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Bayesian Analysis for Random Coefficient Regression Models Using Noninformative Priors

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  • Yang, R. Y.

Abstract

We apply Bayesian approach, through noninformative priors, to analyze a Random Coefficient Regression (RCR) model. The Fisher information matrix, the Jeffreys prior and reference priors are derived for this model. Then, we prove that the corresponding posteriors are proper when the number of full rank design matrices are greater than or equal to twice the number of regression coefficient parameters plus 1 and that the posterior means for all parameters exist if one more additional full rank design matrix is available. A hybrid Markov chain sampling scheme is developed for computing the Bayesian estimators for parameters of interest. A small-scale simulation study is conducted for comparing the performance of different noninformative priors. A real data example is also provided and the data are analyzed by a non-Bayesian method as well as Bayesian methods with noninformative priors.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:55:y:1995:i:2:p:283-311
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    Cited by:

    1. Pedro Delicado & Juan Romo, 1999. "Goodness of Fit Tests in Random Coefficient Regression Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(1), pages 125-148, March.
    2. Natarajan, Ranjini, 2001. "On the propriety of a modified Jeffreys's prior for variance components in binary random effects models," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 409-414, February.
    3. Gwowen Shieh & Jack Lee, 2002. "Bayesian Prediction Analysis for Growth Curve Model Using Noninformative Priors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(2), pages 324-337, June.
    4. 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.
    5. Russell D. Wolfinger & Robert E. Kass, 2000. "Nonconjugate Bayesian Analysis of Variance Component Models," Biometrics, The International Biometric Society, vol. 56(3), pages 768-774, September.
    6. Clemens Elster & Gerd Wübbeler, 2017. "Bayesian inference using a noninformative prior for linear Gaussian random coefficient regression with inhomogeneous within-class variances," Computational Statistics, Springer, vol. 32(1), pages 51-69, March.

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