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A flexible class of parametric distributions for Bayesian linear mixed models

Author

Listed:
  • Mohsen Maleki

    (Shiraz University)

  • Darren Wraith

    (Queensland University of Technology (QUT))

  • Reinaldo B. Arellano-Valle

    (Universidad Católica de Chile)

Abstract

In this paper, we consider a linear mixed effect model (LMM) assuming that the random effect and error terms follow an unrestricted skew-normal generalized-hyperbolic (SUNGH) distribution. The SUNGH is a broad class of flexible distributions that includes various other well-known asymmetric and symmetric families and provides a high degree of flexibility for the modeling of complex multivariate data with different directions and degrees of asymmetry, kurtosis and heavy tails. The choice of the best fitting distribution can proceed quite naturally through parameter estimation or by placing constraints on specific parameters and assessing using model choice criteria. We estimate parameters of the LMM using a Bayesian approach and examine the performance of the proposed methodology on simulated and real data from a clinical trial on treatment options for schizophrenia (Lapierre et al. Acta Psychiatric Scandinavica 82:72–76, 1990; Ho and Lin Biom J 52(4):449–469, 2010).

Suggested Citation

  • Mohsen Maleki & Darren Wraith & Reinaldo B. Arellano-Valle, 2019. "A flexible class of parametric distributions for Bayesian linear mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 543-564, June.
    • Handle: RePEc:spr:testjl:v:28:y:2019:i:2:d:10.1007_s11749-018-0590-6
    DOI: 10.1007/s11749-018-0590-6
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    References listed on IDEAS

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    1. Mohsen Maleki & Mohammad Reza Mahmoudi, 2017. "Two-Piece location-scale distributions based on scale mixtures of normal family," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(24), pages 12356-12369, December.
    2. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    3. Wraith, Darren & Forbes, Florence, 2015. "Location and scale mixtures of Gaussians with flexible tail behaviour: Properties, inference and application to multivariate clustering," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 61-73.
    4. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
    5. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    6. Vilca, Filidor & Balakrishnan, N. & Zeller, Camila Borelli, 2014. "Multivariate Skew-Normal Generalized Hyperbolic distribution and its properties," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 73-85.
    7. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    8. Jara, Alejandro & Quintana, Fernando & San Marti­n, Ernesto, 2008. "Linear mixed models with skew-elliptical distributions: A Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 5033-5045, July.
    9. Fruhwirth-Schnatter, Sylvia & Tuchler, Regina & Otter, Thomas, 2004. "Bayesian Analysis of the Heterogeneity Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 2-15, January.
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    Cited by:

    1. Zeinolabedin Najafi & Karim Zare & Mohammad Reza Mahmoudi & Soheil Shokri & Amir Mosavi, 2022. "Inference and Local Influence Assessment in a Multifactor Skew-Normal Linear Mixed Model," Mathematics, MDPI, vol. 10(15), pages 1-21, August.
    2. 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.

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