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sterw
Netherlands
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 Posted - 05/09/2008 : 05:55:18 AM
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Origin Version : 8 SR1
Operating System: XP
In the NLFit dialog under the Settings -> Advanced tab there is a checkbox for using the reduced chisqr in the parameter error estimation. It is checked by default. Although I would prefer it not to be checked by default, more importantly I would like an indication in the results sheet whether or not it was checked during the fitting. At present I cannot find that out afterwards.
Thanks, Wim.
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easwar
USA
1964 Posts |
Posted - 05/09/2008 : 09:57:48 AM
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Hi Wim,
Thank you for pointing this out. We will look into adding a footnote.
For now, if your output is set with Recalculate of Auto or Manual, you can bring back the dialog by clicking on the lock in the output and select Change Parameters, and the dialog will then load with the settings you had used when the operation was performed.
Easwar
OriginLab
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ahlers01
Germany
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Posted - 05/10/2008 : 01:49:13 AM
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Hi!
Maybe I'm hijacking this thread, but I have a question relating to the reduced chi square.
Basically I have problems understanding its definition. In the online help (under 'Linear Regression Dialog') I find:
"Available when fit with weight, This check box only affects the error on the parameters reported from the fitting process, and does not affect the fitting process or the data in any way. By default, it is checked, and the covariance matrix is calculated by: σ(X'X)^-1, othervise, (X'X)^-1."
And under the link "http://www.originlab.com/www/support/resultstech.aspx?ID=710&language=English&Version=All" I read:
"Origin reports a reduced chi-square value after a nonlinear regression has been performed. This value is the Chi-Square divided by DOF where degrees of freedom is (N-P). N being number of data points and P being number of parameters in the fitting function that is being used...."
Please forgive my ignorance, but I cannot see immediately why these should be the same definitions.
-Franz |
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greg
USA
1378 Posts |
Posted - 05/14/2008 : 3:32:44 PM
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Reduced-Chi-Square is Chi-Square divided by the degrees of freedom, always, no exception. ( Except that we sometimes say Chi-Square when what we really, really mean is Reduced-Chi-Square  )
When you are fitting, we report an error value for each parameter.
When there is no weighting involved, that error is the square root of the product of Reduced-Chi-Square and the appropriate diagonal element of the Variance-Covariance matrix. (Internal unless explicitly requested.)
This is the same case when you DO fit with a weight and you check to use Reduced-Chi-Square in error calculations. But if that box is NOT checked, then the error is just the square root of the appropriate diagonal element of the Variance-Covariance matrix.
Hope this makes it a little clearer.
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shpak27
Spain
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Posted - 03/21/2013 : 3:23:44 PM
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I have similar situation. I am fitting the data to exponential decay with instrumental weights of errors of Y. Depending on checked or unchecked box of Use reduced chi-sqr I get the same values but different errors for parameters I introduce. It is normal because in the first case (Use reduced chi-sqr checked) the diagonal values of the correlation matrix, i.e. the errors of the parameters, are multiplyed by s^2, that is Chi/DoF and are higher than the errors obtained with the option Use reduced chi-sqr unchecked. Up to her everything is clear.
My question is: what is the correct way from the mathematical point of view? Because it is not the same to have 300+-30 ms of the half-life for a nucleus (instrumental weights and box Use reduced chi-sqr checked) than 300+-5 ms (instrumental weights and box Use reduced chi-sqr (instrumental weights and box Use reduced chi-sqr unchecked). It is clear that one prefers the second option becasuse the error is much smaller and physically more acceptable. But is this the way to do it? Is it correct just to choose smaller errors and that is all? There should be an explanation. Does anybody have it? I think that if I use instrumental weights for the errors it is not necessary to include the reduced chi-square but I can proove mathematically.
Thanks in advance. |
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Sam Fang
292 Posts |
Posted - 03/21/2013 : 11:15:18 PM
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If you use weight in fitting, you'd better set Use reduced chi-sqr unchecked because fitted parameter's error can reflect the magnitude of the weight in this way.
In fact you can try the following case:
1. Set Use reduced chi-sqr checked.
2. Multiply the weight for each point by a factor 10.
3. You will find the standard error of parameter is the same as that when the weight is not multiplied.
This means if Use reduced chi-sqr is checked, fitted parameter's standard error can only show the effect of relative magnitude among weights, and it can't show the effect of the magnitude of each point's weight.
This issue may be similar to the last reply in the post:
http://www.originlab.com/forum/topic.asp?TOPIC_ID=18272
Sam
OriginLab Technical Services |
Edited by - Sam Fang on 03/21/2013 11:16:42 PM |
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shpak27
Spain
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Posted - 03/22/2013 : 05:32:41 AM
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Thank you Sam, think I get it.
Cheers |
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reduced chi-sqr