From: glenn andrews <ga_at_aggies.com>

Date: Thu, 27 Mar 2008 18:43:57 -0500

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https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Thu 27 Mar 2008 - 23:46:00 GMT

Date: Thu, 27 Mar 2008 18:43:57 -0500

What should I be looking for in the output of the nls() routine that alerts me to the fact that the Hessian is potentially ill-conditioned?

Glenn

> glenn andrews wrote:

*>
**>> Thanks for the response. I was not very clear in my original request.
**>>
**>> What I am asking is if in a non-linear estimation problem using
**>> nls(), as the condition number of the Hessian matrix becomes larger,
**>> will the t-values of one or more of the parameters being estimated in
**>> general become smaller in absolute value -- that is, are low t-values
**>> a sign of an ill-conditioned Hessian?
**>>
**>
**> In a word: no. Ill-conditioning essentially means that there are one
**> or more directions in parameter space along which estimation is
**> unstable. Along such directions you get a large SE, but also a large
**> variability of the estimate, resulting in t values at least in the
**> usual "-2 to +2" range. The large variation may swamp a true effect
**> along said direction, though.
**>
**>> Typical nls() ouput:
**>>
**>> Formula: y ~ (a + b * log(c * x1^d + (1 - c) * x2^d))
**>>
**>> Parameters:
**>> Estimate Std. Error t value Pr(>|t|) a 0.11918 0.07835 1.521
**>> 0.1403 b -0.34412 0.27683 -1.243 0.2249 c 0.33757 0.13480
**>> 2.504 0.0189 *
**>> d -2.94165 2.25287 -1.306 0.2031
**>> Glenn
**>>
**>> 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.
**>>>
**>>>
**>>
**>>
**>> ______________________________________________
**>> R-help_at_r-project.org mailing list
**>> https://stat.ethz.ch/mailman/listinfo/r-help
**>> PLEASE do read the posting guide
**>> http://www.R-project.org/posting-guide.html
**>> and provide commented, minimal, self-contained, reproducible code.
**>>
**>
**>
**>
*

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https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Thu 27 Mar 2008 - 23:46:00 GMT

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