Chapter 6: Generalized Linear Models: Estimation

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


The previous chapter defined glms and studied the components of a glm. This chapter discusses the estimation of the unknown parameters in the glm: the regression parameters and possibly the dispersion parameter ϕ. Because glms assume a specific probability distribution for the responses from the edm family, maximum likelihood estimation procedures are used for parameter estimation, and general formulae are developed for the glm context. We first derive the score equations and information for the glm context, which are used to form algorithms for estimating the regression parameters for glms. The residual deviance is then defined as a measure of the residual variability across n observations after fitting the model. The standard errors of the regression parameters are developed and matrix formulations are used to estimate the regression parameters. We then explore the important connection between the algorithms for fitting linear regression models and glms. Techniques are then developed for estimating ϕ We conclude with a discussion of using r to fit glms.


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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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