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Residual analysis of linear mixed models using a simulation approach

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  • Schützenmeister, André
  • Piepho, Hans-Peter

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.

Suggested Citation

  • Schützenmeister, André & Piepho, Hans-Peter, 2012. "Residual analysis of linear mixed models using a simulation approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1405-1416.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1405-1416
    DOI: 10.1016/j.csda.2011.11.006
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    References listed on IDEAS

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    Cited by:

    1. Francis K. C. Hui & Samuel Müller & Alan H. Welsh, 2021. "Random Effects Misspecification Can Have Severe Consequences for Random Effects Inference in Linear Mixed Models," International Statistical Review, International Statistical Institute, vol. 89(1), pages 186-206, April.
    2. Emi Tanaka, 2020. "Simple outlier detection for a multi‐environmental field trial," Biometrics, The International Biometric Society, vol. 76(4), pages 1374-1382, December.
    3. 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.
    4. Ahmed Bani-Mustafa & K. M. Matawie & C. F. Finch & Amjad Al-Nasser & Enrico Ciavolino, 2019. "Recursive residuals for linear mixed models," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(3), pages 1263-1274, May.

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