Dale Tronrud wrote:
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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
