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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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    2. 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.
    3. 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.
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    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. 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.
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    8. Juliana Scudilio & Gustavo H. A. Pereira, 2020. "Adjusted quantile residual for generalized linear models," Computational Statistics, Springer, vol. 35(1), pages 399-421, March.
    9. 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.
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    11. 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.
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    13. 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.
    14. 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.
    15. M. Revan Özkale & Stanley Lemeshow & Rodney Sturdivant, 2018. "Logistic regression diagnostics in ridge regression," Computational Statistics, Springer, vol. 33(2), pages 563-593, June.
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    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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