On Tue, 17 Jan 2012, Bert Gunter wrote:
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.
I fully agree with Bert that, in this case, segmented regression does not
seem to be a fruitful approach and that it's best to consult a local
statistician.
However, I just wanted to clarify a theoretical detail about what
breakpoints() does. The breakpoints converge at the faster rate of "n"
while the parameter estimates just converge with "sqrt(n)". This is why in
principle, it is possible to get "the usual" inference from segmented
regressions. The price for this is to assume that the true model is in
fact a segmented regression (with only breakpoints/coefficients unknown).
Hence, segmented regression will be "useful" (in the Tukey
sense) if there are few relatively abrupt changes in a regression
relationship. On the other hand, for approximating smooth changes there
are typically better techniques available.
Best,
Z
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.
______________________________________________
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.
