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MCMC Sampling for a Multilevel Model With Nonindependent Residuals Within and Between Cluster Units

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  • William Browne
  • Harvey Goldstein

Abstract

In this article, we discuss the effect of removing the independence assumptions between the residuals in two-level random effect models. We first consider removing the independence between the Level 2 residuals and instead assume that the vector of all residuals at the cluster level follows a general multivariate normal distribution. We demonstrate how this assumption can allow us to fit higher levels of clustering and school competition effects via an example from education. We then consider removing the assumption of independence between Level 1 residuals within clusters. We show how this extension can allow time series type models. Both normal and binary responses are considered.

Suggested Citation

  • William Browne & Harvey Goldstein, 2010. "MCMC Sampling for a Multilevel Model With Nonindependent Residuals Within and Between Cluster Units," Journal of Educational and Behavioral Statistics, , vol. 35(4), pages 453-473, August.
    • Handle: RePEc:sae:jedbes:v:35:y:2010:i:4:p:453-473
    DOI: 10.3102/1076998609359788
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    References listed on IDEAS

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    1. Harvey Goldstein & Simon Burgess & Brendon McConnell, 2007. "Modelling the effect of pupil mobility on school differences in educational achievement," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(4), pages 941-954, October.
    2. Julian Besag & Jeremy York & Annie Mollié, 1991. "Bayesian image restoration, with two applications in spatial statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(1), pages 1-20, March.
    3. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    4. Browne, William J., 2006. "MCMC algorithms for constrained variance matrices," Computational Statistics & Data Analysis, Elsevier, vol. 50(7), pages 1655-1677, April.
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    Cited by:

    1. Hongwei Xu & John Logan & Susan Short, 2014. "Integrating Space With Place in Health Research: A Multilevel Spatial Investigation Using Child Mortality in 1880 Newark, New Jersey," Demography, Springer;Population Association of America (PAA), vol. 51(3), pages 811-834, June.
    2. Brandon LeBeau & Yoon Ah Song & Wei Cheng Liu, 2018. "Model Misspecification and Assumption Violations With the Linear Mixed Model: A Meta-Analysis," SAGE Open, , vol. 8(4), pages 21582440188, December.
    3. William J. Browne, 2022. "A celebration of Harvey Goldstein’s lifetime contributions: Memories of working with Harvey Goldstein on multilevel modelling methods and applications," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 753-758, July.
    4. Leonardo Grilli & Carla Rampichini, 2015. "Specification of random effects in multilevel models: a review," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 967-976, May.
    5. Ippel, L. & Kaptein, M.C. & Vermunt, J.K., 2016. "Estimating random-intercept models on data streams," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 169-182.
    6. Patrick Lekgothoane & Molefe Maleka & Zeleke Worku, 2018. "Talent Management Predictors that Adversely Affect Job Satisfaction at a South African Parastatal," Journal of Economics and Behavioral Studies, AMH International, vol. 10(2), pages 199-208.

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