[R] Significance of confidence intervals in the Non-Linear Least Squares Program.

bbouling benoit.boulinguiez at ensc-rennes.fr
Thu Jul 31 15:40:36 CEST 2008

Dear Pf. Ripley,

I use the nls() function coupled with the confint() to obtain the confidence
interval of assessed parameters of fitting model.

I don't understand why the confidence intervals estimated with such a method
aren't consistent?


B. Boulinguiez
Ph.D. in Chemistry
Ecole Nationale Supérieure de Chimie de Rennes
35700 Rennes (FRANCE)  

Prof Brian Ripley wrote:
> On Wed, 26 Mar 2008, glenn andrews wrote:
>> I am using the non-linear least squares routine in "R" -- nls.  I have a
>> dataset where the nls routine outputs tight confidence intervals on the
>> 2 parameters I am solving for.
> nls() does not ouptut confidence intervals, so what precisely did you do?
> I would recommend using confint().
> BTW, as in most things in R, nls() is 'a' non-linear least squares 
> routine: there are others in other packages.
>> As a check on my results, I used the Python SciPy leastsq module on the
>> same data set and it yields the same answer as "R" for the
>> coefficients.  However, what was somewhat surprising was the the
>> condition number of the covariance matrix reported by the SciPy leastsq
>> program = 379.
>> Is it possible to have what appear to be tight confidence intervals that
>> are reported by nls, while in reality they mean nothing because of the
>> ill-conditioned covariance matrix?
> The covariance matrix is not relevant to profile-based confidence 
> intervals, and its condition number is scale-dependent whereas the 
> estimation process is very much less so.
> This is really off-topic here (it is about misunderstandings about 
> least-squares estimation), so please take it up with your statistical 
> advisor.
> -- 
> Brian D. Ripley,                  ripley at stats.ox.ac.uk
> Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
> University of Oxford,             Tel:  +44 1865 272861 (self)
> 1 South Parks Road,                     +44 1865 272866 (PA)
> Oxford OX1 3TG, UK                Fax:  +44 1865 272595
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