# Re: [R] Coefficient of Determination for nonlinear function

From: Mike Marchywka <marchywka_at_hotmail.com>
Date: Sun, 06 Mar 2011 08:25:28 -0500

> From: uwe.wolfram_at_uni-ulm.de
> To: andy_liaw_at_merck.com
> Date: Sat, 5 Mar 2011 17:14:12 +0100
> CC: r-help_at_r-project.org; gunter.berton_at_gene.com
> Subject: Re: [R] Coefficient of Determination for nonlinear function
>
> 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

The quality of the fit is determined by how much additional funding it allows you to secure :) Obviously I'm being facetious but there are two real issues here. You may in fact be modeling revenue numbers as another poster here explicitly intended. Money or not, the quality is related to some underlying system you are presumably attempting to understand. Non-linear being a classification of exclusion it is quite open ended and any generic goodness measure may not be of much use to you. The other side of my first sentence would be that it is always easy to shop for a result you want for some purpose other than understanding your data. You may not state this, but you will likely find many ways to measure your results and then end up picking the one that agrees the most with what you want to believe.

The great thing about R is that ad hoc exploratory work is easy and you may find simply plotting residuals and doing simple sensitivity tests by perturbing the data can be of some use. Or you may want a specific test to determine if you have ( say your nonlinear equation is a fit to a spectrum of some kind) a bunch of gaussian or lorentzian lines for example. I think I can say with reasonable certainty, "it depends."

> 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.
>
>
> 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
> > > 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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> > > > 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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