Table of Contents
1. Model
- The outcome (random component) follows a particular class of probability distribution called exponential family.
- The covariates are combined linearly to form systematic component.
- A link function relates the outcome and the systematic component.
1.1. Exponential Family
\begin{equation*}
p_{\theta}(y) = h(y) \exp[\eta(\theta) T(y) - A(\theta)]
\end{equation*}
1.2. Link Function
The natural parameter can be selected and the function that maps the original parameter to the natural parameter is called the link function.
The link function that is commonly used is called the canonical link function.