Generalized linear model: Difference between revisions

Revision as of 06:53, 26 June 2021

Revision as of 07:00, 26 June 2021

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{{Merge from|Testing in binary response index models|discuss=Talk:Generalized linear model#Proposed merge of Testing in binary response index models into Generalized linear model|date=December 2020}}

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In [[statistics]], thea '''generalized linear model''' ('''GLM''') is a flexible generalization of ordinary [[linear regression]] that allows for the [[response variable]]s thatto have an error distribution models other than athe [[normal distribution]]. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a ''link function'' and by allowing the magnitude of the variance of each measurement to be a function of its predicted value.

Generalized linear models were formulated by [[John Nelder]] and [[Robert Wedderburn (statistician)|Robert Wedderburn]] as a way of unifying various other statistical models, including [[linear regression]], [[logistic regression]] and [[Poisson regression]].<ref>{{cite journal | last1= Nelder | first1 = John |author-link = John Nelder | first2 = Robert |last2 = Wedderburn | s2cid = 14154576 |author-link2 = Robert Wedderburn (statistician) | title = Generalized Linear Models | year=1972 | journal = Journal of the Royal Statistical Society. Series A (General) | volume= 135 |issue=3 | pages=370–384 | doi= 10.2307/2344614 | publisher= Blackwell Publishing | jstor= 2344614 }}</ref> They proposed an [[iteratively reweighted least squares]] [[iterative method|method]] for [[maximum likelihood]] estimation of the model parameters. Maximum-likelihood estimation remains popular and is the default method on many statistical computing packages. Other approaches, including [[Bayesian statistics|Bayesian approaches]] and [[least squares]] fits to [[variance-stabilizing transformation|variance stabilized]] responses, have been developed.