[Ifeffit] Athena: the R factor for normalized mu(E)

[Jon-Petter Gustafsson]

Hello all,

I have been a frequent user of Athena for many years, mostly for interpreting P K-edge XANES spectra. Until last week I thought that the R factor in Athena was always defined as:

sum( [data_i - fit_i]^2 )
-------------------------------
       sum( data_i^2 ]

This is also the definition given in the online manual, and it has been stated by me and by other colleagues in a number of papers dealing with P K-edge XANES. But well, this is not true when dealing with normalized XANES spectra! I realized this when I played around with a number of my old LC fits in Excel. While the chi-square value (or maybe more precisely, the sum of squared residuals) was reproduced perfectly, I always got "R factors" (i.e. with the above definition) between 2 and 3 times lower than what Athena gives. After that I consulted the Demeter programming documentation (https://bruceravel.github.io/demeter/pods/Demeter/LCF.pm.html) to find that, for normalized mu(E), "Demeter thus scales the R-factor to make it somewhat closer to 10^-2". However, the equation stated on this page actually reproduces the R factor even more poorly, and therefore I won't reiterate it here.   After inspecting the Perl code, and trying out different alternatives in Excel, I now believe that the following equation provides a more accurate definition of the R factor (correct me if I'm wrong!):

sum( [data_i - fit_i]^2 )
-------------------------------
sum( [data_i - avg data]^2 )

where "avg data" is the arithmetic mean of the data in the LC fitting range. It would be great if others could confirm this. As far as I understand, this won't affect the interpretations that any of us have made over the years, it only affects the understanding of what the R factor actually is...

Kind regards, Jon Petter


Jon Petter Gustafsson, Professor in Soil Chemistry
Department of Soil and Environment
Swedish University of Agricultural Sciences (SLU)
Box 7014
750 07 Uppsala, Sweden
Phone: 018-671284; e-mail: jon-petter.gustafsson at slu.se<mailto:jon-petter.gustafsson at slu.se>


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