Chapter 7: Generalized Linear Models: Inference
Section 4.10 discussed three types of inferential approaches based on likelihood theory: Wald, score and likelihood ratio. In Chap. 7, these approaches are applied in the context of glms. We first consider inference when ϕ is known (Sect. 7.2), then the large-sample asymptotic results (Sect. 7.3) that underlie all the distributional results for the test statistics in that section. Section 7.4 then introduces goodness-of-fit tests to determine whether the linear predictor sufficiently describes the systematic trends in the data. The distributional results for these goodness-of-fit tests rely on small dispersion asymptotic results (the large sample asymptotics do not apply), which are discussed in Sect. 7.5 where guidelines are presented for when these results hold. We then consider inference when ϕ is unknown (Sect. 7.6), and include a discussion of using the different estimates of ϕ.
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