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

From: bbouling <>
Date: Thu, 31 Jul 2008 06:40:36 -0700 (PDT)

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,
> Professor of Applied Statistics,
> 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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> and provide commented, minimal, self-contained, reproducible code.
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