R help - Mar 2008 - Significance of confidence intervals in the Non-Linear Least Squares Program.

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.

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? 

Glenn

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