Hi Romel,
From the logic that the prolate axially symmetric tensor and full
ellipsoid are nested models, it would normally be the case that
chi-squared value for the ellipsoid be smaller than the prolate model,
or at least close to the same. This logic is only broken if
optimisation is incomplete for the ellipsoidal model. However the
model-free problem is much more complicated than just one diffusion
model verses another. The reason is because of two interlinked
problems - that of finding the diffusion tensor and that of finding
the internal dynamics. The prolate tensor has 4 parameters and the
ellipsoid 6. Therefore it is clear from the difference of 1 in the
parameter number k that it is not just the diffusion models that are
different.
If you have a close look at the level of the spin, you will see that
the model-free models selected for each diffusion tensor will
different. This is normal, as in the model-free analysis you have a
chicken and egg problem of finding the diffusion tensor and finding
the internal motions. The result of one influences the optimisation -
and model selection - of the other. The model-free problem is quite
complex, as I tried to parametrise in
http://dx.doi.org/10.1039/b702202f. If the diffusion tensor is too
simplified, you have artificial internal motions appearing (both ns
motions and Rex). Hence the models will be different. This is
described in detail in that paper. The artificial motions also occurs
if the XH bond vector orientation is poorly or incorrectly defined in
the structure - and this is also linked to the diffusion tensor
optimisation.
You do however have a very clean example however of the perfect
nesting of two models. This is quite rare. The oblate and ellipsoid
models have almost identical chi-squared values and a parameter
difference of 2 - this indicates, though not definitively, that the
model-free models selected are the same for both diffusion models.
Anyway, I hope this description helped. If you need more details on
the model-free problem and space, the above link will help explain how
this is not just a simple single-universe optimisation problem, but a
multi-universe optimisation problem with interlinked model selection
and optimisation. You just have your prolate and ellipsoid results in
parallel, but slightly different universes.
Regards,
Edward
P. S. Note that a chi-squared difference of 15 is not too significant
if you consider how many relaxation data points for all spin systems
you have used. If you divide one by the other, you have the reduced
chi-squared difference which you will see is quite small.
On 22 July 2013 17:48, Romel Bobby <rbob002@xxxxxxxxxxxxxxxxx> wrote:
Dear users,
I recently ran a model-free analysis on a ~5kDa protein with relaxation data
measured at three fields (600, 800 & 900 MHz). For the analysis, I used the
fully automated analysis (dauvergne_protocol.py).
At the end of the diffusion tensor optimisation step, a prolate spheroid
tensor seemed to be the best description for diffusion, as assessed by AIC.
See below the AIC scores for the individual models:
Data pipe k n Chi2
Criterion
sphere 102 204 2479.48833 2683.48833
prolate 89 204 2391.34556 2569.34556
oblate 88 204 2405.33989 2581.33989
ellipsoid 90 204 2405.90291 2585.90291
My question now concerns the 'large' deviation of ~15 units in chi-squared
values between the ellipsoid and prolate models. Shouldn't the value of the
ellipsoid be smaller than the axially symmetric models, considering that two
additional parameters are used in the ellipsoid?
Why is the chi-squared value slightly larger for the ellipsoid than the
prolate?
I looked at the individual models and the log files. The optimisation
finished after convergence and the analysis didn't report any errors or the
like.
Many thanks,
Romel
_______________________________________________
relax (http://www.nmr-relax.com)
This is the relax-users mailing list
relax-users@xxxxxxx
To unsubscribe from this list, get a password
reminder, or change your subscription options,
visit the list information page at
https://mail.gna.org/listinfo/relax-users
Re: AIC values