[R] Coefficient of Determination for nonlinear function

[Bert Gunter]

Andy,

You may well be right. I assumed "fitting an equation" means that he
had data to which the equation was being fitted. Maybe that's wrong --
re-reading the post still does not clarify the point for me. In any
case, either way, fitting R^2 makes no sense.

-- Bert

On Fri, Mar 4, 2011 at 8:44 AM, Liaw, Andy <andy_liaw at merck.com> wrote:
> 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
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>> > 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.
>>
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-- 
Bert Gunter
Genentech Nonclinical Biostatistics