General linear model: Difference between revisions

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== Comparison to generalized linear model ==

The general linear model (GLM)<ref>Neter, J., Kutner, M. H., Nachtsheim, C. J., & Wasserman, W. (1996). ''Applied linear statistical models'' (Vol. 4, p. 318). Chicago: Irwin.</ref><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> and the [[Generalized linear model|generalized linear model (GLiM)]]<ref name=":0">{{Citation|last=McCullagh|first=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}}</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 GLM strictly assumes that the [[Errors and residuals|residuals]] will follow a [[Conditional probability distribution|conditionally]] [[normal distribution]],<ref name=":1" /> while the GLiM 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 GLM is a special case of the GLiM in which the distribution of the residuals follow a conditionally normal distribution.