R help - Mar 2006 - How to compare fit of linear and nonlinear models

Dear statistics experts,

I'm looking for a way to compare the fit of the following three models:

LinModel <- lm(y ~ x)
LogModel <- nls(y ~ SSlogis(x, Asym, xmid, scal))
PotModel <- nls(y ~ a * x^n, start=list(a=1, n=1))

I am only interested in whether one of these models has substantial advances in
explaining the variance of y. So my original idea was simply to compare the
adjusted R squared values. This however seems to be problematic for nls models,
as I learned from an earlier thread on this issue (see
http://article.gmane.org/gmane.comp.lang.r.general/40727).

Then I thought about using AIC instead, but again this does not seem to be
trivial (see http://article.gmane.org/gmane.comp.lang.r.general/22438).

Do you have any suggestions on how I should proceed?


Best regards & thanks in advance,
Joerg

Your first model "y~x" is a special case of "y~a*x^n", so it
should
the comparison of those models should be straightforward:  Does the 
confidence inteval for "n" include 1?

	  It is not so easy to compare the second model with either the first 
or the third.  While model 1 is a special case of model 3, we can't get 
either as a special case of model 2 nor vice versa.  For ideas about how 
to approach this comparison, see my earlier post on a related question 
(http://finzi.psych.upenn.edu/R/Rhelp02a/archive/35450.html).  If it's 
sufficiently important, it should not be too dificult to Monte Carlo 
various ways of possibly deciding between the models.

	  hope this helps.
	  spencer graves

Joerg Trojan wrote:
> Dear statistics experts,
> 
> I'm looking for a way to compare the fit of the following three models:
> 
> LinModel <- lm(y ~ x)
> LogModel <- nls(y ~ SSlogis(x, Asym, xmid, scal))
> PotModel <- nls(y ~ a * x^n, start=list(a=1, n=1))
> 
> I am only interested in whether one of these models has substantial
advances in
> explaining the variance of y. So my original idea was simply to compare the
> adjusted R squared values. This however seems to be problematic for nls
models,
> as I learned from an earlier thread on this issue (see
> http://article.gmane.org/gmane.comp.lang.r.general/40727).
> 
> Then I thought about using AIC instead, but again this does not seem to be
> trivial (see http://article.gmane.org/gmane.comp.lang.r.general/22438).
> 
> Do you have any suggestions on how I should proceed?
> 
> 
> Best regards & thanks in advance,
> Joerg
> 
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