R-factor and reduced chi square
Hi, I understand R-factor and reduced chi square are statistical ways to see if the model is reasonable (R-factor) and if one model is better than the others (reduced chi square). But how much should I read into it? I have model A and B, I believe A is more theoretical sound than B. but when I fit them using IFEFFIT, the R-factor and reduced chi square of B is slightly better than A (B: 0.03, 28; A: 0.04, 33). What does that tell me? Is my assumption incorrect? Or are they more or less the same? Owen
At 01:07 PM 10/4/2005 -0500, you wrote:
Hi, I understand R-factor and reduced chi square are statistical ways to see if the model is reasonable (R-factor) and if one model is better than the others (reduced chi square). But how much should I read into it?
I have model A and B, I believe A is more theoretical sound than B. but when I fit them using IFEFFIT, the R-factor and reduced chi square of B is slightly better than A (B: 0.03, 28; A: 0.04, 33). What does that tell me? Is my assumption incorrect? Or are they more or less the same?
There are some entries related to this topic on the ifeffit FAQ: http://cars9.uchicago.edu/cgi-bin/ifeffit/faqwiz?req=index But to answer your question directly, I wouldn't read too much into r-factors and reduced chi-squares that are that close. All you know is that both models fit the data reasonably well, but not extremely well. In other words, statistical quality of fit is not distinguishing the models. You should look, however, at the fitted parameters. It may be that fit B, for example, is giving some physically unreasonable parameters (negative sigma2's, or absurd bond lengths, or E0's that are off of the rising portion of the edge, or...) while fit A is not. In that case, fit A is certainly to be preferred. Or it may be that you have external evidence (including theoretical predictions) that model A is preferable. In that case, you can't use EXAFS to SUPPORT the choice of model A, but you can use it to confirm that model A is a POSSIBLE solution, and to extract additional information (i.e. the guessed parameters) on the assumption that it is correct. --Scott Calvin Sarah Lawrence College
Hi Owen, Whether one fit is statistically different from another is addressed by Hamilton (W.C. Hamilton, Acta Cryst. (1965) V. 18, 502-510). This tests is directly applicable to EXAFS data, but there are a couple of caveats. First, the number of data used to determine the number of degrees of freedom is not the number of data points but the number of independent points (Artemis will tell you this). Second, if I recall correctly, the R-factor used by ifeffit is the square of the crystallographic R-factor, so you need to take the square root of the R-factor given by ifeffit to use Hamilton's test. Having said all that, it looks to me like neither fit is significantly better, but I would need to know the number of parameters and number of independent points to be sure. Sincerely, Wayne Lukens On Oct 4, 2005, at 11:07 AM, OWEN N LI wrote:
Hi, I understand R-factor and reduced chi square are statistical ways to see if the model is reasonable (R-factor) and if one model is better than the others (reduced chi square). But how much should I read into it?
I have model A and B, I believe A is more theoretical sound than B. but when I fit them using IFEFFIT, the R-factor and reduced chi square of B is slightly better than A (B: 0.03, 28; A: 0.04, 33). What does that tell me? Is my assumption incorrect? Or are they more or less the same?
Owen
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Hello, Out of curiosity (and maybe also slackness; I peered over Matt's papers, including Iffefit reference manual, but no equation popped to my eyes): can I have a brief refresher on how the R-factor is calculated in Ifeffit? (a reference will do). Thank you in advance, best regards - Michel
Whether one fit is statistically different from another is addressed by Hamilton (W.C. Hamilton, Acta Cryst. (1965) V. 18, 502-510). This tests is directly applicable to EXAFS data, but there are a couple of caveats. First, the number of data used to determine the number of degrees of freedom is not the number of data points but the number of independent points (Artemis will tell you this). Second, if I recall correctly, the R-factor used by ifeffit is the square of the crystallographic R-factor, so you need to take the square root of the R-factor given by ifeffit to use Hamilton's test.
Having said all that, it looks to me like neither fit is significantly better, but I would need to know the number of parameters and number of independent points to be sure.
Sincerely,
Wayne Lukens
On Oct 4, 2005, at 11:07 AM, OWEN N LI wrote:
Hi, I understand R-factor and reduced chi square are statistical ways to see if the model is reasonable (R-factor) and if one model is better than the others (reduced chi square). But how much should I read into it?
I have model A and B, I believe A is more theoretical sound than B. but when I fit them using IFEFFIT, the R-factor and reduced chi square of B is slightly better than A (B: 0.03, 28; A: 0.04, 33). What does that tell me? Is my assumption incorrect? Or are they more or less the same?
Owen
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_______________________________________________ Ifeffit mailing list Ifeffit@millenia.cars.aps.anl.gov http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit
-- Michel Schlegel Commissariat à l'énergie atomique CEN de Saclay, DEN/DANS/DPC/SCP/LRSI Bat 391 - Piece 205B F91 191 Gif-sur-Yvette Cedex, France Ph: +33 (0)1 69 08 93 84 Fax: +33 (0)1 69 08 54 11
On Wednesday 05 October 2005 06:44, Michel Schlegel wrote:
Hello,
Out of curiosity (and maybe also slackness; I peered over Matt's papers, including Iffefit reference manual, but no equation popped to my eyes): can I have a brief refresher on how the R-factor is calculated in Ifeffit? (a reference will do).
Chapter 5 of the old feffit manual: http://cars9.uchicago.edu/feffit/feffit.ps The program has changed but the formula hasn't. B -- Bruce Ravel ---------------------------------------------- bravel@anl.gov Molecular Environmental Science Group, Building 203, Room E-165 MRCAT, Sector 10, Advance Photon Source, Building 433, Room B007 Argonne National Laboratory phone and voice mail: (1) 630 252 5033 Argonne IL 60439, USA fax: (1) 630 252 9793 My homepage: http://cars9.uchicago.edu/~ravel EXAFS software: http://cars9.uchicago.edu/~ravel/software/exafs/
participants (5)
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Bruce Ravel -
Michel Schlegel -
OWEN N LI -
Scott Calvin -
Wayne Lukens