[R] deviance and variance - GAM models

[Simon Wood]

On 01/13/2012 08:25 PM, collifu wrote:
> Hi all,
>
> This is pretty basic but I am not an expert and I couldn't find anything in
> the forum or my statistics book about it. I was reading a paper and the
> authors were using both "explained deviance" and "explained variance" as
> synonyms. They were describing a GAM regression. Is that right? I performed
> an analysis in R to take a look to the output of GAM regression and I think
> that:
>
> - 'R-sq. (adj)'  is the percentage of variance explained by the regression,
> i.e., I can write "The regression explains xx% of variance".
> - 'Deviance explained' is a simple measure of the quality of the fit but it
> is not related to the percentage of variance that is explained by the
> regression.
The deviance explained will be the same as the variance explained 
(unadjusted) when you have Gaussian errors (deviance is then residual 
sum of squares), but not otherwise. You can write "the regression 
explains xx% of the deviance", of course.

best,
Simon
> Am I right?
>
> Thank you so much
> Ramón
>
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