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- nonlinear fit with fixed starting point

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Sep 29, 2014 7:59 AM
(4302 views)

Hi,

As I am exploring the functions of JMP more and more, here is one I haven't been able to crack yet...

I am trying to fit an exponential 3 parameter function through some datapoints that report yield in response to a certain dosage of products. I can get the nonlinear fit of the model, but what I would like to be able to do is to force the fit to start at the response variable for the dosage zero.

So if the model is y=a+b*exp(c*x), where x=0. I guess my real question is if you can restrict the model and force it through a given point.

Any ideas on how to get this to work?

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If I understand you correctly, you want your model f(x) = a+b*exp(c*x) to agree exactly with the data value you have for x=0, call it y0. Then for x=0 you want

y0 = f(0) = a + b

Solving, say, for a, we get a = y0-b. In other words you can reduce the number of parameters from 3 to 2 by fitting the model for b and c (and get a=y0-b).

f(x) = y0-b + b*exp(c*x) which will automatically satisfy f(0) = y0.

There is also an option in the nonlinear platform dialog to specify constraints on the parameters but the direct route above is the simplest way to approach your problem as I understand it.

Michael

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If I understand you correctly, you want your model f(x) = a+b*exp(c*x) to agree exactly with the data value you have for x=0, call it y0. Then for x=0 you want

y0 = f(0) = a + b

Solving, say, for a, we get a = y0-b. In other words you can reduce the number of parameters from 3 to 2 by fitting the model for b and c (and get a=y0-b).

f(x) = y0-b + b*exp(c*x) which will automatically satisfy f(0) = y0.

There is also an option in the nonlinear platform dialog to specify constraints on the parameters but the direct route above is the simplest way to approach your problem as I understand it.

Michael

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Re: nonlinear fit with fixed starting point

Ah,

It's always so simple when someone explains it... Great tip, thanks!