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

[Prof Brian Ripley]

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