From: Uwe Wolfram <uwe.wolfram_at_uni-ulm.de>

Date: Sat, 05 Mar 2011 17:14:12 +0100

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. Received on Sun 06 Mar 2011 - 05:13:41 GMT

Date: Sat, 05 Mar 2011 17:14:12 +0100

thanks for your answers! I am quite aware that I do not fit a linear model, so r^2 in Pearson's sens is indeed meaningless. Instead, I am "fitting" an equation - or rather using an optimisation - were the experimentally derived point cloud (x1, x2, x3) should deliver something like 1 = f(x1, x2, x3). What I am trying to estimate is the quality of the fit. One thing I computed so far is the standard error of the equation (SEE) which is fine. My former question pointed in the direction of how I could compute a coefficient of determination to estimate a goodness of fit. Calling it r^2 may mislead but there must be something similar in nonlinear regressions.

Thanks for your efforts,

Uwe

Am Freitag, den 04.03.2011, 11:44 -0500 schrieb Liaw, Andy:

> As far as I can tell, Uwe is not even fitting a model, but instead just

*> solving a nonlinear equation, so I don't know why he wants a R^2. I
**> don't see a statistical model here, so I don't know why one would want a
**> statistical measure.
**>
**> Andy
**>
**> > -----Original Message-----
**> > From: r-help-bounces_at_r-project.org
**> > [mailto:r-help-bounces_at_r-project.org] On Behalf Of Bert Gunter
**> > Sent: Friday, March 04, 2011 11:21 AM
**> > To: uwe.wolfram_at_uni-ulm.de; r-help_at_r-project.org
**> > Subject: Re: [R] Coefficient of Determination for nonlinear function
**> >
**> > The coefficient of determination, R^2, is a measure of how well your
**> > model fits versus a "NULL" model, which is that the data are constant.
**> > In nonlinear models, as opposed to linear models, such a null model
**> > rarely makes sense. Therefore the coefficient of determination is
**> > generally not meaningful in nonlinear modeling.
**> >
**> > Yet another way in which linear and nonlinear models
**> > fundamentally differ.
**> >
**> > -- Bert
**> >
**> > On Fri, Mar 4, 2011 at 5:40 AM, Uwe Wolfram
**> > <uwe.wolfram_at_uni-ulm.de> wrote:
**> > > Dear Subscribers,
**> > >
**> > > I did fit an equation of the form 1 = f(x1,x2,x3) using a
**> > minimization
**> > > scheme. Now I want to compute the coefficient of
**> > determination. Normally
**> > > I would compute it as
**> > >
**> > > r_square = 1- sserr/sstot with sserr = sum_i (y_i - f_i) and sstot =
**> > > sum_i (y_i - mean(y))
**> > >
**> > > sserr is clear to me but how can I compute sstot when there
**> > is no such
**> > > thing than differing y_i. These are all one. Thus
**> > mean(y)=1. Therefore,
**> > > sstot is 0.
**> > >
**> > > Thank you very much for your efforts,
**> > >
**> > > Uwe
**> > > --
**> > > Uwe Wolfram
**> > > Dipl.-Ing. (Ph.D Student)
**> > > __________________________________________________
**> > > Institute of Orthopaedic Research and Biomechanics
**> > > Director and Chair: Prof. Dr. Anita Ignatius
**> > > Center of Musculoskeletal Research Ulm
**> > > University Hospital Ulm
**> > > Helmholtzstr. 14
**> > > 89081 Ulm, Germany
**> > > Phone: +49 731 500-55301
**> > > Fax: +49 731 500-55302
**> > > http://www.biomechanics.de
**> > >
**> > > ______________________________________________
**> > > 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.
**> > >
**> >
**> >
**> >
**> > --
**> > Bert Gunter
**> > Genentech Nonclinical Biostatistics
**> > 467-7374
**> > http://devo.gene.com/groups/devo/depts/ncb/home.shtml
**> >
**> > ______________________________________________
**> > 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.
**> >
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