Solved – Curve fitting and max slope calculation

correlationlogisticregression

I have a dataset:

  • X variable is date (from April to October)
  • Y variable is vegetation biomass data

In my study area, growing season starts around April when vegetation biomass is low and peaks around at the end of August when biomass is highest, and finishes around October.

The purpose is to determine the exactly date when the vegetation biomass increased at maximum during the start of growing season.
It should be in April.

First, I did the curve fitting using Sigmoid, logistic, 4 parameter method which was the best fit for this dataset. And I got a formula of sigmoid, logistic 4 parameter method.

Now, how can I calculate maximum increase date of vegetation biomass from curve fitting line to accomplish the purpose as mentioned above?

Thanks a lot.

Best Answer

You basically need to differentiate the sigmoid to get some bell-like curve; this is how it looks like for standard sigmoid $1/(1+e^{-t})$:

enter image description here

Then it will be only a peak finding. You can do this either analytically from the fit, or calculate the differences from the data and look for a peak there.

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