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tony_lincoln
USA
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 Posted - 10/02/2006 : 11:19:22 PM
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Dear colleagues,
I try to fit some curves using either Mono-exponential function
y= A0 + A1*(1-exp(tau1*x))
or Bi-exponential function
y=A0+A1*(1-exp(tau1*x))+A2*(1-exp(tau2*x)),
For some curves (I did global fitting), I will get strange values if I use Mono-exponential function, like: Tau = -1.55E-06 (Tau should never be negative),
but still the same curves, if I use Bi-exponential fitting, I will get positive values which look reasonable, like: Tau1 = 0.13609, Tau2 = 0.13575.
But for some other curves, I was suggested (for example, by Larry in OriginLab GZ Office) that Bi-exponential function is over-parametrize (The parameter "Dependency" value in NLSF dialog is close to 1), so the result of Bi-exponential fitting is unreliable.
So, my question is, what is the standard to choose Mono-exponential or Bi-exponential fitting ??? Thanks :-)
Tony |
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larry_lan
China
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Posted - 10/03/2006 : 09:52:35 AM
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Hi Tony:
Maybe you can fit both function and compare the R^2 of the two model to decide which one is better.
By the way, you can also use Origin's build-in function to fit your data, it runs much faster and auto initialize the parameters. Take mono-exponential function as example:
y = A0 + A1 * (1-exp(tau * x))
= (A0 + A1) - A1*exp(tau * x)
= A0' + A1' * exp(tau * x)
This just is the function "ExpDec1" in "Exponential" category:
y = y0 + A*exp(-x/t1)
After you fit, you can get the parameters value by:
tau = -1/t1
A1 = -A
A0 = y0 + A
Larry
OriginLab Technical Services
Edited by - larry_lan on 10/03/2006 10:21:28 AM |
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easwar
USA
1965 Posts |
Posted - 10/03/2006 : 11:59:01 AM
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Hi Tony,
Note that you can place bounds and constraints on parameters, such as not allowing your tau1 parameter to go below zero.
As to the question on how to decide if mono or bi exponential is the right function for your data, that can be done using statistical tests. Once you have performed fitting on the data with both functions, the Sum of Squares, degrees of freedom etc values from the fit can be used to compute an F-test value or the Akaike Information Criterion test.
Origin currently does not include tool to compare two models to one dataset, but there is a temporary solution available in File Exchange. The Origin C code associated with that download has details on the formula. You can simply use the formula and perform hand computation as well:
http://originlab.com/FileExchange/details.aspx?fid=64
Easwar
OriginLab
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Mono-exponential or Bi-exponential fitting ???