# Generalized linear model

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

[itex] \mu = \mbox{E}(y) \,[itex]
[itex] g(\mu) = \nu \,[itex]
[itex] \nu = a_0 + a_1 x_1 + \cdots + a_n x_n \, {\rm .}[itex]

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.

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