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Residual analysis of linear mixed models using a simulation approach

  • Schützenmeister, André
  • Piepho, Hans-Peter
Registered author(s):

    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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    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
    Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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    1. 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.
    2. Huang, Xianzheng, 2011. "Detecting random-effects model misspecification via coarsened data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 703-714, January.
    3. 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.
    4. Shi, Lei & Huang, Mei, 2011. "Stepwise local influence analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 973-982, February.
    5. 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.
    6. Jean-Marie Dufour & Abdeljelil Farhat & Lucien Gardiol & Lynda Khalaf, 1998. "Simulation-based finite sample normality tests in linear regressions," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages C154-C173.
    7. Piepho, Hans-Peter, 1996. "Weighted estimates of interlaboratory consensus values," Computational Statistics & Data Analysis, Elsevier, vol. 22(5), pages 471-479, September.
    8. 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.
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