| T O P I C R E V I E W |
| espenhjo |
Posted - 04/08/2003 : 07:27:05 AM
When using the NLSF tool one gets an output of the dependency for each fitted parameter.
What exactly says the dependency for the parameter?
I understand that it tells something about the relation between the parameters and that when it is close to one varying one parameter affects another. When fitting several parameters to an exponential curve I get the dependency for each parameter close to one. Is this good or bad? Does it tell anything about the reliability of the estimation?
Regards,
EJ
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| 2 L A T E S T R E P L I E S (Newest First) |
| H.Steen |
Posted - 04/08/2003 : 09:34:19 AM
If the function you are using is on the form A1*Exp((x-x0)/t1), you can rewrite this function as B1*Exp((x)/t1) where B1 = A1*Exp(-x0/t1).
As long as t1 has found its value you can select any combination of A1 and x0 that match B1 = A1*Exp(-x0/t1). They might change several orders of magnitude. However, hopefully can one or more of the parameters be fixed when you study the physical mechanisms involved (x0=start time for example). With a fixed value of x0 you should be able to find a more accurate A1.
In the case above you will get a dependency = 1 and you must fix either x0 or A1 to get and more accurate estimate for the other. If you are not able to fix one or more of the values you must take into account that it is only B1 an t1 in the example above you can find.
[Added:As you might see Easwar wrote the reply while I was writing mine, it looks as our conclutions is the same]
Helge
Edited by - H.Steen on 04/08/2003 09:37:35 AM |
| easwar |
Posted - 04/08/2003 : 09:26:47 AM
Hi EJ,
The following is from the Origin help files, under the topic "When the Fitting Procedure Does Not Converge":
"The parameter dependence (for one or more parameters) is very close to one. This is a certain indication that you have to remove (or fix) one of the parameters whose dependency is close to one since the fit does not depend on the parameter (or a combination thereof) very much."
You could try fixing some of the paramters to specific values (if that makes sense) or try to optimize the equation by reducing the number of parameters.
For example, the equation
y=A*exp(x-x0)
is over-parametrized. If both A and x0 are allowed to vary, the fit will not coverge, and will result in large (close to 1) dependencies for A and x0 since an infinite number of value for A and x0 could satisfy the equation. In this case one can either fix the value of x0 (offset in x), or rewrite the equation as:
y=B*exp(x)
where the parameter B replaces A*exp(-x0).
Easwar
OriginLab.
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