Meaning of linear combination fit reports
Hi everyone, I doing LCF on my XANES data. I wonder if someone can tell me the meaning of the values in parentheses following the weight value in the Fit results window?. I looked into the respective document section of the Manuel but could not find the answer, yet. I am asking because I did a Fitting with over 20 standards (STD) to find all combination of max 4 standards which describe my unknown sample spectra. This results in a lot of combination with similar chi-square(reduced) and R-values. I know a relative changes between these values are more probably meaningful than absolute values. A lot of the possible combinations provided by after the fit yieled combinations with at lest on STD having a weight of 0.000. (Fit 1). I thought that this would mean, that 3 standards are sufficient to describe the system. However, repeating the fit with only the three standards with weight > 0.0 yielded a complete different proportions (Fit 2). How can this be explain and how should I deal with combinations or standards having a weight of 0.000? Thanks a lot for your thoughts and suggesting, Cheers Paul *Results **Fit 1:* 3: STD3 0.324(0.025) 7: STD7 0.686(0.021) 20: STD2O 0.127(0.016) 27: STD27 0.000(0.036) vs. *Results Fit 2:* 3: STD3 0.473(0.019) 7: STD7 0.620(0.023) 20: STD20 0.000(0.030)
On 08/18/2014 10:12 AM, Jens Kruse wrote:
I doing LCF on my XANES data. I wonder if someone can tell me the meaning of the values in parentheses following the weight value in the Fit results window?. I looked into the respective document section of the Manuel but could not find the answer, yet.
If you are asking the simplest interpretation of your question: they are the evaluated uncertainties, also known as error bars. If you are asking what kind of uncertainties: they are the diagonal elements of the covariance matrix scaled by the square root of reduced chi-square. Thus they are 1sigma uncertainties, presuming that you trust that the only mistake made in evaluation of statistic is evaluation of epsilon (which Athena does not attempt for an linear combination fit). The scaling of the diagonal elements yields defensible 1sigma error bars with the assumption that each fit is a good fit -- an assumption that it is up to you to defend. As I will discuss below, you should not trust that evaluation of epsilon is your only problem.
I am asking because I did a Fitting with over 20 standards (STD) to find all combination of max 4 standards which describe my unknown sample spectra. This results in a lot of combination with similar chi-square(reduced) and R-values. I know a relative changes between these values are more probably meaningful than absolute values. A lot of the possible combinations provided by after the fit yieled combinations with at lest on STD having a weight of 0.000. (Fit 1). I thought that this would mean, that 3 standards are sufficient to describe the system. However, repeating the fit with only the three standards with weight > 0.0 yielded a complete different proportions (Fit 2). How can this be explain and how should I deal with combinations or standards having a weight of 0.000?
You seem to have allowed the fit to run without the constraint that the weights add up to 1. The reason Athena allows you to lift this constraint is to accommodate the situation where you have some systematic uncertainty in how your spectra are normalized. To say that another way, if you could somehow know that you have done a perfect job normalizing your data and all your standards, it would not be necessary -- indeed, it would be a mistake -- to lift the constraint that the weights add to 1. In you case, it is clear (or at least as clear as it could be, given that I have not seen your data) that you have issues with normalization. Fit #1 has weights that sum to 1.137. Fit #2 has weights that sum to 1.093. Thus, your inconsistencies in normalization have introduced systematic error into your analysis at the level of about 10%. In fit #1, standard 20 accounts for about 10% of the spectral weight. That is, it's contribution to the fit is at the level of the systematic uncertainty in your model. When you remove standard 27, the fit finds a different way to resolve the model. I would guess -- although I have no way of proving this in the absence of data -- that the contours of the surface in the space of your fitting parameters is altered by the presence of a second standard whose contribution is hard to distinguish from the effect of error in normalization. So my conclusiona (again, not authoritative since I have not seen the data) are: 1. your data likely contains only standards 3 and 7, it likely does not contain any of 20 or 27 2. you seem not to have done a very good job normalizing your data in a consistent manner 3. your uncertainties are at about the 10% level, when you include the systematic effect of inconsistent normalization -- the purely statistical uncertainties represented by the reported error bars are much smaller, thus your error budget is dominated by systematics HTH, B -- Bruce Ravel ------------------------------------ bravel@bnl.gov National Institute of Standards and Technology Synchrotron Science Group at NSLS --- Beamlines U7A, X24A, X23A2 Building 535A Upton NY, 11973 Homepage: http://bruceravel.github.io/home/ Software: https://github.com/bruceravel Demeter: http://bruceravel.github.io/demeter/
Hi Bruce, thanks a lot for the very fast response. Maybe you are right and I did not well on normalization but I tried to be consistent as much as possible. Find attached a demo Athena project. The fit the box "to weight to sum to 1" was checked. But you are right it did still not sum up to 1. But why? Or did I something wrong? Thanks, PJ Am 18.08.2014 16:48, wrote Bruce Ravel:
On 08/18/2014 10:12 AM, Jens Kruse wrote:
I doing LCF on my XANES data. I wonder if someone can tell me the meaning of the values in parentheses following the weight value in the Fit results window?. I looked into the respective document section of the Manuel but could not find the answer, yet.
