ABSTRACT
This chapter focuses on whether a probability distribution can be expressed in one-parameter exponential family form. It analyses the canonical links for distributions of one-parameter exponential family form. Generalized linear models (GLMs) are a broader class of models that generalizes the multiple linear regression. All GLMs have similar forms for their likelihoods, maximum likelihood estimate, and variances. This makes it easier to find model estimates and their corresponding uncertainty. The canonical link is often a good choice to model as a linear function of the explanatory variables. GLM theory suggests that the canonical link can be modeled as a linear combination of the explanatory variables. This approach unifies a number of modeling results used throughout the text. For example, likelihoods can be used to compare models in the same way for any member of the one-parameter exponential family. The chapter explains the three components of a GLM: distribution, link function and linear predictor.
