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Thread: Curve Fitting for 4 parameter logistic equation

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    Curve Fitting for 4 parameter logistic equation

    I am new to this math forum, and I hope that this is an appropriate place to post this question...

    I need to fit data to the "4 parameter logisitic equation" for biological relationships. Essentially the equation is the following:

    y = ((A-D) / (1+ ((x/C)^B))) + D

    Basically, I'll have an equally sized array of x and y values that are used to solve for variables A,B,C, and D. Right now I need to use one function from a statistical package to solve for this. I'd like to reproduce this function in the language that I am confortable with (VBA), but don't have a clue about how to approach the math! Does anyone know how to do this?!

  2. #2
    pathfinder NotLKH's Avatar
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    I think your equation can be expressed more cleanly as :



    which could lead to some more simplification useing log identities.

    However, I'm stumped on the direction to go to solve for A, B, C, and D when you have sets of {X, Y}.
    It seems like it will require alot of interpolation.
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    Hyperactive Member DavidHooper's Avatar
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    I think you could use the Solver feature in Excel to find A, B, C & D for given x & y, although your post suggests you want/need to use statistical functions. Post back if we can help you with the Solver feature.
    There are 10 types of people in the world - those that understand binary, and those that don't.

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    Thanks NotLKH and David for your insight so far. I really appreciate the input. Ideally, I'd like to use pure VB or VBA code. The vendor for the package that I have been using so far said their non-linear regression algorithm is based on the Levenberg-Marquardt method in the publication Numerical Recipes in C (http://chemistry.about.com/gi/dynami...Fbookcpdf.html). Being a dummy in C, C++, and matrix algebra, it all looks like jibberish to me! Does anyone know how to apply the stated method for the model that I originally posted?! From the looks of it, this is starting to be a bear of a project!

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    Typically, I would have 18 {X,Y} pairs. The data is made up of triplicate observations at 6 input values. I hope this helps!

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