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Generalized Linear Model Diagnostics Using the Deviance and Single Case Deletions

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  • D. A. Williams

Abstract

This paper exploits the one step approximation, derived by Pregibon (1981), for the changes in the deviance of a generalized linear model when a single case is deleted from the data. This approximation suggests a particular set of residuals which can be used, not only to identify outliers and examine distributional assumptions, but also to calculate measures of the influence of single cases on various inferences that can be drawn from the fitted model using likelihood ratio statistics.

Suggested Citation

  • D. A. Williams, 1987. "Generalized Linear Model Diagnostics Using the Deviance and Single Case Deletions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(2), pages 181-191, June.
    • Handle: RePEc:bla:jorssc:v:36:y:1987:i:2:p:181-191
    DOI: 10.2307/2347550
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    Cited by:

    1. Cordeiro, Gauss M. & Simas, Alexandre B., 2009. "The distribution of Pearson residuals in generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3397-3411, July.
    2. Rubén Moreno-Opo & Mariana Fernández-Olalla & Antoni Margalida & Ángel Arredondo & Francisco Guil, 2012. "Effect of Methodological and Ecological Approaches on Heterogeneity of Nest-Site Selection of a Long-Lived Vulture," PLOS ONE, Public Library of Science, vol. 7(3), pages 1-9, March.
    3. Xie, Xian-Jin & Pendergast, Jane & Clarke, William, 2008. "Increasing the power: A practical approach to goodness-of-fit test for logistic regression models with continuous predictors," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2703-2713, January.
    4. Nyangoma, S.O. & Fung, W.-K. & Jansen, R.C., 2006. "Identifying influential multinomial observations by perturbation," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2799-2821, June.
    5. Parra Álvarez, Juan Carlos & Misas A., Martha & López-Enciso, Enrique Antonio, 2011. "Heterogeneidad en la fijación de precios en Colombia : análisis de sus determinantes a partir de modelos de conteo," Chapters, in: López Enciso, Enrique & Ramírez Giraldo, María Teresa (ed.), Formación de precios y salarios en Colombia T.1, volume 1, chapter 8, pages 251-293, Banco de la Republica de Colombia.
    6. Saemi Choi & Jae Gon Lee & A-reum Lee & Chang Soo Eun & Dong Soo Han & Chan Hyuk Park, 2019. "Helicobacter pylori antibody and pepsinogen testing for predicting gastric microbiome abundance," PLOS ONE, Public Library of Science, vol. 14(12), pages 1-14, December.
    7. José Osvaldo De Sordi & Marco Antonio Conejero & Manuel Meireles, 2016. "Bibliometric indicators in the context of regional repositories: proposing the D-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 107(1), pages 235-258, April.
    8. 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.
    9. Preisser, John S. & Garcia, Daniel I., 2005. "Alternative computational formulae for generalized linear model diagnostics: identifying influential observations with SAS software," Computational Statistics & Data Analysis, Elsevier, vol. 48(4), pages 755-764, April.
    10. Shiyu Wang & Houping Xiao & Allan Cohen, 2021. "Adaptive Weight Estimation of Latent Ability: Application to Computerized Adaptive Testing With Response Revision," Journal of Educational and Behavioral Statistics, , vol. 46(5), pages 560-591, October.
    11. Juliana Scudilio & Gustavo H. A. Pereira, 2020. "Adjusted quantile residual for generalized linear models," Computational Statistics, Springer, vol. 35(1), pages 399-421, March.
    12. Johan Koskinen & Peng Wang & Garry Robins & Philippa Pattison, 2018. "Outliers and Influential Observations in Exponential Random Graph Models," Psychometrika, Springer;The Psychometric Society, vol. 83(4), pages 809-830, December.
    13. Munoz-Garcia, J. & Munoz-Pichardo, J.M. & Pardo, L., 2006. "Cressie and Read power-divergences as influence measures for logistic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3199-3221, July.
    14. M. Revan Özkale & Stanley Lemeshow & Rodney Sturdivant, 2018. "Logistic regression diagnostics in ridge regression," Computational Statistics, Springer, vol. 33(2), pages 563-593, June.
    15. Monfort, Abel & Villagra, Nuria & Sánchez, Joaquín, 2021. "Economic impact of corporate foundations: An event analysis approach," Journal of Business Research, Elsevier, vol. 122(C), pages 159-170.
    16. Boehm, Martin, 2008. "Determining the impact of internet channel use on a customer's lifetime," Journal of Interactive Marketing, Elsevier, vol. 22(3), pages 2-22.
    17. Colin Cameron, A. & Windmeijer, Frank A. G., 1997. "An R-squared measure of goodness of fit for some common nonlinear regression models," Journal of Econometrics, Elsevier, vol. 77(2), pages 329-342, April.

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