General linear model: Difference between revisions

Revision as of 10:24, 9 November 2020

Revision as of 22:27, 21 November 2020

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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.

The distribution of the residuals largely depends on the type and distribution of the outcome variable; different types of outcome variables lead to the variety of models within the GLiM family. Commonly used models in the GLiM family include [[Logistic regression|binary logistic regression]]<ref>Hosmer Jr, D. W., Lemeshow, S., & Sturdivant, R. X. (2013). ''Applied logistic regression'' (Vol. 398). John Wiley & Sons.</ref> for binary or dichotomous outcomes, [[Poisson regression]]<ref>{{cite journal |last1=Gardner, |first1=W., |last2=Mulvey, |first2=E. P., & |last3=Shaw, |first3=E. C. (1995). |title=Regression analyses of counts and rates: Poisson, overdispersed Poisson, and negative binomial models. ''|journal=Psychological bulletin'',Bulletin ''|date=1995 |volume=118''( |issue=3), 392|pages=392–404 |doi=10.1037/0033-2909.118.3.392}}</ref> for count outcomes, and [[linear regression]] for continuous, normally distributed outcomes. This means that GLiM may be spoken of as a general family of statistical models or as specific models for specific outcome types.

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