[R] R² for non-linear model

[Kjetil Halvorsen]

see inline.

On Thu, Mar 17, 2011 at 4:58 AM, Rubén Roa <rroa at azti.es> wrote:
> 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)."

My  reading of this is that AIC can be used to compare models with
densities relative to the same
dominating measure.

Kjetil

> 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 at r-project.org on behalf of Alexx Hardt
> Sent: Wed 3/16/2011 7:42 PM
> To: r-help at 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 at alexx-fett:~$ vi .emacs
>
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