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

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  • 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
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. 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.
    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.
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