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Chapter 8: Generalized Linear Models: Diagnostics

  • Peter K. Dunn
  • Gordon K. Smyth
Chapter
Part of the Springer Texts in Statistics book series (STS)

Abstract

This chapter introduces some of the necessary tools for detecting violations of the assumptions in a glm, and then discusses possible solutions. The assumptions of the glm are first reviewed (Sect. 8.2), then the three basic types of residuals (Pearson, deviance and quantile) are defined (Sect. 8.3). The leverages are then given in the glm context (Sect. 8.4) leading to the development of standardized residuals (Sect. 8.5). The various diagnostic tools for checking the model assumptions are introduced (Sect. 8.7) followed by techniques for identifying unusual and influential observations (Sect. 8.8). Comments about using each type of residual and the nomenclature of residuals are given in Sect. 8.6. We then discuss techniques to remedy or ameliorate any weaknesses in the models (Sect. 8.9), including the introduction of quasi-likelihood (Sect. 8.10). Finally, collinearity is discussed (Sect. 8.11).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Peter K. Dunn
    • 1
  • Gordon K. Smyth
    • 2
  1. 1.Faculty of Science, Health, Education and EngineeringSchool of Health of Sport Science, University of the Sunshine CoastQueenslandAustralia
  2. 2.Bioinformatics DivisionWalter and Eliza Hall Institute of Medical ResearchParkvilleAustralia

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