What methods could be used to fit to this case?

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Sun, 04/14/2013 - 08:28 am

I have a set of N data curves and an equation in three fitting variables (K, A, and ro) to fit each curve. Two of those variables (K and A) must be exactly the same across all N sets. One of the variables (ro) should be different for each set. The approximate constraint ranges of K, A, and ro are known in advance.

How should I set up the fitting for this problem?

My first approach will be to fit each curve separately in order to get first-guess parameters for K, A, and ro. I would very much like to take advantage of the statistical improvements in K and A that would come from doing a combined fit on the N sets for these two parameters only, in the meantime allowing ro to vary.

I had an idea to concatenate the N data sets and create one general purpose fitting equation. The form of the fitting equation would end with N + 2 parameters (K, A, and ro[1 .. N]). I suspect this should work, though I hesitate to think about inconsistencies at boundaries or the enormity of the fitting equation as N gets large. Right now, N ~ 10.

Does a different and more elegant method exist to tackle such a problem?
jjweimer wrote:
How should I set up the fitting for this problem?

You've just described global fitting. Any reason you can't simply use Igor's global fit package? (analysis -> packages -> global fit).

jjweimer wrote:
I had an idea to concatenate the N data sets and create one general purpose fitting equation. The form of the fitting equation would end with N + 2 parameters (K, A, and ro[1 .. N]). I suspect this should work, though I hesitate to think about inconsistencies at boundaries or the enormity of the fitting equation as N gets large. Right now, N ~ 10.

This is how the global fit package works. I'm not sure what you mean about inconsistencies at boundaries - the fitting function must know how the different datasets are grouped into the single bigger dataset. The global fit packages will take care of this for you.

April 14, 2013 at 10:08 am - Permalink

741 wrote:
jjweimer wrote:
How should I set up the fitting for this problem?

You've just described global fitting. Any reason you can't simply use Igor's global fit package? (analysis -> packages -> global fit).


No reason other than ignorance.

Seems it is time to play with some tutorials.

--
J. J. Weimer
Chemistry / Chemical & Materials Engineering, UAHuntsville

April 15, 2013 at 10:30 am - Permalink