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Compare parameter estimates of a nlsList object

3 messages · Frank Scherr, Joerg van den Hoff, Simon Blomberg

Frank Scherr
# 
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

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2 days later
Joerg van den Hoff
#
On Wed, Mar 26, 2008 at 05:27:22PM +1300, Frank Scherr wrote:
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