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Is marginal AIC similar to AIC obtained through mixed-model regression? I understand that conditional AIC has another penalty level.


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There are two differences for a usual linear regression model (lm) between AIC and extractAIC: AIC accounts for the estimation of the unknown variance of the error (i.e., scale) while extractAIC does not, hence $k$ is one less with extractAIC. AIC uses the formula $n\log\frac{RSS}{n}+n+n\log\left(2\pi\right)$ for the -2 log likelihood, while extractAIC ...


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If you compare multiple model fits based on some criterion and then try to compare the pairs of models, then you have the same pairwise comparisons problem that Tukey's method solves in the one-way ANOVA. A major wrinkle here is that the the statistics you are comparing are highly correlated, being based on nearly the same models. This problem has been ...


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From wiki : $AIC = 2k - 2\ln(L)$ where $L$ is maximum of the likelihood function and $k$ is the number of parameters estimated. x = [[1, 0], [1, 1], [1, 2], [1, 3], [1, 4]] y = [[0], [49], [101], [149], [201]] res = sm.OLS(y, x).fit() # Façon 1 res.aic # gives 16.5468 # Façon 2 llf = res.llf # log-like value k = 2 aic = -2*llf + 2 * k # gives 16.5468 @...


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