IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v34y2019i3d10.1007_s00180-018-0854-3.html
   My bibliography  Save this article

Robust Bayesian seemingly unrelated regression model

Author

Listed:
  • Chamberlain Mbah

    (Ghent University)

  • Kris Peremans

    (KU Leuven)

  • Stefan Van Aelst

    (KU Leuven)

  • Dries F. Benoit

    (Ghent University)

Abstract

A robust Bayesian model for seemingly unrelated regression is proposed. By using heavy-tailed distributions for the likelihood, robustness in the response variable is attained. In addition, this robust procedure is combined with a diagnostic approach to identify observations that are far from the bulk of the data in the multivariate space spanned by all variables. The most distant observations are downweighted to reduce the effect of leverage points. The resulting robust Bayesian model can be interpreted as a heteroscedastic seemingly unrelated regression model. Robust Bayesian estimates are obtained by a Markov Chain Monte Carlo approach. Complications by using a heavy-tailed error distribution are resolved efficiently by representing these distributions as a scale mixture of normal distributions. Monte Carlo simulation experiments confirm that the proposed model outperforms its traditional Bayesian counterpart when the data are contaminated in the response and/or the input variables. The method is demonstrated on a real dataset.

Suggested Citation

  • Chamberlain Mbah & Kris Peremans & Stefan Van Aelst & Dries F. Benoit, 2019. "Robust Bayesian seemingly unrelated regression model," Computational Statistics, Springer, vol. 34(3), pages 1135-1157, September.
  • Handle: RePEc:spr:compst:v:34:y:2019:i:3:d:10.1007_s00180-018-0854-3
    DOI: 10.1007/s00180-018-0854-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-018-0854-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s00180-018-0854-3?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. James Berger & Elías Moreno & Luis Pericchi & M. Bayarri & José Bernardo & Juan Cano & Julián Horra & Jacinto Martín & David Ríos-Insúa & Bruno Betrò & A. Dasgupta & Paul Gustafson & Larry Wasserman &, 1994. "An overview of robust Bayesian analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 3(1), pages 5-124, June.
    2. Choi, Hee Min & Hobert, James P., 2013. "Analysis of MCMC algorithms for Bayesian linear regression with Laplace errors," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 32-40.
    3. Peremans, Kris & Van Aelst, Stefan, 2018. "Robust inference for seemingly unrelated regression models," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 212-224.
    4. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, October.
    5. Chib, Siddhartha & Greenberg, Edward, 1995. "Hierarchical analysis of SUR models with extensions to correlated serial errors and time-varying parameter models," Journal of Econometrics, Elsevier, vol. 68(2), pages 339-360, August.
    6. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 19-40, Suppl. De.
    7. Zellner, Arnold & Ando, Tomohiro, 2010. "A direct Monte Carlo approach for Bayesian analysis of the seemingly unrelated regression model," Journal of Econometrics, Elsevier, vol. 159(1), pages 33-45, November.
    8. Ng, Vee Ming, 2002. "Robust Bayesian Inference for Seemingly Unrelated Regressions with Elliptical Errors," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 409-414, November.
    9. Monica Billio & Roberto Casarin & Luca Rossini, 2016. "Bayesian nonparametric sparse seemingly unrelated regression model (SUR)," Working Papers 2016:20, Department of Economics, University of Venice "Ca' Foscari".
    10. Olcay Arslan, 2010. "An alternative multivariate skew Laplace distribution: properties and estimation," Statistical Papers, Springer, vol. 51(4), pages 865-887, 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. Zellner, Arnold & Ando, Tomohiro, 2010. "Bayesian and non-Bayesian analysis of the seemingly unrelated regression model with Student-t errors, and its application for forecasting," International Journal of Forecasting, Elsevier, vol. 26(2), pages 413-434, April.
    2. Wang, Hao, 2010. "Sparse seemingly unrelated regression modelling: Applications in finance and econometrics," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2866-2877, November.
