Re: [R] Coefficient of Determination for nonlinear function

From: Liaw, Andy <andy_liaw_at_merck.com>
Date: Fri, 04 Mar 2011 11:44:37 -0500

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
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> > 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
>
> ______________________________________________
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> PLEASE do read the posting guide
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>
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