From: Peter Dalgaard <p.dalgaard_at_biostat.ku.dk>

Date: Fri, 28 Mar 2008 09:01:47 +0100

Date: Fri, 28 Mar 2008 09:01:47 +0100

glenn andrews wrote:

> 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?
**>
*

Unreasonably large s.e.'s and large correlations in the
variance-covariance matrix of estimates (cov2cor(vcov(nlmod)) or
summary(nlmod, corr=TRUE)).

Notice that the former requires at least some feel for what is the natural scale of each parameter, which in turn requires subject-matter knowledge.

> Glenn

*>
**> Peter Dalgaard wrote:
**>
**>> 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.
**>>>
**>>
**>>
**>>
**>
*

-- O__ ---- Peter Dalgaard ุster Farimagsgade 5, Entr.B c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - (p.dalgaard_at_biostat.ku.dk) FAX: (+45) 35327907 ______________________________________________ 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.Received on Fri 28 Mar 2008 - 08:05:31 GMT

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