R help - Mar 2008 - Compare parameter estimates of a nlsList object

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.
 
Regards
Frank Scherr

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
WARNING: This email and any attachments may be confidential and/or privileged.
They are intended for the addressee only and are not to be read, used, copied or
disseminated
by anyone receiving them in error. If you are not the intended recipient, please
notify the sender by
return email and delete this message and any attachments.

The views expressed in this email are those of the sender and do not necessarily
reflect the
official views of Landcare Research. 
http://www.landcareresearch.co.nz
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

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