[R] R² for non-linear model

[Rubén Roa]

> -----Mensaje original-----
> De: Kjetil Halvorsen [mailto:kjetilbrinchmannhalvorsen at gmail.com] 
> Enviado el: jueves, 17 de marzo de 2011 16:19
> Para: Rubén Roa
> CC: Alexx Hardt; r-help at r-project.org
> Asunto: Re: [R] R² for non-linear model
> 
> 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

I think this is correct. 
It is probably not wise to use the AIC to compare distribution models based on the counting measure with distribution models based on the Lebesgue measure!

____________________________________________________________________________________ 

Dr. Rubén Roa-Ureta
AZTI - Tecnalia / Marine Research Unit
Txatxarramendi Ugartea z/g
48395 Sukarrieta (Bizkaia)
SPAIN