[Ifeffit] Linear Combination Fitting - More Questions

[Bruce Ravel]

On Thursday 17 July 2008 08:53:00 Gudrun Lisa Bovenkamp wrote:
> Hi everyone,
>
> I just learned that before Athena there was no such program to check on
> all combinations, so it was not that confusing - or just more work?
> I think this feature of Athena is very good tool, but when I really do
> not know what is in my sample how can it help?
> I try to answer it myself and someone can correct me:
> Certainly not all of my, say 10 reference spektra, are that similar that
> I can get several LCFs with the same say R-factor. So, I will get some
> clue to narrow the components. But still there can be, for example:
> Standard-combi 1, 2, 3 equal to 1, 4, 6.
> So,
>   my analysis gives two solutions and one must be wrong, but both can be
> wrong. How can I tell?
>
> Can a PCA help me in this case?

Lisa,

I would like to expand upon Dean's answer to your excellent question.

At the base of your problem is a very fundamental question any of us
have to ask for a lot of the problem we face: how do we make progress
in the absence of information about our samples.  All of Dean's advice
was excellent -- particularly the bit about comparing your answer to
elemental analysis.  If there is any scrap of information you can
bring to bear on the XANES analysis, you are wise to do so.  In many
cases, you can resolve the problem of two (or more) statistically
equivalent LCF fits by asserting that one of them is inconsistent with
some bit of data extrinsic to the XAS measurement.

Can PCA help?  Possibly.  It is certainly another tool to throw at a
problem.  It is certainly better to have more tools than fewer tools.
(PCA is loooooooong overdue in Athena.  I apologize to all my users
that it has not risen up on my list of things to do yot.)

PCA, though, suffers from the exact same limitation as the thing that
I called "combinatorial fitting" in Athena.  Either approach to
disentangling a XANES spectra requires that you have an exhaustive set
of standrads.  If you are missing one of the components in your sample
sequence, then either approach will suffer.  I suspect (though I
encourage someone out there to argue otherwise and prove me wrong)
that your results would be just as ambiguous after PCA analysis as
they are after combinatorial LCF analysis.  In that case, you would,
again, need some extrinsic piece of information.

> The results change significantly when I change the normalization. How do
> I know what is the 'correct' adjustment?  - Yes, I read the Athena
> turorials, but I got no answers from there.

Correct normalization is one the central problems to this kind of
analysis and is a problem in PCA analysis as well.  (That is, if your
ensemble of standards and unknowns are not normalized consistently --
whatever that means -- then you will have an additional component that
accommodates the variations in normalization.)

I always tell people to "normalize consistently".  That is a pretty
squishy bit of advice.  In this I agree again with Dean that you
should make a few artificial samples -- perhaps combinations of your
standards that you yourself make.  Measure and analyze these
artificial samples in as simuilar a manner as possible to how you
measure and analyze the real samples.  Using LCF to get the right
answer for your artificial samples (for whcih you, presumably, know
the answer) gives you confidence in approaching your real samples.

> I searched quite a while to find a complete documentation of the LCF
> formula used in Athena, but I could not find it.

That is an excellent point.  I will make a note to expand that part
of the Athena document in the near future.

The executive summary is that the standards are interpolated onto the
energy grid of the sample.  If any "fit E0" buttons are ticked, then
the interpolation is continuously reperformed throughout the fit as
the E0 is updated.  A variable parameter representing the weight of
the component is defined for all but one of the standards.  The final
standard's weight is 1 minus the sum of the other weight, unless the
contraint that the weights sum to one is lifted.  In that case, the
final standard gets its own variable.  From there a
Levenberg-Marquardt non-linear minimization is performed using
Ifeffit's "minimize" function in the fitting range indicated at the
top of the LCF dialog.  

The statistics are a bit ambiguous because one doesn't have a way of
measuring epsilon or the number of independent points.  Consequently,
the reduced chi-square values tend to be much smaller than 1.  Error
bars are rescaled by the square root of reduced chi-sqaure -- thus the
error bars reported assume that every fit is a good fit.  It is, of
course, up to your to figure out if that is a true statement. ;-)

HTH,
B


-- 
 Bruce Ravel  ------------------------------------ bravel at bnl.gov

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