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
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
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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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[R] Coefficient of Determination for nonlinear function
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.
[R] Coefficient of Determination for nonlinear function
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.
Re: [R] How to plot Ellipsoid like function
Dear R-Users,
I am trying to plot an ellipsoid like function that represents some
physical threshold in its eigenvalue space. I am facing a few problems
generating a figure I need for my thesis. A small example looks as
follwos where the two contour3d plots do NOT overlay as desired so you
may try plotting the surfaces one by one to see what I mean.
# begin example
require(rgl)
require(misc3d)
require(MASS);
f - function(x, y, z){
chi0=-0.6603368
eps0=0.006590395
xi0=0.01117194
(x^2 + y^2 + z^2 - chi0*(x*y + x*z + y*z))/eps0^2 + (x + y + z)/xi0
}
ff - function(x, y, z)x + y + z
open3d()
clear3d(all)
bg3d(color=#88)
light3d()
x - seq(-.02,.02,len=20)
# plot ellipsoid
contour3d(f,1,x,x,x,color=#FF,alpha=0.5)
# plot plane
contour3d(ff,1,x,x,x,color=#FF,alpha=0.5)
# plot data points
spheres3d(c(-0.009379952, 0.007899338), c(-0.00879318, 0.00700924),
c(-0.009009740, 0.007656409),radius=0.0005,color=#FF)
# plot hydrostatic pressure line
lines3d(c(-0.012, 0.012), c(-0.012, 0.012), c(-0.012, 0.012),
col=#A8A8A8, lwd=4)
# end example
I have three questions regarding this problem and I hope you could help
me.
1. How can I overlay the plan plotted using contours3d(ff, ...) and
the ellipsoid plotted with contours3d(f, ...)
2. Instead of using spheres3d(...) I would love to use plot3d to
obtain proper x, y and z coordinate axes. Is there a possibility
to overly the contour3d() and line3d() commands with pot3d?
Otherwise is there a possibility to plot proper coordinate axes
with tics and such as usual R plots?
3. How can I save the scene to an image? pdf(...) ... dev.off()
seems not to work on my machine. I am using Ubuntu on a 32 Bit
Laptop.
Thanks a million for your help!
Uwe
Am Montag, den 13.12.2010, 10:20 -0500 schrieb Duncan Murdoch:
On 13/12/2010 10:13 AM, Uwe Wolfram wrote:
I am currently trying to fit a tensorial function in its principal
coorinate system. The function is given by:
1~(x1^2 + x2^2 + x3^2 - chi0*(x1*x2 + x1*x3 + x2*x3))/eps0^2 + (x1 + x2
+ x3)/xi0
Where eps0 = 0.0066, chi0 = -0.66 and xi0 = 0.011 are obtained from
experimental data using nls().I am able to plot the experimental points
that delivered the parameters of the function. For my thesis, however, I
need to overlay the fitted surface. So far I am using the following code
which wonderfully plots the experimental points in 3D:
===
# from demo(bivar)
require(rgl)
require(misc3d)
require(MASS);
# New window
open3d()
# clear scene:
clear3d(all)
# setup env. That is, background, light and so on:
bg3d(color=#88)
light3d()
# spheres at points in principal strain space
#spheres3d(e1,e2,e3,radius=0.00025,color=#FF)
# draws points alternatively
plot3d(e1,e2,e3, col=#FF)
===
According to the examples on http://rgl.neoscientists.org/gallery.shtml
I tried to overlay the point plot using surface3d. However, these were
only functions of type y ~f(x1, x2). I think that the surface could be
plotted if I could provide the gridpoints correctly. Using
xyz.coords(1~(x1^2 + x2^2 + x3^2 - chi0*(x1*x2 + x1*x3 + x2*x3))/eps0^2
+ (x1 + x2 + x3)/xi0, y = NULL, z = NULL) did unfortunately not solve
the problem.
Is there any function that can generate the surface for the given
function such as ContourPlot3D in Mathematica.
See ?misc3d::contour3d
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R-help@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.
[R] How to plot Ellipsoid like function
Dear R-Users, I am currently trying to fit a tensorial function in its principal coorinate system. The function is given by: 1~(x1^2 + x2^2 + x3^2 - chi0*(x1*x2 + x1*x3 + x2*x3))/eps0^2 + (x1 + x2 + x3)/xi0 Where eps0 = 0.0066, chi0 = -0.66 and xi0 = 0.011 are obtained from experimental data using nls().I am able to plot the experimental points that delivered the parameters of the function. For my thesis, however, I need to overlay the fitted surface. So far I am using the following code which wonderfully plots the experimental points in 3D: === # from demo(bivar) require(rgl) require(misc3d) require(MASS); # New window open3d() # clear scene: clear3d(all) # setup env. That is, background, light and so on: bg3d(color=#88) light3d() # spheres at points in principal strain space #spheres3d(e1,e2,e3,radius=0.00025,color=#FF) # draws points alternatively plot3d(e1,e2,e3, col=#FF) === According to the examples on http://rgl.neoscientists.org/gallery.shtml I tried to overlay the point plot using surface3d. However, these were only functions of type y ~f(x1, x2). I think that the surface could be plotted if I could provide the gridpoints correctly. Using xyz.coords(1~(x1^2 + x2^2 + x3^2 - chi0*(x1*x2 + x1*x3 + x2*x3))/eps0^2 + (x1 + x2 + x3)/xi0, y = NULL, z = NULL) did unfortunately not solve the problem. Is there any function that can generate the surface for the given function such as ContourPlot3D in Mathematica. Thanks a million! 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.
[R] Plotting 3d surfaces
Dear Subscribers, I am using R for quite a while nowadays on Ubuntu 10.04 LTS. I a using R for doing my statistics. Furthermore I am using it as a tool to generate the graphics for my publications. I am currently working on a project which involves nls-fits of three dimensional surfaces such as ellipsoids or even more complex. I have been searching R help and the manuals for a possibility to plot these surfaces. Is there any package in R that allows plotting something like this: http://uwwo.in-chemnitz.de/R-Problem/tsai-wu-principal-strain.pdf This plot was generated using Mathematicas ContourPlot3D function. I would love to be able to plot this in R. However, I could not find something which could this. Thanks a million for the help! 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.
