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giordandue
Italy
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 Posted - 09/11/2024 : 03:43:22 AM
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Dears, I observe that once defined range of input parameters for user defined function fitting, the resulting 95% Confidence limits (LCL and UCL) for the same parameters are out of the defined intervals and without any sense... For esample, I fix the range of rock uniaxial strength 50<UCS<100MPa and similarly for other two independent input parameters, and I derive 95%LCL=-4080 and 95%UCL=4280 (unit=MPa).
Note that the limits of input intervals are consistent with the variability of input points to be fitted.
Thank you in advance for your help |
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YimingChen
1594 Posts |
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giordandue
Italy
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Posted - 09/11/2024 : 09:46:47 AM
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Thank you James for your comment. In reality, it is still unclear to me how it is possible to get so different results for each dependent parameters than the relative input ranges. Just as an example, I enter data points to be fitted as some simple equation results y=f(x1,x2..) where x1, x2... are the independent values with a defined range, and of course I enter values in the range for each parameters.
In any case will try to understand better the formulation you suggested. |
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giordandue
Italy
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Posted - 09/11/2024 : 10:03:02 AM
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| "..for each independent parameters" |
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YimingChen
1594 Posts |
Posted - 09/11/2024 : 10:44:08 AM
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I am getting confused. Assume we are fitting with function y = a*x1+b*x2+c. Are you fixing the range of the fitting parameters (a, b,c) or the independent variables (x1, x2)? When you say confident limits, are you talking about the CIs of the fitting parameters or the predicted y value?
Could you also share your project file here?
Thank you.
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giordandue
Italy
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Posted - 09/13/2024 : 02:55:39 AM
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James, as you previously asked, I attach the file to be sure that there is not misunderstanding..
I input the ranges of some parameters (GSI, mi..) included in the function y=f(x) and I derive resulting LCL-UCL of these parameters extremely out of the ranges.
https://my.originlab.com/ftp/forum_and_kbase/Images/grs_test.opj |
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YimingChen
1594 Posts |
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giordandue
Italy
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Posted - 09/13/2024 : 11:04:58 AM
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Thank you again James...
Among other, it seems to me interesting that "over-parameterization does not necessarily mean that the parameters in the model have no physical meanings. It may suggest that there are infinite solutions and you should apply constraints to the fit process".. |
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Sam Fang
292 Posts |
Posted - 09/14/2024 : 07:57:07 AM
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Hi giordandue,
"apply constraints" means to fix parameters or apply constraints among parameters.
But your fitted result is not caused by over-parameterization, but your input data itself.
It is obvious that your input data includes three different types: rows 1-29, 30-58, 59-87.
When I fit these three segments separately, parameters are:
sigci mi GSI
1-29: 50 8 40
30-58: 75 10 50
59-87: 100 12 60
And all parameters' standard errors are very small, so LCL and UCL are very close to fitted parameters.
Therefore, we suggested you fit three segments separately instead of fit all together because three parts are quite different. Otherwise, residual sum of squares in the fit will be very large, and the standard error of parameters will also be very large.
Sam
OriginLab Technical Services |
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giordandue
Italy
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Posted - 09/15/2024 : 03:16:48 AM
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| Hi Sam, thank you for your suggestion. I understand your point and I need to clarifiy the following. The analysis is just an exercise, with objective of estimating the 95% LCL for using in design the corresponding parameters (GSI, mi,sigci..). As you remarked, in place of experimental data to be fitted, I used the main equation y=f(x_gsi,mi,sigci) to derive the 3 sets of points for min-med-max parameters setting, and I launched the fitting analysis with reference to the resulting values. In the specific case, You suggest to fit separately the three segment (for min-med-max), but how consequently to derive the "overall" 95% LCL, if possible? |
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Sam Fang
292 Posts |
Posted - 09/18/2024 : 03:18:21 AM
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Hi giordandue,
If you can estimate the mean and standard error of y for each x according to your min-med-max y data, you can fit your mean data, with standard error as instrumental weight, and you can derive the 95% LCL.
If you know the distribution of your min-med-max y data at each x, you can also generate random samples, fit them separately, and perform statistics on fitted parameters to derive the 95% LCL similar to bootstrap method.
Sam
OriginLab Technical Services |
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giordandue
Italy
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Posted - 09/18/2024 : 05:00:34 AM
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| Thank you Sam, I will try to follow your suggestions |
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95% Confidence limits out of fixed parameter range