    3. Zellner, Arnold & Ando, Tomohiro, 2010. "A direct Monte Carlo approach for Bayesian analysis of the seemingly unrelated regression model," Journal of Econometrics, Elsevier, vol. 159(1), pages 33-45, November.
    4. Dimitrios P. Louzis, 2019. "Steady‐state modeling and macroeconomic forecasting quality," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(2), pages 285-314, March.
    5. Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(3), pages 409-431, August.
    6. Bresson Georges & Chaturvedi Anoop & Rahman Mohammad Arshad & Shalabh, 2021. "Seemingly unrelated regression with measurement error: estimation via Markov Chain Monte Carlo and mean field variational Bayes approximation," The International Journal of Biostatistics, De Gruyter, vol. 17(1), pages 75-97, May.
    7. Donovan, Stuart & de Graaff, Thomas & Grimes, Arthur & de Groot, Henri L.F. & Maré, David C., 2022. "Cities with forking paths? Agglomeration economies in New Zealand 1976–2018," Regional Science and Urban Economics, Elsevier, vol. 95(C).
    8. Kakamu, Kazuhiko & Polasek, Wolfgang & Wago, Hajime, 2008. "Spatial interaction of crime incidents in Japan," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(2), pages 276-282.
    9. Chiara Landi & Gianluca Stefani & Benedetto Rocchi & Ginevra Virginia Lombardi & Sabina Giampaolo, 2016. "Regional Differentiation and Farm Exit: A Hierarchical Model for Tuscany," Journal of Agricultural Economics, Wiley Blackwell, vol. 67(1), pages 208-230, February.
    10. Shun Matsuura & Hiroshi Kurata, 2020. "Covariance matrix estimation in a seemingly unrelated regression model under Stein’s loss," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 79-99, March.
    11. Shun Matsuura & Hiroshi Kurata, 2022. "Optimal estimator under risk matrix in a seemingly unrelated regression model and its generalized least squares expression," Statistical Papers, Springer, vol. 63(1), pages 123-141, February.
    12. Zhifeng Gao & Ted C. Schroeder, 2009. "Consumer responses to new food quality information: are some consumers more sensitive than others?," Agricultural Economics, International Association of Agricultural Economists, vol. 40(3), pages 339-346, May.
    13. Cheng, Leilei & Yin, Changbin & Chien, Hsiaoping, 2015. "Demand for milk quantity and safety in urban China: evidence from Beijing and Harbin," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 59(2), April.
    14. Wen, Chieh-Hua & Huang, Chia-Jung & Fu, Chiang, 2020. "Incorporating continuous representation of preferences for flight departure times into stated itinerary choice modeling," Transport Policy, Elsevier, vol. 98(C), pages 10-20.
    15. Johannes Buggle & Thierry Mayer & Seyhun Orcan Sakalli & Mathias Thoenig, 2023. "The Refugee’s Dilemma: Evidence from Jewish Migration out of Nazi Germany," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 138(2), pages 1273-1345.
    16. Hansen, Lars Peter, 2013. "Uncertainty Outside and Inside Economic Models," Nobel Prize in Economics documents 2013-7, Nobel Prize Committee.
    17. Christelis, Dimitris & Dobrescu, Loretti I. & Motta, Alberto, 2020. "Early life conditions and financial risk-taking in older age," The Journal of the Economics of Ageing, Elsevier, vol. 17(C).
    18. García, Irene & Huo, Stella & Prado, Raquel & Bravo, Lelys, 2020. "Dynamic Bayesian temporal modeling and forecasting of short-term wind measurements," Renewable Energy, Elsevier, vol. 161(C), pages 55-64.
    19. Ortega, David L. & Wang, H. Holly & Wu, Laping & Hong, Soo Jeong, 2015. "Retail channel and consumer demand for food quality in China," China Economic Review, Elsevier, vol. 36(C), pages 359-366.
    20. Tina Birgitte Hansen & Jes Sanddal Lindholt & Axel Diederichsen & Rikke Søgaard, 2019. "Do Non-participants at Screening have a Different Threshold for an Acceptable Benefit–Harm Ratio than Participants? Results of a Discrete Choice Experiment," The Patient: Patient-Centered Outcomes Research, Springer;International Academy of Health Preference Research, vol. 12(5), pages 491-501, October.

    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:34:y:2019:i:3:d:10.1007_s00180-018-0854-3. 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.