Origin offers the very useful and rather rare capability in commercial software
to calculate the profile likelihood confidence intervals for parameters in non
linear curve fitting.This feature is not new in ver. 5 but available already in ver. 3.7 I think
where it was documented; it disappeared in the ver.4 manual and is now
mentioned in the Origin 5.0 Update.wri File:
Curve Fitting
After clicking the Param. Worksheet button in the Generate Results dialog box
(Action:Results), a Parameters worksheet is created containing the fitting
results. LLimit and ULimit are the Lower and Upper Confidence Limits for the
parameter. They are computed by searching for the values of each parameter p
that give an SSR(p) (minimized over the remaining parameters) greater than SSR
by a factor (1+F/(N-P):
SSR(p) = SSR * (1+F/(N-P))
where F=FTable(Confidence, 1, N-P) and SSR is the minimum SSR found during the
fitting session.
The last column, ConfIntv, is Err * T, where Err is the approximate Standard
Error for the parameter and T=TTable((1+Confidence)/2, N-P), the Student t
value.
ULimit and LLimit are the more accurate confidence limits for your parameters.
To change the confidence level (for example, from 95% to 68%), type 0.68 in the
text box associated with the Conf. Band button and then click the Conf. Band
button. Origin displays 68% confidence bands on your graph. Click the Param.
Worksheet button to view the results for a confidence level of 68%. You can
rename the Parameters worksheet reflecting the confidence level, such as
Parameters_68.
Recent calculations I have made for the confidence limits in Origin 5 and ver.
4 showed differences for ULimit and LLimit in all data sets which I have
analysed.
My questions is what are the reasons for that? What has changed in ver.5? Which
results are correct? The formulae given above and those in the manual of ver. 3
don't differ.
Calculation of Confidence Intervals when curve fitting in Origin 4.1 and 5.0
Posted - 08/20/1998 : 3:04:00 PM
