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Cook’s distance for generalized linear mixed models

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  • Pinho, Luis Gustavo B.
  • Nobre, Juvêncio S.
  • Singer, Julio M.

Abstract

We consider an extension of Cook’s distance for generalized linear mixed models with the objective of identifying observations with high influence in the predicted conditional means of the response variable. The proposed distance can be decomposed into factors that help to distinguish between influence on the estimation of fixed effects and on the prediction of random effects. Joint and conditional influence are also considered. A first-order approximation is proposed for more efficient computation and a Monte Carlo simulation is considered to evaluate the efficacy of the proposal. An application to a dataset obtained from the literature is presented to show how such tools can be used in practice.

Suggested Citation

  • Pinho, Luis Gustavo B. & Nobre, Juvêncio S. & Singer, Julio M., 2015. "Cook’s distance for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 126-136.
    • Handle: RePEc:eee:csdana:v:82:y:2015:i:c:p:126-136
    DOI: 10.1016/j.csda.2014.08.008
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    References listed on IDEAS

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    1. 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.
    2. de Jong,Piet & Heller,Gillian Z., 2008. "Generalized Linear Models for Insurance Data," Cambridge Books, Cambridge University Press, number 9780521879149, September.
    3. Liming Xiang & Andy Lee & Siu-Keung Tse, 2003. "Assessing local cluster influence in generalized linear mixed models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(4), pages 349-359.
    4. Juvêncio S. Nobre & Julio M. Singer, 2011. "Leverage analysis for linear mixed models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 1063-1072, February.
    5. Eric J. Tchetgen & Brent A. Coull, 2006. "A diagnostic test for the mixing distribution in a generalised linear mixed model," Biometrika, Biometrika Trust, vol. 93(4), pages 1003-1010, December.
    6. Xiang, Liming & Tse, Siu-Keung & Lee, Andy H., 2002. "Influence diagnostics for generalized linear mixed models: applications to clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 40(4), pages 759-774, October.
    7. Stasinopoulos, D. Mikis & Rigby, Robert A., 2007. "Generalized Additive Models for Location Scale and Shape (GAMLSS) in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i07).
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    Cited by:

    1. Annalivia Polselli, 2023. "Influence Analysis with Panel Data," Papers 2312.05700, arXiv.org.

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