On Tue, Jan 17, 2012 at 8:06 AM, Kenneth Frost <kfr...@wisc.edu> wrote: > Sorry, that wasn't to helpful...I see that the intervals and se.fit argument > are currently ignored.
Yes, because the fitted values are nonlinear in the parameters, which makes finding exact confidence regions impossible. I think the "usual" approach (subject to correction by experts) is to use a delta method approximation for the fitted variances from the varcov matrix of the parameters at the converged optimum (itself an approximation) and then a standard t-interval based on that. However, this approximation can be quite bad, because "degrees of freedom" don't mean much for nonlinear models -- in fact, that's the essential (and huge!) difference between linear and nonlinear models -- and the likelihood surface may not be close enough to quadratic. So one may do better with, e.g. a bootstrap approximation, although this can be problematic, too, due to convergence and other issues. What I think can be said with some certainty is that the idea of approximating by a segmented regression and then using CI's for each linear part in the "usual" way is a particularly bad one -- the CI's will be underestimated because they don't take into account the uncertainty in the location of the fitted breakpoints, which are nonlinear **and** non-smooth functions of the data. So if confidence intervals for the fitted values are really important, I suggest that Julian work with his local statistician to come up with the best approach for his particular situation. It's tricky. Cheers, Bert > > On 01/17/12, crimsonengineer87 <julianjonre...@gmail.com> wrote: >> Dear Forum, >> >> I have been wracking my head over this problem for the past few days. I have >> a dataset of (x,y). I have been able to obtain a nonlinear regression line >> using nls. However, we would like to do some statistical analysis. I would >> like to obtain a confidence interval for the curve. We thought we could >> divide up the curve into piecewise linear regressions and compute CIs from >> those portions. There is a package called strucchange that seems helpful, >> but I am thoroughly confused. >> >> 'breakpoints' is used to calculate the number of breaks in the data for >> linear regressions. I have the following in my script: >> >> bp.pavlu <- breakpoints(Na ~ f(yield, a, b), h=0.15, breaks=3, >> data=pavludata) >> plot(bp.pavlu) >> breakpoints(bp.pavlu) >> >> But I am confused as to how to graph the piecewise functions that make up >> the curve. I am not even sure if I am using breakpoints correctly. Do I just >> give it a linear relationhip (Na ~ yield), instead of what I have? >> >> Is there an easier way to calculate the confidence interval for a non-linear >> regression? >> >> I am new to R (as I've read in many questions), but I have most certainly >> tried many things and am just getting frustrated with the lack of examples >> for what I'd like to do with my data... I'd appreciate any insight. I can >> also provide more information if I am not clear. Thanks in advance. >> >> Julian >> >> -- >> View this message in context: >> http://r.789695.n4.nabble.com/breakpoints-and-nonlinear-regression-tp4303629p4303629.html >> Sent from the R help mailing list archive at Nabble.com. >> >> ______________________________________________ >> 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. >> >> > > ______________________________________________ > 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. > -- Bert Gunter Genentech Nonclinical Biostatistics Internal Contact Info: Phone: 467-7374 Website: http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm ______________________________________________ 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.
