IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v32y2005i7p741-755.html
   My bibliography  Save this article

Bayesian analysis of a linear mixed model with AR(p) errors via MCMC

Author

Listed:
  • M. A. Alkhamisi
  • Ghazi Shukur

Abstract

We develop Bayesian procedures to make inference about parameters of a statistical design with autocorrelated error terms. Modelling treatment effects can be complex in the presence of other factors such as time; for example in longitudinal data. In this paper, Markov chain Monte Carlo methods (MCMC), the Metropolis-Hastings algorithm and Gibbs sampler are used to facilitate the Bayesian analysis of real life data when the error structure can be expressed as an autoregressive model of order p. We illustrate our analysis with real data.

Suggested Citation

  • M. A. Alkhamisi & Ghazi Shukur, 2005. "Bayesian analysis of a linear mixed model with AR(p) errors via MCMC," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 741-755.
    • Handle: RePEc:taf:japsta:v:32:y:2005:i:7:p:741-755
    DOI: 10.1080/02664760500079688
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664760500079688
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664760500079688?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. Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 183-206.
    2. J. C. Lee & C. H. Chang, 2000. "Bayesian Analysis of a Growth Curve Model with a General Autoregressive Covariance Structure," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 703-713, December.
    3. Barnett, Glen & Kohn, Robert & Sheather, Simon, 1996. "Bayesian estimation of an autoregressive model using Markov chain Monte Carlo," Journal of Econometrics, Elsevier, vol. 74(2), pages 237-254, October.
    4. Jack Lee & Kuo-Ching Liu, 2000. "Bayesian analysis of a general growth curve model with predictions using power transformations and AR(1) autoregressive dependence," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(3), pages 321-336.
    5. Yang, R. Y., 1995. "Bayesian Analysis for Random Coefficient Regression Models Using Noninformative Priors," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 283-311, November.
    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. Billio, M. & Monfort, A. & Robert, C. P., 1999. "Bayesian estimation of switching ARMA models," Journal of Econometrics, Elsevier, vol. 93(2), pages 229-255, December.
    2. João Henrique Gonçalves Mazzeu & Esther Ruiz & Helena Veiga, 2018. "Uncertainty And Density Forecasts Of Arma Models: Comparison Of Asymptotic, Bayesian, And Bootstrap Procedures," Journal of Economic Surveys, Wiley Blackwell, vol. 32(2), pages 388-419, April.
    3. Martin R. Young & Peter J. Lenk, 1998. "Hierarchical Bayes Methods for Multifactor Model Estimation and Portfolio Selection," Management Science, INFORMS, vol. 44(11-Part-2), pages 111-124, November.
    4. Goldman Elena & Tsurumi Hiroki, 2005. "Bayesian Analysis of a Doubly Truncated ARMA-GARCH Model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(2), pages 1-38, June.
    5. Myroslav Pidkuyko, 2014. "Dynamics of Consumption and Dividends over the Business Cycle," CERGE-EI Working Papers wp522, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    6. Ippei Fujiwara & Koji Takahashi, 2012. "Asian Financial Linkage: Macro‐Finance Dissonance," Pacific Economic Review, Wiley Blackwell, vol. 17(1), pages 136-159, February.
    7. Kai Yang & Qingqing Zhang & Xinyang Yu & Xiaogang Dong, 2023. "Bayesian inference for a mixture double autoregressive model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(2), pages 188-207, May.
    8. Vasco Cúrdia & Marco Del Negro & Daniel L. Greenwald, 2014. "Rare Shocks, Great Recessions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(7), pages 1031-1052, November.
    9. Barnett, Glen & Kohn, Robert & Sheather, Simon, 1996. "Bayesian estimation of an autoregressive model using Markov chain Monte Carlo," Journal of Econometrics, Elsevier, vol. 74(2), pages 237-254, October.
    10. Tripathi Praveen Kumar & Sen Rijji & Upadhyay S. K., 2021. "A Bayes algorithm for model compatibility and comparison of ARMA(p,q) models," Statistics in Transition New Series, Statistics Poland, vol. 22(2), pages 95-123, June.
    11. McCoy, E. J. & Stephens, D. A., 2004. "Bayesian time series analysis of periodic behaviour and spectral structure," International Journal of Forecasting, Elsevier, vol. 20(4), pages 713-730.
    12. Philippe, Anne, 2006. "Bayesian analysis of autoregressive moving average processes with unknown orders," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1904-1923, December.
    13. Zhang, Bo & Chan, Joshua C.C. & Cross, Jamie L., 2020. "Stochastic volatility models with ARMA innovations: An application to G7 inflation forecasts," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1318-1328.
    14. Deschamps, Philippe J., 2012. "Bayesian estimation of generalized hyperbolic skewed student GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3035-3054.
    15. Yuri A. Dubnov & Alexandr V. Boulytchev, 2023. "Accelerated Maximum Entropy Method for Time Series Models Estimation," Mathematics, MDPI, vol. 11(18), pages 1-15, September.
    16. Chan, Joshua C.C., 2013. "Moving average stochastic volatility models with application to inflation forecast," Journal of Econometrics, Elsevier, vol. 176(2), pages 162-172.
    17. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    18. Martin X. Dunbar & Hani M. Samawi & Robert Vogel & Lili Yu, 2014. "Steady-state Gibbs sampler estimation for lung cancer data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(5), pages 977-988, May.
    19. Ohtsuka, Yoshihiro & Oga, Takashi & Kakamu, Kazuhiko, 2010. "Forecasting electricity demand in Japan: A Bayesian spatial autoregressive ARMA approach," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2721-2735, November.
    20. Tsionas, Mike, 2012. "Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models," MPRA Paper 40966, University Library of Munich, Germany, revised 20 Aug 2012.

    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:taf:japsta:v:32:y:2005:i:7:p:741-755. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.