Hi,
I'm analysing a dataset containg XY data and I would like to fit a curve to my data.
My intention is to model the response of Y as a function of X. The function I'm looking for should have the following characteristics:
- The y value should be bounded between a minimun (0) and a maximum value (100)
- decreasing function with high Y values at low X value
- an inflection point where the function decreases slower until reaching an horizontal asymptote.
I'm intersted in estimating two important parameters: the asymptote and the inflection point
The function should be similar a sigmoid function (e.g. Weibull model which allows to estimate the asymptote, the scale (inflection point) and the shape (the growth rate) of the curve) but with a decreasing trend (as opposed to a sigmoidal function).
Thank you!
Hi. One potential solution would be to generate the square term for your x variable and run a model of Y = a + bX + cX^2. This would show you the effects of X on Y along the whole distribution. Hope this helps? Cheers, Marc
Take a look at this paper. It could help.
Thinking about U: theorizing and testing U- and inverted U-shaped relationships in strategy researchRichard F. J. Haans, Constant Pieters and Zi-Lin He
Article first published online: 28 JUN 2015 | DOI: 10.1002/smj.2399
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what about a good old stretched exponential ?
f(x) = (100-finfinity)*exp(-(x/xc)b) + finfinity
it has most of the characteristics you require but it is quite tricky to fit ...
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3966632/
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Thank you for the answers. The stretched exponential function seems good but is quite hard to fit for me. I use curve expert software to fit my data and so I prefer models that have been included in the software or other ready to use,
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i may be wrong but curve expert allows the definition (and parameter fit) of custom models doesn't it ?
the stretched exponential model is not very hard to define and would be a good test for the nonlinear fit software !
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of course, if you set b = 1 or b = 2 you recover very classical (and easy to fit) models but they are far less expressive
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Effectively curve expert allows the definition of custom model. I'm sorry but I'm not a mathematician (or statistician) and I find hard to custom this model. I've tried but without good results.
Thanks
Dear Sir,
With best wishes please, try least square for exponential distribution function.
yours sincerely,
saeid parsa
Did you try curve fitting toolbox in Matlab?
You should just add your X and Y, then type "cftool".
After that, you can select your suitable function and compare RMSE and R2.
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