Chi-square error-XPS multipeak fitting

I looked at your data and have several comments. I actually can't solve the problem why you are getting this Chi square value with the particular approach you are taking, but maybe by changing the processing the problem will solve itself.
First a question: Is there any particular reason why you are using the old Multipeak Fitting package (version 1.4) and not the new one (version 2.0)? You didn't write your Igor version but then I guess you don't have the latest version (6.34).
OK, here are my comments (also see the attached Igor file).

1) I would recommend to use the proper wave scaling instead of the xy-data approach. This will make things much easier. Either scale the y-wave according to your x wave values manually or you might write a simple script to do this automatically on load (I have the same problem for much of my data and thus have everything fully automated). If this explanation doesn't make ay sense to you, you might want to consider reading about it by executing the following in the command line: DisplayHelpTopic "The Waveform Model of Data"

2) You seem to simple assume that the background can be described by a cubic spline. I strongly recommend to do a proper background processing to your data first or your fit may get very wrong depending on the amount of background signal. The brute force way is to apply at least background subtraction after the Shirley method for XPS. I did this to your data in the attached file. But I see that there is some visible shape in your background (which is common) like the enhanced region around 180. This would actually require a more sophisticated approach to remove the background signal completely (maybe the Tougaard model with the right parameters would already help).

3) Your peaks seem to be not purely of Gaussian shape. I have no information about your experimental parameters or the sample you are measuring, but depending on natural line shape and resolution, a Voigt shape may be more appropriate. But this depends on several things. I tried to fit this shape with mixed results. It also depends somewhat on what you want to achieve with the fit.

Hope that helps a bit.

Attachments Fit Test.pxp (80.83 KB)

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May 15, 2014 at 10:55 pm - Permalink

manojphy

Dear Chazo,

Thank you very much for your response and sorry for late reply. I am using IGOR Pro 5.04B. I did the wave scaling using Interpolate. After scaling I tried the fitting but could not succeed, still getting the high value of Chi-square. I don't find all the command for peak fitting and proper background subtraction. I need you help in this regards. Please suggest me where to find all the commands required for background subtraction and peak fitting. I think my package is also old so I am unable to use advance options for peak fitting and background subtraction. I would appreciate if you could please send the script file for the same.

Best Regards,
manojphy

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May 20, 2014 at 12:55 am - Permalink

chozo

First let me note that, of course, scaling the wave does not solve the particular problem but is a rather general recommendation of how to use data in Igor, as it will get rid of a separate x-wave and thus many annoying "extra steps".

I see that you use Igor 5, which explains why you are using the old (or with this version only) MPF procedure. As for the background subtraction, I'm afraid there is currently no implementation of PES background subtraction methods in Igor Pro. I wrote a program for this, which I am considering to release here. But even if I did, there is no way it runs in Igor 5 (because it would be a time-consuming task to make the procedure compatible with Igor 5). So, I am wondering if you can't achieve this already with your original measurement software. Many of these programs already have at least a simple Shirley type background procedure implemented. You may want to take a look into the manual of your particular program.

Regarding the fitting and Chi^2, I actually don't thing you are seeing an error here, but rather normal behavior. I am no expert on statistics or fitting, but looking around in the Igor help revealed this:

ChiSquare: A measure of the goodness of fit. It has absolute meaning only if you've specified a weighting wave containing the reciprocal of the standard error for each data point.

So, I actually get an equally high Chi^2 when fitting my data, not only with MPF but also I normal fits. So I think that high number is expected. But maybe the experts here can say more about this.

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May 20, 2014 at 03:02 am - Permalink

johnweeks

Your chi-square value is large because your data values are large. When you add up a bunch of big numbers, the result is big :)

Igor simply reports Sum(Yi - YHati)^2, so if your data values are large, then the difference between the data and the model will be relatively large. Square and sum, and you have a big number. The important thing is for the chi-square value to be the minimum value; the absolute number has significance only relative to your data values.

John Weeks
WaveMetrics, Inc.
support@wavemetrics.com

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May 20, 2014 at 10:49 am - Permalink