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Residual analysis of linear mixed models using a simulation approach

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  • Schützenmeister, André
  • Piepho, Hans-Peter
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    Abstract

    In the framework of the general linear model, residuals are routinely used to check model assumptions, such as homoscedasticity, normality, and linearity of effects. Residuals can also be employed to detect possible outliers. Various types of residuals may be defined for linear mixed models. It is shown how residual plots can be used to check model assumptions by comparing empirical residual distributions with appropriate null distributions based on a parametric bootstrap approach. This allows constructing simultaneous tolerance bounds, which helps in assessing the normality and homoscedasticity of residuals of linear mixed models, identifying possible outliers and interpreting residual plots. The usefulness of this method is demonstrated by applying it to several previously published datasets.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311004038
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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 56 (2012)
    Issue (Month): 6 ()
    Pages: 1405-1416

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    Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1405-1416

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Studentized residual; Simultaneous tolerance band; Simultaneous tolerance interval; Diagnostic plot; Conditional residual; Empirical size;

    References

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    1. John Haslett & Dominic Dillane, 2004. "Application of 'delete = replace' to deletion diagnostics for variance component estimation in the linear mixed model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 131-143.
    2. Shi, Lei & Huang, Mei, 2011. "Stepwise local influence analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 973-982, February.
    3. DUFOUR, Jean-Marie & FARHAT, Abdeljelil & GARDIOL, Lucien, 1998. "Simulation-Based Finite-Sample Normality Tests in Linear Regressions," Cahiers de recherche 9811, Universite de Montreal, Departement de sciences economiques.
    4. Gumedze, Freedom N. & Welham, Sue J. & Gogel, Beverley J. & Thompson, Robin, 2010. "A variance shift model for detection of outliers in the linear mixed model," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2128-2144, September.
    5. Huang, Xianzheng, 2011. "Detecting random-effects model misspecification via coarsened data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 703-714, January.
    6. Nicholas T. Longford, 2001. "Simulation-based diagnostics in random-coefficient models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(2), pages 259-273.
    7. Shi, Lei & Chen, Gemai, 2012. "Deletion, replacement and mean-shift for diagnostics in linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 202-208, January.
    8. Piepho, Hans-Peter, 1996. "Weighted estimates of interlaboratory consensus values," Computational Statistics & Data Analysis, Elsevier, vol. 22(5), pages 471-479, September.
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    Cited by:
    1. Ma, Jinxing & Wang, Zhiwei & Zhu, Chaowei & Xu, Yinlun & Wu, Zhichao, 2014. "Electrogenesis reduces the combustion efficiency of sewage sludge," Applied Energy, Elsevier, vol. 114(C), pages 283-289.

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