Abstract
Chapters 5–8 develop the theory of glms in general. This chapter focuses on one specific glm: the binomial glm. The binomial glm is the most commonly used of all glms. It is used to model proportions, where the proportions are obtained as the number of ‘positive’ cases out of a total number of independent cases. We first compile important information about the binomial distribution (Sect. 9.2), then discuss the common link functions used for binomial glms (Sect. 9.3), and the threshold interpretation of the link function (Sect. 9.4). We then discuss model interpretation in terms of odds (Sect. 9.5), and how binomial glms can be used to estimate the median effective dose ed50 (Sect. 9.6).
We believe no statistical model is ever final; it is simply a placeholder until a better model is found.
Singer and Willett [22, p. 105]
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Dunn, P.K., Smyth, G.K. (2018). Chapter 9: Models for Proportions: Binomial GLMs. 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_9
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