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-boun...@r-project.org > > [mailto:r-help-boun...@r-project.org] On Behalf Of Bert Gunter > > Sent: Friday, March 04, 2011 11:21 AM > > To: uwe.wolf...@uni-ulm.de; r-help@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.wolf...@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@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@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}} ______________________________________________ R-help@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.
