Role of "Weighting Wave" in curve fitting

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Wed, 04/22/2020 - 07:24 am

Hi, I am using FuncFit in my procedure for fitting my experimental results. However, I'm little bit confused about the role of weighting wave.

I know that without assigning a weighting wave will simply take standard deviation at every point=1.

Now when I'm fitting a certain curve without assigning a weighting wave, I'm getting a good fit (decision only based on residual plot). After changing the coefficient values always forces to those optimised values only (may be reached a local minima or global minima).0

But when I'm assigning a weighting wave (in terms of SD) calculated from mean of my repeated experimental results, although I'm starting with the optimised coefficient values but still the coefficient values changes to abnormal situations (residuals are also unsatisfactory).

In Igor Help file it is written "The weighting wave is used in the calculation of chi-square". Does it mean that it will only effect my chi square value after fitting or the whole fitting process will be affected?

The whole fitting process will be affected.

At each iteration, the chi-square is computed: chisq = sum<over xi>( ((yhati - yi)/wi)^2 )

Here xi are the X data values, yi are the corresponding y data values, and h, yhati is the model value for xi, wi are the weighting values you entered. The curve fit seeks the minimum value of chisq. The absolute value of chisq doesn't matter for the process of iteratively finding the minimum, but the minimum value may be at a different set of coefficients if the wi are not uniform. A large value of wi will make a given data point contribute less to chisq, causing that data point to have less influence over the solution.

In addition, the weighting values will be used after the fit to compute the errors associated with the solution coefficients. Without weighting, the residuals are used to scale the errors appropriately; with weighting, it is assumed that you have some reason for your weighting values and the coefficient errors are scaled accordingly. If you supply good estimates of your measurement errors as weighting, then you can use the final value of chisq as an indication of how well the model fits the data. Without proper weighting, you can't do that.

Read more in our help:

DisplayHelpTopic "Overview of Curve Fitting"

DisplayHelpTopic "Weighting"

April 22, 2020 at 10:58 am - Permalink