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
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
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
Dieter Menne
2011-Mar-04 18:09 UTC
[R] Coefficient of Determination for nonlinear function
Uwe Wolfram wrote:> > > 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. > >Try http://r-project.markmail.org/search/?q=r+square+nonlinear to find heated debates on this subject. But I fear you supervisor or the reviewer wants it anyway. Dieter -- View this message in context: http://r.789695.n4.nabble.com/Coefficient-of-Determination-for-nonlinear-function-tp3335236p3335719.html Sent from the R help mailing list archive at Nabble.com.