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Bulkovnik
3 Posts |
 Posted - 04/20/2020 : 06:06:15 AM
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Origin: 2018G 64-bit b9.5.0.193
Operating System: Windows 10
Hello everyone,
this is less of a technical question and more about the analysis itself. I am analyzing data in order to determine transport mechanisms. Most of the equations can be linearized so that every data points gets the same weight. However, one group of mechanisms consist of a hyperbolic sine with various pre-sinh-functions so I can't linearize that plot.
Of course for a serious analysis it would be desirable that like in the linearized plots every data point should have the same weight while in a direct plot the higher values intrinsically get a higher weight.
Now my question is: which of these weighting methods:
https://www.originlab.com/doc/Origin-Help/FIt-with-Err-Weight
accounts for that? As far as I can see, the "statistical" and the "Variance ~ y^2" seem to account for the absolute value, so should I take those or another one? |
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YimingChen
1592 Posts |
Posted - 04/20/2020 : 10:35:42 AM
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Hi,
As you mentioned "a direct plot the higher values intrinsically get a higher weight", I assume you would like to use the y value as weight. Then you should use Direct Weighting (=ci), and set Weight Data to your y value column.
James |
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Bulkovnik
3 Posts |
Posted - 04/21/2020 : 03:34:36 AM
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Hi James,
actually, I want to do the opposite: if you fit an exponential function directly in a non-linearized plot, the high value data are intrinsically weighted strongly and I want to compensate for that. That means I want to give the low y values a relatively stronger weight.
This is why I suggested the "statistical" and the "Variance ~ y^2" in my original suggestion because they weigh somehow on the reciprocal value; however, I am not sure that this has the same effect on the weighting as the linearization of the simple exponentials would have.
I could also imagine doing the direct weighting with a (w*sinh[x])^-1 function, but I'm not sure what w value I would pick to make this serious. |
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YimingChen
1592 Posts |
Posted - 04/21/2020 : 11:32:50 AM
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Hi,
Based on the calculation of chi-square in weighted fitting (check link below), it is suitable to use "Variance ~ y^2" as weight. But if the variation of each point is a concern, then more proper way would be to take logarithm of the y values and run linear fit.
https://www.originlab.com/doc/Origin-Help/NLFit-Theory#Weighted_Fitting
James |
Edited by - YimingChen on 04/21/2020 12:24:21 PM |
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Bulkovnik
3 Posts |
Posted - 04/22/2020 : 05:46:07 AM
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| OK, I'll use "Variance ~ y^2" then. |
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Which weighting scenario matches the issue?