Hi,
To compare the results what you need to employ is a technique from the
statistical field of model selection. The spherical diffusion
(isotropic) + all model-free models of all selected residues is one
single mathematical model. The prolate and oblate spheroids (prolate
and oblate axially symmetric anisotropic diffusion tensors) + all
model-free models, and the ellipsoid (fully anisotropic or three
different eigenvalues) + all model-free models, are three additional
mathematical models. Therefore to compare these four different models
you need to select the model which best represents your relaxation
data. These models are, however, not nested and therefore cannot be
compared using ANOVA F-tests! Firstly the three types of diffusion
tensor are not nested (there is a reference from Dominique Marion's
group in which they say ANOVA statistics cannot be used but I can't
find it at the moment (although it shouldn't be too hard to track
down, it's related to Tensor)). Secondly the model-free models
selected will be different between the four models. Hence chi-squared
and F-tests cannot be used.
A useful reference (I'm not at all biased ;) for this problem is my
paper d'Auvergne, E. J. and Gooley, P. R. (2003), (see
http://www.nmr-relax.com/refs.html for the full reference). On page
37 at the end of that paper I discuss how AIC model selection is
perfect for selecting between these non-nested models. The AIC
criterion is still
AIC = chi2 + 2k,
however chi2 is the minimised chi-squared value for the complete model
and k is the sum of the number of diffusion parameters and number of
model-free parameters for all spin systems. BIC model selection is
likely to work quite well as well. If you have four runs, one for
each of the diffusion models, then the relax user function
'model_selection()' is designed to select between these models. I
hope this helps and hasn't been too biased.
Cheers,
Edward
P.S. Prior to model selection between the diffusion models, the
diffusion models must have fully converged. Multiple iterations of
optimisation of the model-free models, AIC model selection, and
optimisation of all parameters together (diffusion tensor + model-free
parameter of all residues) must be executed. Convergence is when two
iterations possess identical chi-squared values, identical model-free
models, and identical parameter values.
On 3/2/07, Hongyan Li <hylichem@xxxxxxxxxxxx> wrote:
Dear relax users,
I have managed to use Relax to run my dynamics data by both isotropic and
axial-oblate models. My qestion is how to compare the results, by chi-square??
what is the criteria to make judgment that which residues is beter simulated
with which model?
Thanks for your kind help!
Best wishes,
Hongyan
Dr. Hongyan Li
Department of Chemistry
The University of Hong Kong
Pokfulam Road
Hong Kong
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Re: comparison between different models