[R] function in nls argument -- robust estimation

[Martin Maechler]

Hi Kate and Fernando,

I'm late into this thread,
but from reading it I get the impression that Fernando really
wants to do *robust* (as opposed to least-squares) non-linear
model fitting.  His proposal to set residuals to zero when they
are outside a given bound is a very special case of an
M-estimator, namely (if I'm not mistaken) the so-called "Huber
skipped-mean", an M-estimator with psi-function 
   psi <- function(x, k) ifelse(abs(x) <= k, x, 0)
It is known that this can be far from optimal, and either using
Huber-psi or "a redescender" such as Tukey's biweight can be
considerably better.
Also note that the standard inference (std.errors, P-values, ...)
that you'd get from summary(nlsfit) or anova(nls1, nl2) is 
*invalid* here, since you are effectively using *random* weighting.

The nlrob() function in package 'robustbase'
implements M-estimation of nonlinear models directly.
Unfortunately, how to do correct inference in this situation
is a hard problem, probably even an open research question in
parts. I would expect that "the" bootstrap should work if you only
have a few outliers.

I don't have time at the moment to look at the example data and
the model, and show you how to use it for nlrob();
if you find a way to you it for nls() , then the same should
work for nlrob().

I'm CCing this to the specialists for "Robust Stats with R"
mailing list, R-SIG-robust.

Best regards,
Martin Maechler
ETH Zurich

>>>>> "KateM" == Katharine Mullen <kate at few.vu.nl>
>>>>>     on Fri, 9 May 2008 15:50:08 +0200 (CEST) writes:

    KateM> You can take minpack.lm_1.1-0 (source code and MS Windows build,
    KateM> respectively) from here:

    KateM> http://www.nat.vu.nl/~kate/minpack.lm_1.1-0.tar.gz
    KateM> http://www.nat.vu.nl/~kate/minpack.lm_1.1-0.zip

    KateM> The bug that occurs when nprint = 0 is fixed.  Also fixed is another
    KateM> problem suggested your example: when the argument par is a list, calling
    KateM> summary on the output of nls.lm was not working.

    KateM> I'll submit the new version to CRAN soon.

    KateM> This disscusion has been fruitful - thanks for it.

    KateM> On Fri, 9 May 2008, Katharine Mullen wrote:

    >> You indeed found a bug.  I can reproduce it (which I should have tried to
    >> do on other examples in the first place!).  Thanks for finding it.
    >> 
    >> It will be fixed in version 1.1-0 which I will submit to CRAN soon.
    >> 
    >> On Fri, 9 May 2008, elnano wrote:
    >> 
    >> >
    >> > Find the data (data_nls.lm_moyano.txt) here:
    >> > ftp://ftp.bgc-jena.mpg.de/pub/outgoing/fmoyano
    >> >
    >> >
    >> >
    >> > Katharine Mullen wrote:
    >> > >
    >> > > Thanks for the details - it sounds like a bug.  You can either send me the
    >> > > data in an email off-list or make it available on-line somewhere, so that
    >> > > I and other people can download it.
    >> > >
    >> > >
    >> > > ______________________________________________
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    >> > > https://stat.ethz.ch/mailman/listinfo/r-help
    >> > > PLEASE do read the posting guide
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    >> > > and provide commented, minimal, self-contained, reproducible code.
    >> > >
    >> > >
    >> >
    >> > --
    >> > View this message in context: http://www.nabble.com/function-in-nls-argument-tp17108100p17146812.html
    >> > Sent from the R help mailing list archive at Nabble.com.
    >> >
    >> > ______________________________________________
    >> > 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.
    >> >
    >> 
    >> ______________________________________________
    >> 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.
    >> 

    KateM> ______________________________________________
    KateM> R-help at r-project.org mailing list
    KateM> https://stat.ethz.ch/mailman/listinfo/r-help
    KateM> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
    KateM> and provide commented, minimal, self-contained, reproducible code.