| T O P I C R E V I E W |
| shpak27 |
Posted - 03/21/2013 : 11:43:53 AM
Hi.
I am fitting data to tge exponential decay using in the vqluesnstrumental weights. When the box Use reduced chi-square is marked the parameters errors are sometines even greater the values and it is physically unacceptable. But if I uncheck this option the errors become reasonables. I understand that using the instrumental weights it is not necessary to include the reduced chi square for the correlation matrix. From tge other side, if the curve fits very good to the data the reduced chi-squareshould be closed to unity and does not affect in this case.
Does anybody know in which cases it is necessary to include the reduced chi-sqr for tgeerrors of parameters? There is no infornation in Origin manual about this. In my case I need smaller errors and uncheck the reduced chi-sqr box is great, but I do not if it is correct.
Thanks in advance for everybody. |
| 4 L A T E S T R E P L I E S (Newest First) |
| shpak27 |
Posted - 03/21/2013 : 5:12:12 PM
I will try to explain it again. 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 again |
| matthew@originlab.com |
Posted - 03/21/2013 : 1:58:46 PM
Hi,
Using the Reduced Chi-Square value simply changes how your parameter error is reported. Leaving the box unchecked simply divides the error by the square root of the Reduced Chi-Square value, but in each case the analysis and fit itself are exactly the same.
You may also want to read this topic to see if it answers your question:
http://www.originlab.com/forum/topic.asp?TOPIC_ID=6819
Matthew
OriginLab |
| shpak27 |
Posted - 03/21/2013 : 12:46:24 PM
Dear Matthew.
Thanks for reply. I have already read this help manual and the only thing they say is that you can use the reduced chi-square for the errors when you use the weights. The problem is if it is correct to do it or not. If you do not use reduced chi-sqr with instrunental weights you will get much smaller errors, like 10 or 100 times. The question is when shoul I check this box and when not. For example if I fit data to parabola without weighting errors the Use reduced chi-square is marked automatically and you csn not uncheck it. It is clear that if you use reduced chi-square you are multiplying the diagonal elements of the correlation matrix by a
factor of s^2 and you will get higher errors of tge fitting parameters. Normally one neds smaller errors and uncheck the Use reduced chi-sqr is one possible way to do it. The question is whether it is the correct way to proceed o r not when you use instrumental weights of errors. |
| matthew@originlab.com |
Posted - 03/21/2013 : 12:19:46 PM
Hi,
I was able to find some information on this hidden deep in the help manual.
"Use Reduced Chi-Sqr
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: #963;2(F'F) - 1, otherwise, (F'F) - 1."
I found this under the Main help guide by going to Regression and Curve Fitting > Nonlinear Curve Fitting > NLFit Dialog Box > Settings Tab, and scrolling down to section titled Advanced
I hope this is sufficient
Matthew
OriginLab |
