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Bayesian multi-way balanced nested MANOVA models with random effects and a large number of the main factor levels

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  • Chun-Lung Su

    (Tunghai University)

Abstract

This article considers the balanced nested multi-way multivariate analysis of variance (MANOVA) models with random effects and a large number of main factor levels under certain prior assumptions. Two different parametrizations for the MANOVA models with random effects and the corresponding explicit asymptotics are established. The asymptotic approximations are then compared with those obtained from the classical large-sample approximation and Markov chain Monte Carlo method via a balanced nested two-way MANOVA model with random effects. Simulation results demonstrate that our approach is superior to the classical approximation method on estimating the posterior standard deviations of variance component parameters.

Suggested Citation

  • Chun-Lung Su, 2021. "Bayesian multi-way balanced nested MANOVA models with random effects and a large number of the main factor levels," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 663-692, July.
    • Handle: RePEc:spr:metrik:v:84:y:2021:i:5:d:10.1007_s00184-020-00796-w
    DOI: 10.1007/s00184-020-00796-w
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    3. Su, Chun-Lung & Johnson, Wesley O., 2006. "Large-Sample Joint Posterior Approximations When Full Conditionals Are Approximately Normal: Application to Generalized Linear Mixed Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 795-811, June.
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    6. Chun-Lung Su, 2017. "Asymptotic posterior distributions for balanced nested multi-way models with a large number of main effect levels," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(19), pages 9425-9440, October.
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