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Generalized Linear Model


A generalized linear model relates the expectation value mu of a response variable to a linear predictor x^Tbeta through a specified link function g,

 g(mu)=x^Tbeta.

The conditional distribution of the response is chosen from an exponential family. The link function and response distribution are parts of the model and determine how changes in the predictors affect the mean response.

Ordinary linear regression with normal distribution errors and the identity link is one example. For responses with a binomial distribution, the logit function and the probit function are common choices of link. Responses with a Poisson distribution commonly use the logarithmic link. A generalized linear model is distinct from a general linear model, which is a linear model for a continuous response vector.


See also

Exponential Family, General Linear Model, Linear Regression

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References

McCullagh, P. and Nelder, J. A. Generalized Linear Models, 2nd ed. London, England: Chapman and Hall, 1989.

Cite this as:

Weisstein, Eric W. "Generalized Linear Model." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GeneralizedLinearModel.html

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