Link function - Definition and Overview

In statistics, a generalized linear model is a model relating the expected value E(y) of a dependent variable y to one or more independent variables x₁, ..., x_n, with the relation stated as follows.

<math> \mu = \mbox{E}(y) \,<math>

<math> g(\mu) = a_1 x_1 + \cdots + a_n x_n <math>

where g is an invertible function, called the link function. Each specific choice of the link function and the distribution for the dependent variable yields a different generalized linear model.

Generalized linear models include, as special cases, ordinary linear regression, logistic regression, Poisson regression, and several other interesting models.

References

• P. McCullagh and J.A. Nelder. Generalized Linear Models. London: Chapman and Hall, 1989.

External links

• Module 9: Generalized Linear Models (http://genetics.agrsci.dk/biometry/courses/statmaster/course/module09)