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Influence diagnostics in mixed effects logistic regression models

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Abstract

Correlated binary responses are commonly described by mixed effects logistic regression models. This article derives a diagnostic methodology based on the Q-displacement function to investigate local influence of the responses in the maximum likelihood estimates of the parameters and in the predictive performance of the mixed effects logistic regression model. An appropriate perturbation strategy of the probability of success is established, as a form of assessing the perturbation in the response. The diagnostic methodology is evaluated with Monte Carlo simulations. Illustrations with two real-world data sets (balanced and unbalanced) are conducted to show the potential of the proposed methodology.

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Acknowledgements

The authors thank the Editors and two referees for their constructive comments on an earlier version of this manuscript which resulted in this improved version. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001, by HPC resources provided by the Information Technology Superintendence of the University of São Paulo, and also by CNPq from Brazil; as well as by the Chilean Council for Scientific and Technology Research (CONICYT) through fellowship “Becas-Chile” (A. Tapia) and FONDECYT 1160868 Grant (V. Leiva) from the Chilean government.

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Authors and Affiliations

  1. Institute of Statistics, Faculty of Economic and Administration Sciences, Universidad Austral de Chile, Valdivia, Chile

    Alejandra Tapia

  2. School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile

    Victor Leiva

  3. School of Nutrition, Faculty of Medical Sciences and INICSA-CONICET, Universidad Nacional de Córdoba, Córdoba, Argentina

    Maria del Pilar Diaz

  4. Institute of Mathematics and Statistics, Universidade de São Paulo, São Paulo, Brazil

    Viviana Giampaoli

Authors
  1. Alejandra Tapia
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  2. Victor Leiva
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  3. Maria del Pilar Diaz
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  4. Viviana Giampaoli
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Corresponding author

Correspondence to Victor Leiva.

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Tapia, A., Leiva, V., Diaz, M.d.P. et al. Influence diagnostics in mixed effects logistic regression models. TEST 28, 920–942 (2019). https://doi.org/10.1007/s11749-018-0613-3

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  • DOI: https://doi.org/10.1007/s11749-018-0613-3

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