Re: [R] Compare parameter estimates of a nlsList object

From: Joerg van den Hoff <j.van_den_hoff_at_fzd.de>
Date: Fri, 28 Mar 2008 11:10:46 +0100

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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