Generalized linear model

In statistics, a generalized linear model (GLM) 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.

${\displaystyle \mu ={\mbox{E}}(y)\,}$

${\displaystyle g(\mu )=a_{1}x_{1}+\cdots +a_{n}x_{n}}$

where g is an invertible function, called the link function, and the distribution of y is in the 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
• Module 9: Generalized Linear Models