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A non-iterative sampling Bayesian method for linear mixed models with normal independent distributions

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  • Victor H. Lachos
  • Celso R.B. Cabral
  • Carlos A. Abanto-Valle

Abstract

In this paper, we utilize normal/independent (NI) distributions as a tool for robust modeling of linear mixed models (LMM) under a Bayesian paradigm. The purpose is to develop a non-iterative sampling method to obtain i.i.d. samples approximately from the observed posterior distribution by combining the inverse Bayes formulae, sampling/importance resampling and posterior mode estimates from the expectation maximization algorithm to LMMs with NI distributions, as suggested by Tan et al . [33]. The proposed algorithm provides a novel alternative to perfect sampling and eliminates the convergence problems of Markov chain Monte Carlo methods. In order to examine the robust aspects of the NI class, against outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback--Leibler divergence. Further, some discussions on model selection criteria are given. The new methodologies are exemplified through a real data set, illustrating the usefulness of the proposed methodology.

Suggested Citation

  • Victor H. Lachos & Celso R.B. Cabral & Carlos A. Abanto-Valle, 2012. "A non-iterative sampling Bayesian method for linear mixed models with normal independent distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(3), pages 531-549, July.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:3:p:531-549
    DOI: 10.1080/02664763.2011.603292
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    References listed on IDEAS

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    1. Russo, Cibele M. & Paula, Gilberto A. & Aoki, Reiko, 2009. "Influence diagnostics in nonlinear mixed-effects elliptical models," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4143-4156, October.
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    5. Osorio, Felipe & Paula, Gilberto A. & Galea, Manuel, 2007. "Assessment of local influence in elliptical linear models with longitudinal structure," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4354-4368, May.
    6. Thaís C. O. Fonseca & Marco A. R. Ferreira & Helio S. Migon, 2008. "Objective Bayesian analysis for the Student-t regression model," Biometrika, Biometrika Trust, vol. 95(2), pages 325-333.
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    Cited by:

    1. Lin, Tsung-I & Wang, Wan-Lun, 2024. "On moments of truncated multivariate normal/independent distributions," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    2. Fengkai Yang & Haijing Yuan, 2017. "A Non-iterative Bayesian Sampling Algorithm for Linear Regression Models with Scale Mixtures of Normal Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 49(4), pages 579-597, April.

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