Dale Tronrud wrote:
>
----
> In summary, this argument depends on two assertions that you can
> argue with me about:
>
> 1) When a parameter is being used to fit the signal it was designed
> for, the resulting model develops predictive power and can lower
> both the working and free R. When a signal is perturbing the value
> of a parameter for which is was not designed, it is unlikely to improve
> its predictive power and the working R will tend to drop, but the free
> R will not (and may rise).
>
> 2) If the unmodeled signal in the data set is a property in real
> space and has the same symmetry as the molecule in the unit cell,
> the inappropriate fitting of parameters will be systematic with
> respect to that symmetry and the presence of a reflection in the
> working set will tend to cause its symmetry mate in the test set
> to be better predicted despite the fact that this predictive power
> does not extend to reflections that are unrelated by symmetry.
> This "bias" will occur for any kind of "error" as long as that
> "error" obeys the symmetry of the unit cell in real space.
>
Dear Dale,
Thanks for taking the time to think about my problem and for
composing what is obviously a well-thought-out explanation.
I am a little over my head here, but I think I see your point.
Inappropriate fitting of this residual error has poor predictive
power so does not reduce {Fc-Fo| for general free reflections.
However the error is symmetrical, so attempts to fit it will
result in symmetrical changes which reduce |Fo-Fc| for those
free reflections that are related to working reflections.
I need to read the references that were mentioned in this
discussion, and think about it a little more in order to
resolve some remaining conflicts in my thinking.
But I don't need to bother everyone else with my
struggles, unless I come up with something useful.
Thanks for the guidance!
Ed
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