[R] Coefficient of Determination for nonlinear function

[Uwe Wolfram]

Dear Bert, dear Andy,

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.
> > 
> Notice:  This e-mail message, together with any attach...{{dropped:26}}