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).
Since all models are wrong the scientist must be alert to what is importantly wrong. It is inappropriate to be concerned about mice when there are tigers abroad.
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Dunn, P.K., Smyth, G.K. (2018). Chapter 8: Generalized Linear Models: Diagnostics. In: Generalized Linear Models With Examples in R. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0118-7_8
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