General linear model: Difference between revisions

Revision as of 02:17, 9 June 2019

Revision as of 21:41, 17 June 2019

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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|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 [[dichotomy|dichotomous]] outcomes, [[Poisson regression]]<ref>Gardner, W., Mulvey, E. P., & Shaw, E. C. (1995). Regression analyses of counts and rates: Poisson, overdispersed Poisson, and negative binomial models. ''Psychological bulletin'', ''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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