The Origin Forum - Reply to Topic: Nonlinear Curve Fitting
Jean Louis Gallani:
You write:
Has anyone ever encontered a 'stuck' fitting procedure, which
keep returning the same wrong values and does not try to improve
chi-square? This seems to happen when fitting many times with
the same fitting function.
Response
It is not uncommon for any fitting procedure, including Origin's non-linear curve fitter, to fail to converge. There are many reasons for this behavior, but in your case I believe the problem to be related to the fitting algorithm (Levenburgh-Marquardt)
finding a relative (local or false) minimum, as opposed to an absolute minimum for the sum-of-squares.
In other words, the fitter goes through an iterative (step-by-step) process that essentially attempts to minimize the sum-of-
squares by changing the parameter values in small amounts. When your data is somewhat scattered, the iterative process can
reach a relative minimum sum-of-squares value before finding the actual absolute minimum. In the fitter's mind, since the ensuing sum-of-squares values are higher than this local minimum, it thinks it is done. It does not bother to look any further for an even smaller value for the sum-of-squares. Thus the fit does not converge (or improve chi-square).
In order to test this theory you might want to try the following:
- Note the values of the parameters and the Chi-Sqr from the first fit.
- Make a large change to the initial values of one or more parameters and run the fit again.
- Repeat step 2 several times.
- Ideally, the curve fitter will end up reporting nearly the same parameter values regardless of the initial values. However, if the values are different, accept the ones with the lowest Chi-Square.
Furthermore, if they are different, this suggests that the fitter had reached a relative minimum prior to changing the parameter values. I should stress that this is not a bug, but merely something that is intrinsic to nonlinear curve fitting (nonlinear regression).
Another explanation of this can be found in the Origin 5.0 User's Manual on page 536 or the 4.0/4.1 Manual on page 346. There are
also some other theories presented there which may be the cause of your problems. Take a look at those and try the suggestions that are there. You may find that they are helpful in improving your fit.If you have any other questions or comments please feel free to contact your local Origin technical support representatives.
Sincerely,
Ryan Toomey
Technical Support engineer
Microcal Software, Inc.
[This message has been edited by rtoomey (edited 09-24-98).]
