Chapter 9: Models for Proportions: Binomial GLMs

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


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).


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© 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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