If you are asking the simplest interpretation of your question: they are the evaluated uncertainties, also known as error bars.
If you are asking what kind of uncertainties: they are the diagonal elements of the covariance matrix scaled by the square root of reduced chi-square. Thus they are 1sigma uncertainties, presuming that you trust that the only mistake made in evaluation of statistic is evaluation of epsilon (which Athena does not attempt for an linear combination fit). The scaling of the diagonal elements yields defensible 1sigma error bars with the assumption that each fit is a good fit -- an assumption that it is up to you to defend.
As I will discuss below, you should not trust that evaluation of epsilon is your only problem.
I am asking because I did a Fitting with over 20 standards (STD) to find all combination of max 4 standards which describe my unknown sample spectra. This results in a lot of combination with similar chi-square(reduced) and R-values. I know a relative changes between these values are more probably meaningful than absolute values. A lot of the possible combinations provided by after the fit yieled combinations with at lest on STD having a weight of 0.000. (Fit 1). I thought that this would mean, that 3 standards are sufficient to describe the system. However, repeating the fit with only the three standards with weight > 0.0 yielded a complete different proportions (Fit 2). How can this be explain and how should I deal with combinations or standards having a weight of 0.000?
You seem to have allowed the fit to run without the constraint that the weights add up to 1. The reason Athena allows you to lift this constraint is to accommodate the situation where you have some systematic uncertainty in how your spectra are normalized.
To say that another way, if you could somehow know that you have done a perfect job normalizing your data and all your standards, it would not be necessary -- indeed, it would be a mistake -- to lift the constraint that the weights add to 1.
In you case, it is clear (or at least as clear as it could be, given that I have not seen your data) that you have issues with normalization. Fit #1 has weights that sum to 1.137. Fit #2 has weights that sum to 1.093. Thus, your inconsistencies in normalization have introduced systematic error into your analysis at the level of about 10%.
In fit #1, standard 20 accounts for about 10% of the spectral weight. That is, it's contribution to the fit is at the level of the systematic uncertainty in your model. When you remove standard 27, the fit finds a different way to resolve the model. I would guess -- although I have no way of proving this in the absence of data -- that the contours of the surface in the space of your fitting parameters is altered by the presence of a second standard whose contribution is hard to distinguish from the effect of error in normalization.
So my conclusiona (again, not authoritative since I have not seen the data) are:
1. your data likely contains only standards 3 and 7, it likely does not contain any of 20 or 27
2. you seem not to have done a very good job normalizing your data in a consistent manner
3. your uncertainties are at about the 10% level, when you include the systematic effect of inconsistent normalization -- the purely statistical uncertainties represented by the reported error bars are much smaller, thus your error budget is dominated by systematics
HTH, B
participants (3)
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4.meinereiner＠gmx.de -
Bruce Ravel -
Jens Kruse