# Formula for the AIC for a GLM

By definition, for a linear model we have that $$\text{AIC}=n\log(\frac{\text{RSS}}{n})+2p$$ where $n$ is the number of observations, $p$- the number of parameters and RSS - the residual sum of squares

My question is: If we have the Residual Deviance for a given GLM can we find the AIC?

Thanks!

• This only works under the assumption of normality of errors. Otherwise you would have likelihood in place of RSS. – Richard Hardy Apr 11 '18 at 9:59
• The definition for AIC is well defined on Wikipedia. However, how the formula looks like depend on what GLM family you're talking about. – SmallChess Apr 11 '18 at 9:59
• My issue (poorly written in the question) is if I'm given only the Residual Deviance, can I find the AIC? Will edit the question – asdf Apr 11 '18 at 10:20
• AIC is in general calculated as $$\text{AIC} =2k-2\ln(\hat{L}),$$ where $k$ are the number of parameters and $\hat{L}$ is the maximized likelihood of the model with $k$ parameters. – BloXX Apr 11 '18 at 10:33
• But does this have any relation to the Residual Deviance? – asdf Apr 11 '18 at 14:47