[R] Compare parameter estimates of a nlsList object

[Joerg van den Hoff]

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