R help - Apr 2013 - Model selection: On the use of the coefficient determination(R2) versus the frequenstist (AIC) and Bayesian (AIC) approaches

Dear all,

I'm modeling growth curve of some ecosystems with respect to their
rainfall-productivity relationship using a simple linear regression
(ANPP(t)=a+b*Rain(t)) and a modified version of the Brody Model
ANPP(t)=a*(1-exp(-b*rain(t)))

I would like to know why the "best model" is function of the criteria
that I use (maximizing the fit using R2 or testing the Null hypothesis with
BIC/AIC).
To compute the R2, I used the following formula r2=mss/(mss+rss) where
mss=sum((fitted(model)-mean(fitted(model)))^2) and rss=sum(resid(model)^2)

I think that the R2 is good enough for the model selection knowing the candidate
models both have two parameters (so no to care about the principle of parsimony)
and my guess is that the models needs to have the same form (which is not the
case here: linear form vs exponential form) ) or nested to be compared with
frequentist or Bayesian approaches such as the AIC and BIC criterion .

Thank you very much in advance

Armel

	[[alternative HTML version deleted]]

This is off topic here-- it has nothing to do with R, per se.

Post on a statistics list  such as stats.stackexchange.com instead.

-- Bert

On Sat, Apr 13, 2013 at 5:41 PM, Kaptue Tchuente, Armel
<armel.kaptue at sdstate.edu> wrote:
> Dear all,
>
> I'm modeling growth curve of some ecosystems with respect to their
rainfall-productivity relationship using a simple linear regression
(ANPP(t)=a+b*Rain(t)) and a modified version of the Brody Model
ANPP(t)=a*(1-exp(-b*rain(t)))
>
> I would like to know why the "best model" is function of the
criteria that I use (maximizing the fit using R2 or testing the Null hypothesis
with BIC/AIC).
> To compute the R2, I used the following formula r2=mss/(mss+rss) where
mss=sum((fitted(model)-mean(fitted(model)))^2) and rss=sum(resid(model)^2)
>
> I think that the R2 is good enough for the model selection knowing the
candidate models both have two parameters (so no to care about the principle of
parsimony) and my guess is that the models needs to have the same form (which is
not the case here: linear form vs exponential form) ) or nested to be compared
with frequentist or Bayesian approaches such as the AIC and BIC criterion .
>
> Thank you very much in advance
>
> Armel
>
>         [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.


-- 

Bert Gunter
Genentech Nonclinical Biostatistics

Internal Contact Info:
Phone: 467-7374
Website:
http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm