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Application of ‘delete = replace’ to deletion diagnostics for variance component estimation in the linear mixed model

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  • John Haslett
  • Dominic Dillane

Abstract

Summary. ‘Delete = replace’ is a powerful and intuitive modelling identity. This paper extends previous work by stating and proving the identity in more general terms and extending its application to deletion diagnostics for estimates of variance components obtained by restricted maximum likelihood estimation for the linear mixed model. We present a new, fast, transparent and approximate computational procedure, arising as a by‐product of the fitting process. We illustrate the effect of the deletion of individual observations, of ‘subjects’ and of arbitrary subsets. Central to the identity and its application is the conditional residual.

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  • 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, February.
    • Handle: RePEc:bla:jorssb:v:66:y:2004:i:1:p:131-143
    DOI: 10.1046/j.1369-7412.2003.05211.x
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    Cited by:

    1. Shi, Lei & Chen, Gemai, 2008. "Case deletion diagnostics in multilevel models," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1860-1877, October.
    2. 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.
    3. Li, Zaixing & Xu, Wangli & Zhu, Lixing, 2009. "Influence diagnostics and outlier tests for varying coefficient mixed models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2002-2017, October.
    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. Xu, Liang & Lee, Sik-Yum & Poon, Wai-Yin, 2006. "Deletion measures for generalized linear mixed effects models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1131-1146, November.
    6. Shi, Lei & Lu, Jun & Zhao, Jianhua & Chen, Gemai, 2016. "Case deletion diagnostics for GMM estimation," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 176-191.
    7. 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.
    8. Víctor Leiva & Shuangzhe Liu & Lei Shi & Francisco José A. Cysneiros, 2016. "Diagnostics in elliptical regression models with stochastic restrictions applied to econometrics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(4), pages 627-642, March.
    9. Chengcheng Hao & Dietrich Rosen & Tatjana Rosen, 2014. "Local Influence Analysis in AB–BA Crossover Designs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1153-1166, December.

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