[Ifeffit] doubt on number of variables

[Bruce Ravel]

On 05/26/2016 10:02 AM, Jesús Eduardo Vega Castillo wrote:
> Just for clarifying, this is not what I have been doing. I just was
> asked to add new independent variables (individual DW factors for each
> path) while I am already at the limit of independent points.
>
> I have been using a number of parameter always lower than the number of
> independent points. I have also been managing high correlations by not
> varying two strongly correlated parameters at the time. But at the end I
> do a final fit setting to guess all the parameters, no matter the
> correlations, in order to obtain a "true" reduced Chi2 to report which
> includes all parameters. Do you consider this procedure right?

Well, "truth" is a difficult concept and isn't really what EXAFS 
analysis is all about.

When we do an EXAFS analysis we are testing the extent to which data are 
consistent with a fitting model.  The goal is to find a fitting model 
that is a defensible description of the data and which yields fitting 
results and uncertainties that are, themselves, defensible and which 
tell us something that we want to know about the sample which was measured.

Some parameters are highly correlated and there is nothing you can do 
about it, regardless of how much you might want to.  In a one-shell fit, 
S02 and coordination number are 100% correlated.  It doesn't matter how 
much your thesis advisor wants you to get the "true" coordination number 
from the one-shell fit, it won't happen.

So, in the end, you settle upon a fitting model and write a paper.  In 
that paper you report on the fitting results.  If the referee asks why 
you chose to fix a certain parameter, you better have a good reason. 
That's what I mean by "defensible" -- that you can explain and justify 
all the choices you made when fitting the data.

The "procedure" is that you define a fitting model, press the big Fit 
button, and interpret the results.  The parameters that you float, the 
parameters that you fix ... they are defensible when you can defend 
them.  "Because the boss wanted two more sigma^2 parameters" is probably 
not a defensible argument.

Here are a couple of my papers:

http://dx.doi.org/10.1016/j.radphyschem.2009.05.024
http://dx.doi.org/10.1107/S1600577514014982

I refer you to these not because they are necessarily relevant to your 
work or even because they are especially good papers.  But, in each, I 
discuss defensibility of fitting model in a situation where there is not 
nearly enough information in the measured data to properly describe the 
actual structure of the sample.  Perhaps you'll find it helpful to see 
how I address this issue.

B

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

  National Institute of Standards and Technology
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