
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    13. Basso, Rodrigo M. & Lachos, Víctor H. & Cabral, Celso Rômulo Barbosa & Ghosh, Pulak, 2010. "Robust mixture modeling based on scale mixtures of skew-normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2926-2941, December.
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    1. Valeriano, Katherine A.L. & Galarza, Christian E. & Matos, Larissa A. & Lachos, Victor H., 2023. "Likelihood-based inference for the multivariate skew-t regression with censored or missing responses," Journal of Multivariate Analysis, Elsevier, vol. 196(C).

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