Hi Alexx,

I don't see any problem in comparing models based on different distributions for the same data using the AIC, as long as they have a different number of parameters and all the constants are included.
For example, you can compare distribution mixture models with different number of components using the AIC.
This is one example:
Roa-Ureta. 2010. A Likelihood-Based Model of Fish Growth With Multiple Length Frequency Data. Journal of Biological, Agricultural and Environmental Statistics 15:416-429.
Here is another example:
www.education.umd.edu/EDMS/fac/Dayton/PCIC_JMASM.pdf
Prof. Dayton writes above that one advantage of AIC over hypothesis testing is:
"(d) Considerations related to underlying distributions   for   random   variables   can   be 
incorporated  into  the  decision-making  process rather than being treated as an assumption whose 
robustness  must  be  considered  (e.g.,  models based  on  normal  densities  and  on  log-normal 
densities can be compared)."
Last, if you read Akaike's theorem you will see there is nothing precluding comparing models built on different distributional models. Here it is:
" the expected (over the sample space and the space of parameter estimates) maximum log-likelihood of some data on a working model overshoots the expected (over the sample space only) maximum log-likelihood of the data under the true model that 
generated the data by exactly the number of  parameters in the working model."
A remarkable result.

Rubén

-----Original Message-----
From: r-help-bounces@r-project.org on behalf of Alexx Hardt
Sent: Wed 3/16/2011 7:42 PM
To: r-help@r-project.org
Subject: Re: [R] R² for non-linear model
 
Am 16.03.2011 19:34, schrieb Anna Gretschel:
> Am 16.03.2011 19:21, schrieb Alexx Hardt:
>> And to be on-topic: Anna, as far as I know anova's are only useful to
>> compare a submodel (e.g. with one less regressor) to another model.
>>
> thanks! i don't get it either what they mean by fortune...

It's an R-package (and a pdf [1]) with collected quotes from the mailing 
list.
Be careful with the suggestion to use AIC. If you wanted to compare two 
models using AICs, you need the same distribution (that is, 
Verteilungsannahme) in both models.
To my knowledge, there is no way to "compare" a gaussian model to an 
exponential one (except common sense), but my knowledge is very limited.

[1] http://cran.r-project.org/web/packages/fortunes/vignettes/fortunes.pdf

-- 
alexx@alexx-fett:~$ vi .emacs

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