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?
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@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.
