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Analysis of multivariate skew normal models with incomplete data

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  • Lin, Tsung I.
  • Ho, Hsiu J.
  • Chen, Chiang L.

Abstract

We establish computationally flexible methods and algorithms for the analysis of multivariate skew normal models when missing values occur in the data. To facilitate the computation and simplify the theoretic derivation, two auxiliary permutation matrices are incorporated into the model for the determination of observed and missing components of each observation. Under missing at random mechanisms, we formulate an analytically simple ECM algorithm for calculating parameter estimation and retrieving each missing value with a single-valued imputation. Gibbs sampling is used to perform a Bayesian inference on model parameters and to create multiple imputations for missing values. The proposed methodologies are illustrated through a real data set and comparisons are made with those obtained from fitting the normal counterparts.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:10:p:2337-2351
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    References listed on IDEAS

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    9. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
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    14. M. Teimourian & T. Baghfalaki & M. Ganjali & D. Berridge, 2015. "Joint modeling of mixed skewed continuous and ordinal longitudinal responses: a Bayesian approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(10), pages 2233-2256, October.
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    17. Timothy Opheim & Anuradha Roy, 2021. "Linear models for multivariate repeated measures data with block exchangeable covariance structure," Computational Statistics, Springer, vol. 36(3), pages 1931-1963, September.
    18. 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.
    19. 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.
    20. Liseo, Brunero & Parisi, Antonio, 2013. "Bayesian inference for the multivariate skew-normal model: A population Monte Carlo approach," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 125-138.

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