Editing Generalized linear model (section)

=== Correlated or clustered data ===
The standard GLM assumes that the observations are [[uncorrelated]]. Extensions have been developed to allow for [[correlation]] between observations, as occurs for example in [[longitudinal studies]] and clustered designs:
* '''[[Generalized estimating equation]]s''' (GEEs) allow for the correlation between observations without the use of an explicit probability model for the origin of the correlations, so there is no explicit [[likelihood]]. They are suitable when the [[random effects]] and their variances are not of inherent interest, as they allow for the correlation without explaining its origin. The focus is on estimating the average response over the population ("population-averaged" effects) rather than the regression parameters that would enable prediction of the effect of changing one or more components of '''X''' on a given individual. GEEs are usually used in conjunction with [[Huber–White standard errors]].<ref>{{cite journal
 |title = Models for Longitudinal Data: A Generalized Estimating Equation Approach |first1 = Scott L. |last1 = Zeger |last2 = Liang |first2 = Kung-Yee |last3 = Albert |first3 = Paul S. |author-link1=Scott Zeger |author-link2=Kung-Yee Liang |journal = Biometrics |volume = 44 |year = 1988 |pages = 1049–1060 |issue = 4
 |doi = 10.2307/2531734
 |pmid = 3233245
 |publisher = International Biometric Society
 |jstor = 2531734 
}}</ref><ref>{{cite book |last1 = Hardin |first1 = James |last2 = Hilbe |first2 = Joseph |author2-link = Joseph Hilbe |title = Generalized Estimating Equations |url = https://archive.org/details/generalizedestim0000hard |url-access = registration |location = London, England |publisher = Chapman and Hall/CRC |year = 2003 |isbn = 1-58488-307-3 }}</ref>
* '''[[Generalized linear mixed model]]s''' (GLMMs) are an extension to GLMs that includes [[random effects]] in the linear predictor, giving an explicit probability model that explains the origin of the correlations. The resulting "subject-specific" parameter estimates are suitable when the focus is on estimating the effect of changing one or more components of '''X''' on a given individual. GLMMs are also referred to as [[multilevel model]]s and as [[mixed model]]. In general, fitting GLMMs is more computationally complex and intensive than fitting GEEs.