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
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