Generalized linear model

In statistics, a generalized linear model (GLM) is a model relating a response variable y to one or more covariates x₁, ..., x_n by the following relation

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

<math> g(\mu) = \nu \,<math>

<math> \nu = a_0 + a_1 x_1 + \cdots + a_n x_n \, {\rm .}<math>

where g is an invertible function, called the link function, and y has some determined variance. It is often assumed that the distribution of y is a member of an exponential family. 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

• MSc Generalised Linear Models (http://www.personal.rdg.ac.uk/~snscolet/MScGLMs/)
• Module 9: Generalized Linear Models (http://genetics.agrsci.dk/biometry/courses/statmaster/course/module09)