[R] R² for non-linear model

[Alexander Engelhardt]

Hi,
thank you for your elaborate answer. I downloaded Prof. Dayton's pdf and 
will read it tomorrow.

A friend also told me that our professor said you can actually compare 
AICs for different distributions. Apparently it's not correct strictly 
speaking, because of the two different likelihoods, but you can get 
meaningful information out of it. Did I understand that right?

By the way, what is the etiquette way of answering your post? Should I 
mail to you /and/ the list?

Regards,
  Alex (with a new e-mail address, in case this mixes something up)

Am 17.03.2011 09:58, schrieb Rubén Roa:
> 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 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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