Non-linear curve fitting fail to converge

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Yanxin Liu
Yanxin Liu on 27 Jun 2021
Commented: Bjorn Gustavsson on 28 Jun 2021
I'm using the curve fitting toolbox to fit the data to a function: y = a*(1-b*exp(-c*x)-(1-b)*exp(-d*x)).
For a certain group of data, the fitting fails to converge. (Algorithm: Trust region. The boudaries set for the parameters are: a: 0.25 - Inf, b: 0-1, c: 0-Inf, d: 0-Inf)
For some groups of data, the fitting can converge but the standard error of the fitted parameters are very big.
I have a feeling that this is because my function is overparameterised, but I can't prove.
Thanks a lot in advance.
Bjorn Gustavsson
Bjorn Gustavsson on 28 Jun 2021
Overparameterized? You have some 30 data-points and a 4-parameter model - so some 5 data-points per parameter. I've understood overparameterization as when the model starts to fit to noise in the data. The problem rather seems to be that your model does not capture the data in the first graph. Your model should aproach a while that data seems to trail off towards a "constant growth" - that's not a good match even if your model fits the data reasonably well.

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