IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v28y2013i5p2007-2027.html
   My bibliography  Save this article

Semi-parametric Bayesian estimation of mixed-effects models using the multivariate skew-normal distribution

Author

Listed:
  • Reyhaneh Rikhtehgaran
  • Iraj Kazemi

Abstract

In this paper, we develop a semi-parametric Bayesian estimation approach through the Dirichlet process (DP) mixture in fitting linear mixed models. The random-effects distribution is specified by introducing a multivariate skew-normal distribution as base for the Dirichlet process. The proposed approach efficiently deals with modeling issues in a wide range of non-normally distributed random effects. We adopt Gibbs sampling techniques to achieve the parameter estimates. A small simulation study is conducted to show that the proposed DP prior is better at the prediction of random effects. Two real data sets are analyzed and tested by several hypothetical models to illustrate the usefulness of the proposed approach. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:5:p:2007-2027
    DOI: 10.1007/s00180-012-0392-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00180-012-0392-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00180-012-0392-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Verbeke, Geert & Lesaffre, Emmanuel, 1997. "The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 23(4), pages 541-556, February.
    2. Frees,Edward W., 2004. "Longitudinal and Panel Data," Cambridge Books, Cambridge University Press, number 9780521828284, September.
    3. Yisheng Li & Xihong Lin & Peter Müller, 2010. "Bayesian Inference in Semiparametric Mixed Models for Longitudinal Data," Biometrics, The International Biometric Society, vol. 66(1), pages 70-78, March.
    4. Frees,Edward W., 2004. "Longitudinal and Panel Data," Cambridge Books, Cambridge University Press, number 9780521535380, September.
    5. Daowen Zhang & Marie Davidian, 2001. "Linear Mixed Models with Flexible Distributions of Random Effects for Longitudinal Data," Biometrics, The International Biometric Society, vol. 57(3), pages 795-802, September.
    6. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    7. 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.
    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. Wendimagegn Ghidey & Emmanuel Lesaffre & Paul Eilers, 2004. "Smooth Random Effects Distribution in a Linear Mixed Model," Biometrics, The International Biometric Society, vol. 60(4), pages 945-953, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Peng Zhang & Peter X.-K. Song & Annie Qu & Tom Greene, 2008. "Efficient Estimation for Patient-Specific Rates of Disease Progression Using Nonnormal Linear Mixed Models," Biometrics, The International Biometric Society, vol. 64(1), pages 29-38, March.
    4. Ye, Rendao & Wang, Tonghui & Gupta, Arjun K., 2014. "Distribution of matrix quadratic forms under skew-normal settings," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 229-239.
    5. F. Kahrari & C. S. Ferreira & R. B. Arellano-Valle, 2019. "Skew-Normal-Cauchy Linear Mixed Models," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 185-202, December.
    6. 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.
    7. Rendao Ye & Tonghui Wang & Saowanit Sukparungsee & Arjun Gupta, 2015. "Tests in variance components models under skew-normal settings," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(7), pages 885-904, October.
    8. Leonardo Grilli & Carla Rampichini, 2015. "Specification of random effects in multilevel models: a review," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 967-976, May.
    9. 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.
    10. 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.
    11. Bao, Junshu & Hanson, Timothy E., 2016. "A mean-constrained finite mixture of normals model," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 93-99.
    12. Ho, Remus K.W. & Hu, Inchi, 2008. "Flexible modelling of random effects in linear mixed models--A Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1347-1361, January.
    13. Kerstens, Kristiaan & Van de Woestyne, Ignace, 2014. "Comparing Malmquist and Hicks–Moorsteen productivity indices: Exploring the impact of unbalanced vs. balanced panel data," European Journal of Operational Research, Elsevier, vol. 233(3), pages 749-758.
    14. Naima Chrid & Sami Saafi & Mohamed Chakroun, 2021. "Export Upgrading and Economic Growth: a Panel Cointegration and Causality Analysis," Journal of the Knowledge Economy, Springer;Portland International Center for Management of Engineering and Technology (PICMET), vol. 12(2), pages 811-841, June.
    15. Patricio Aroca & Juan Gabriel Brida & Juan Sebastián Pereyra & Serena Volo, 2014. "Tourism statistics: correcting data inadequacy using coarsened exact matching," BEMPS - Bozen Economics & Management Paper Series BEMPS22, Faculty of Economics and Management at the Free University of Bozen.
    16. Fulvia Pennoni & Beata Bal-Domańska, 2022. "NEETs and Youth Unemployment: A Longitudinal Comparison Across European Countries," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 162(2), pages 739-761, July.
    17. Marco Angrisani & Kevin Foster & Marcin Hitczenko, 2015. "The 2013 Survey of Consumer Payment Choice: technical appendix," Research Data Report 15-5, Federal Reserve Bank of Boston.
    18. Fabienne Comte & Adeline Samson, 2012. "Nonparametric estimation of random-effects densities in linear mixed-effects model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 951-975, December.
    19. Rodrigo V. Ventura & Manoela Cabo & Rafael Caixeta & Elton Fernandes & Vicente Aprigliano Fernandes, 2020. "Air Transportation Income and Price Elasticities in Remote Areas: The Case of the Brazilian Amazon Region," Sustainability, MDPI, vol. 12(15), pages 1-18, July.
    20. Lynn, Peter & Bosch, Oriol, 2021. "Methodological lessons from the pilot longitudinal survey on debt advice," ISER Working Paper Series 2021-03, Institute for Social and Economic Research.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:28:y:2013:i:5:p:2007-2027. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.