General linear model: Difference between revisions

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== Comparison to generalized linear model ==
 
The general linear model and the [[Generalized linear model|generalized linear model (GLM)]]<ref name=":0">{{Citation|last1=McCullagh|first1=P.|title=An outline of generalized linear models|date=1989|work=Generalized Linear Models|pages=21–47|publisher=Springer US|isbn=9780412317606|last2=Nelder|first2=J. A.|doi=10.1007/978-1-4899-3242-6_2|doi-broken-date=13 December 2024 }}</ref><ref>Fox, J. (2015). ''Applied regression analysis and generalized linear models''. Sage Publications.</ref> are two commonly used families of [[Statistics|statistical methods]] to relate some number of continuous and/or categorical [[Dependent and independent variables|predictors]] to a single [[Dependent and independent variables|outcome variable]].
 
The main difference between the two approaches is that the general linear model strictly assumes that the [[Errors and residuals|residuals]] will follow a [[Conditional probability distribution|conditionally]] [[normal distribution]],<ref name=":1">Cohen, J., Cohen, P., West, S. G., & [[Leona S. Aiken|Aiken, L. S.]] (2003). Applied multiple regression/correlation analysis for the behavioral sciences.</ref> while the GLM loosens this assumption and allows for a variety of other [[Distribution (mathematics)|distributions]] from the [[exponential family]] for the residuals.<ref name=":0" /> Of note, the general linear model is a special case of the GLM in which the distribution of the residuals follow a conditionally normal distribution.