Re: AIC values -- July 23, 2013 - 17:00

Dear Edward,

Thank you for clarification and giving a comprehensive reply to my query. It all makes sense now. In my logic, I had assumed that the same models are selected for the internal dynamics when swapping to a different diffusion tensor (obviously not the case). 

I had read your paper some time ago. It's time for a refresher!

Regards,

Romel

PS : Also thanks for sending me the link with the figure.

On 22 July 2013 18:23, Edward d'Auvergne <edward@xxxxxxxxxxxxx> wrote:

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
>

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--
Romel Bobby
Biomolecular NMR Research Group
School of Chemical Sciences/School of Biological Sciences
The University of Auckland
+64 (09) 3737599 Ext 83157