[R] breakpoints and nonlinear regression

[Bert Gunter]

On Tue, Jan 17, 2012 at 8:06 AM, Kenneth Frost <kfrost at 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  <julianjonreyes at 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.
>>
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>
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>



-- 

Bert Gunter
Genentech Nonclinical Biostatistics

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