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Linear mixed models with skew-elliptical distributions: A Bayesian approach

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  • Jara, Alejandro
  • Quintana, Fernando
  • San Marti­n, Ernesto

Abstract

Normality of random effects and error terms is a routine assumption for linear mixed models. However, such an assumption may be unrealistic, obscuring important features of within- and among-unit variation. A simple and robust Bayesian parametric approach that relaxes this assumption by using a multivariate skew-elliptical distribution, which includes the Skew-t, Skew-normal, t-Student, and Normal distributions as special cases and provides flexibility in capturing a broad range of non-normal and asymmetric behavior is presented. An appropriate posterior simulation scheme is developed and the methods are illustrated with an application to a longitudinal data example.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:11:p:5033-5045
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    5. Hanze Zhang & Yangxin Huang, 2020. "Quantile regression-based Bayesian joint modeling analysis of longitudinal–survival data, with application to an AIDS cohort study," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(2), pages 339-368, April.
    6. Julio M. Singer & Francisco M.M. Rocha & Juvêncio S. Nobre, 2017. "Graphical Tools for Detecting Departures from Linear Mixed Model Assumptions and Some Remedial Measures," International Statistical Review, International Statistical Institute, vol. 85(2), pages 290-324, August.
    7. Pereira, Luz Adriana & Gutiérrez, Luis & Taylor-Rodríguez, Daniel & Mena, Ramsés H., 2023. "Bayesian nonparametric hypothesis testing for longitudinal data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    8. Tao Lu, 2017. "Bayesian inference on longitudinal-survival data with multiple features," Computational Statistics, Springer, vol. 32(3), pages 845-866, September.
    9. Cancho, Vicente G. & Dey, Dipak K. & Lachos, Victor H. & Andrade, Marinho G., 2011. "Bayesian nonlinear regression models with scale mixtures of skew-normal distributions: Estimation and case influence diagnostics," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 588-602, January.
    10. 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.
    11. Marjan Mansourian & Anoshirvan Kazemnejad & Iraj Kazemi & Farid Zayeri & Masoud Soheilian, 2012. "Bayesian analysis of longitudinal ordered data with flexible random effects using McMC: application to diabetic macular Edema data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1087-1100, November.
    12. Reyhaneh Rikhtehgaran & Iraj Kazemi, 2013. "Semi-parametric Bayesian estimation of mixed-effects models using the multivariate skew-normal distribution," Computational Statistics, Springer, vol. 28(5), pages 2007-2027, October.
    13. Xin-Yuan Song & Zhao-Hua Lu & Jing-Heng Cai & Edward Ip, 2013. "A Bayesian Modeling Approach for Generalized Semiparametric Structural Equation Models," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 624-647, October.
    14. Gallardo, Diego I. & Bolfarine, Heleno & Pedroso-de-Lima, Antonio Carlos, 2016. "Destructive weighted Poisson cure rate models with bivariate random effects: Classical and Bayesian approaches," Computational Statistics & Data Analysis, Elsevier, vol. 98(C), pages 31-45.
    15. Chunzheng Cao & Yahui Wang & Jian Qing Shi & Jinguan Lin, 2018. "Measurement Error Models for Replicated Data Under Asymmetric Heavy-Tailed Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 531-553, August.
    16. Mohammadi, Raziyeh & Kazemi, Iraj, 2022. "A robust linear mixed-effects model for longitudinal data using an innovative multivariate skew-Huber distribution," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    17. Yangxin Huang & Tao Lu, 2017. "Bayesian inference on partially linear mixed-effects joint models for longitudinal data with multiple features," Computational Statistics, Springer, vol. 32(1), pages 179-196, March.
    18. Wang, Wan-Lun, 2013. "Mixtures of common factor analyzers for high-dimensional data with missing information," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 120-133.

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