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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, ..., xn, 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.
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