Thanks Bruce for your answer,

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?








2016-05-26 10:36 GMT-03:00 Bruce Ravel <bravel@bnl.gov>:
On 05/26/2016 09:17 AM, Jesús Eduardo Vega Castillo wrote:
As far as I understand the number of variables refers to those
parameters which have been "guessed" in the fit and it is limited by the
number of independent points.

 Correct.

If I have a group of variables but only set to guess a few of them while
fixing the others, then fix some of the obtained values and guess other
variables; I might include a large number of parameters in the resulting
fit (even more than the independent points) without increasing the
Number of variables of each individual fit. This also would keep reduced
chi2 from increasing too much.

Would this be cheating?

 The answer, almost certainly, is "yes".

The total number of parameters included is always restricted by the
Number of independent points?

 I'm going with this one ...

or
Can I include all the parameters I want as long as I set to guess no
more that the number of independent points at the time?

 ... and I really don't like this one.


The thing you seem not to be considering is that parameters have correlations.  The correlations between parameters are an important part of the assessment of uncertainty.

If you artificially suppress correlations between parameters in the way that you are describing, it is unlikely that the fitted results and their uncertainties would be defensible.

While it is possible to probe correlations between parameters in a defensible manner by selectively setting and guessing parameters in a lengthy sequence of fits, your brief description does not give me confidence that that is what you are doing.

The trick to EXAFS analysis (and any non-linear minimization analysis) is to defensibly get what information you can from the data.  Rarely do we get everything we want.  In those situations where we aspire to  more than our data can provide, it's important to remember that something is better than nothing.

B

--
 Bruce Ravel  ------------------------------------ bravel@bnl.gov

 National Institute of Standards and Technology
 Synchrotron Science Group at NSLS-II
 Building 535A
 Upton NY, 11973

 Homepage:    http://bruceravel.github.io/home/
 Software:    https://github.com/bruceravel
 Demeter:     http://bruceravel.github.io/demeter/
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