Use nlme. Here is an example, fitting the Michaelis-Menten model to some enzyme data:

library(nlme)
data(Puromycin)
fit.nls <- nlsList(rate ~ SSmicmen(conc, Vm, K)|state, data=Puromycin)
summary(fit.nls)

# Use the output to calculate starting values for the nlme fit.

fit.nlme <- nlme(rate ~ SSmicmen(conc, Vm, K), fixed=Vm+K~state, groups=~state, start=c(212, -52, 0.06,- 0.01), data=Puromycin)

summary(fit.nlme)

You get explicit tests between the states for each of the two model parameters. This example is from Pinheiro and Bates. Thankyou Jose and Doug! I use it in a course that I teach.

Cheers,

Simon.

Simon Blomberg, BSc (Hons), PhD, MAppStat. 
Lecturer and Consultant Statistician 
Faculty of Biological and Chemical Sciences 
The University of Queensland 
St. Lucia Queensland 4072 
Australia 
T: +61 7 3365 2506 
email: S.Blomberg1_at_uq.edu.au

Policies:
1.  I will NOT analyse your data for you.
2.  Your deadline is your problem.

The combination of some data and an aching desire for 
an answer does not ensure that a reasonable answer can 
be extracted from a given body of data. - John Tukey.



-----Original Message-----
From: r-help-bounces@r-project.org on behalf of Joerg van den Hoff
Sent: Fri 28/03/2008 8:10 PM
To: Frank Scherr
Cc: r-help@r-project.org
Subject: Re: [R] Compare parameter estimates of a nlsList object
 
On Wed, Mar 26, 2008 at 05:27:22PM +1300, Frank Scherr wrote:
> Hello together,
>  
> Is there a tool to test the statistical differences between parameter estimates of a nlsList fit?
>  
> I fitted degradation data using the nlsList method and want to find out whether derived rate constants are significantly different from each other at the grouping factors soil and temperature.
>  

here is a physicist's (not a mathematician's)  answer:

from each nls-fit you get an estimate of the std. error of the parameter
estimate.

so you have,e.g., (a1  +/- del_a1) from fit 1 and (a2 +/- del_a2) -- where
a1 and a2 are actually the same parameter in the model -- from fit 2.
since you thus have actual estimated errors, I'd simply ask "what is the error
estimate of the difference", i.e.

a1 - a2

and, assuming independent underlying data,
compute this by gaussian error propagation (i.e. assuming normal
distributions of the parameter estimates). here, the variances (squares
of ths std. errors) add up:

del_[a1-a2]^2 = del_a1^2 + del_a2^2

if (a1-a2) +/- del_[a-a2]  (or rather 2-3 times that error) is
compatible with zero, a and a2 do not differ significantly, else
they do.

HTH

joerg

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