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Bayesian Inference for Skew-normal Linear Mixed Models

Author

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  • R.B. Arellano-Valle
  • H. Bolfarine
  • V.H. Lachos

Abstract

Linear mixed models (LMM) are frequently used to analyze repeated measures data, because they are more flexible to modelling the correlation within-subject, often present in this type of data. The most popular LMM for continuous responses assumes that both the random effects and the within-subjects errors are normally distributed, which can be an unrealistic assumption, obscuring important features of the variations present within and among the units (or groups). This work presents skew-normal liner mixed models (SNLMM) that relax the normality assumption by using a multivariate skew-normal distribution, which includes the normal ones as a special case and provides robust estimation in mixed models. The MCMC scheme is derived and the results of a simulation study are provided demonstrating that standard information criteria may be used to detect departures from normality. The procedures are illustrated using a real data set from a cholesterol study.

Suggested Citation

  • R.B. Arellano-Valle & H. Bolfarine & V.H. Lachos, 2007. "Bayesian Inference for Skew-normal Linear Mixed Models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(6), pages 663-682.
    • Handle: RePEc:taf:japsta:v:34:y:2007:i:6:p:663-682
    DOI: 10.1080/02664760701236905
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    Cited by:

    1. Azzalini, Adelchi, 2022. "An overview on the progeny of the skew-normal family— A personal perspective," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. Huang Yangxin & Chen Jiaqing & Yan Chunning, 2012. "Mixed-Effects Joint Models with Skew-Normal Distribution for HIV Dynamic Response with Missing and Mismeasured Time-Varying Covariate," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-30, November.
    3. Mastrantonio, Gianluca, 2018. "The joint projected normal and skew-normal: A distribution for poly-cylindrical data," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 14-26.
    4. A. Ghalamfarsa Mostofi & M. Kharrati-Kopaei, 2012. "Bayesian nonparametric inference for unimodal skew-symmetric distributions," Statistical Papers, Springer, vol. 53(4), pages 821-832, November.
    5. Huang, Pei & McCarl, Bruce A., 2014. "Estimating Decadal Climate Variability Effects on Crop Yields: A Bayesian Hierarchical Approach," 2014 Annual Meeting, July 27-29, 2014, Minneapolis, Minnesota 169828, Agricultural and Applied Economics Association.
    6. Yangxin Huang & Xiaosun Lu & Jiaqing Chen & Juan Liang & Miriam Zangmeister, 2018. "Joint model-based clustering of nonlinear longitudinal trajectories and associated time-to-event data analysis, linked by latent class membership: with application to AIDS clinical studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(4), pages 699-718, October.
    7. Yangxin Huang & X. Hu & Getachew Dagne, 2014. "Jointly modeling time-to-event and longitudinal data: a Bayesian approach," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(1), pages 95-121, March.
    8. Melkamu Molla Ferede & Samuel Mwalili & Getachew Dagne & Simon Karanja & Workagegnehu Hailu & Mahmoud El-Morshedy & Afrah Al-Bossly, 2022. "A Semiparametric Bayesian Joint Modelling of Skewed Longitudinal and Competing Risks Failure Time Data: With Application to Chronic Kidney Disease," Mathematics, MDPI, vol. 10(24), pages 1-21, December.
    9. Tzy-Chy Lin & Tsung-I Lin, 2010. "Supervised learning of multivariate skew normal mixture models with missing information," Computational Statistics, Springer, vol. 25(2), pages 183-201, June.
    10. Kassahun Abere Ayalew & Samuel Manda & Bo Cai, 2021. "A Comparison of Bayesian Spatial Models for HIV Mapping in South Africa," IJERPH, MDPI, vol. 18(21), pages 1-10, October.
    11. 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.
    12. 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.
    13. Chénangnon Frédéric Tovissodé & Aliou Diop & Romain Glèlè Kakaï, 2021. "Inference in skew generalized t-link models for clustered binary outcome via a parameter-expanded EM algorithm," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-31, April.
    14. 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.
    15. Murray, Paula M. & Browne, Ryan P. & McNicholas, Paul D., 2017. "Hidden truncation hyperbolic distributions, finite mixtures thereof, and their application for clustering," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 141-156.
    16. Yangxin Huang & Getachew Dagne, 2012. "Bayesian Semiparametric Nonlinear Mixed-Effects Joint Models for Data with Skewness, Missing Responses, and Measurement Errors in Covariates," Biometrics, The International Biometric Society, vol. 68(3), pages 943-953, September.
    17. 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.
    18. 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.
    19. Yuanyuan Ju & Yan Yang & Mingxing Hu & Lin Dai & Liucang Wu, 2022. "Bayesian Influence Analysis of the Skew-Normal Spatial Autoregression Models," Mathematics, MDPI, vol. 10(8), pages 1-19, April.
    20. Hossein Boojari & Majid Khaledi & Firoozeh Rivaz, 2016. "A non-homogeneous skew-Gaussian Bayesian spatial model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(1), pages 55-73, March.
    21. Chihmao Hsieh & Sérgio Giovanetti Lazzarini & Jackson A. Nickerson & Marcio Laurini, 2010. "Does Ownership Affect the Variability of the Production Process? Evidence from International Courier Services," Organization Science, INFORMS, vol. 21(4), pages 892-912, August.
    22. Tu, Wangshu & Browne, Ryan & Subedi, Sanjeena, 2024. "A mixture of logistic skew-normal multinomial models," Computational Statistics & Data Analysis, Elsevier, vol. 196(C).
    23. Oludare Samuel Ariyo & Matthew Adekunle Adeleke, 2022. "Simultaneous Bayesian modelling of skew-normal longitudinal measurements with non-ignorable dropout," Computational Statistics, Springer, vol. 37(1), pages 303-325, March.

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