# Global Fitting X Range Full Width of Graph

saferr

Mon, 01/29/2018 - 11:52 am

I am doing a Global Fitting and I have a simple question regarding the output wave. How can I make it as long as the X range?

Thank you

You can do this yourself after the fit using the individual coefficient waves for each data set and the fitting function specified for the data set. You will need to change the range of the fit waves and execute the function to fill the wave with the expanded range.

John Weeks

WaveMetrics, Inc.

support@wavemetrics.com

January 29, 2018 at 01:17 pm - Permalink

I have another question regarding Global Fitting. Iis it possible to constrain one of the coefficients within a given range of values as done in the Curve Fitting?

Thank you in advance.

February 9, 2018 at 06:55 am - Permalink

John Weeks

WaveMetrics, Inc.

support@wavemetrics.com

February 9, 2018 at 09:30 am - Permalink

Hello,

I have a question regarding the output of the Global Fitting. I know for individual fitting, but for Global Fitting, how can I get the confidence intervals for the fitted coefficients?

Sorry, I just found that I could add to the end of my FuncFit /F= {0.950000,4}. I gonna try.

Thank you.

January 17, 2019 at 09:47 am - Permalink

I've calculated after fitting using the W_sigma. I hope it is still correct after Global Fitting.

January 17, 2019 at 11:15 am - Permalink

Global Fit is just a curve fit. What the Global Fit procedure adds is the bookkeeping required to keep track of which coefficients should go to which data sets. So what you're doing should be fine.

January 17, 2019 at 01:03 pm - Permalink

Hi,

thanks for the answer. I still have a question regarding CI calculation after fitting. The problem comes because I am not sure what is exactly the wave called w_sigma. In the manual is indicated that "each point of W_sigma is set to the estimated error (standard deviation) of the corresponding coefficients in the fit". I don't really know if those values are the standard deviation (s) or the standard deviation of the error in the sample (s/sqrt(n)).

I am assuming that is the standard deviation of the error because that is was is used to calculate confidence interval; moreover, in the Igor manual is indicated that to calculate CI we need to use this w_sigma times the t value.

I just need to be sure that w_sigma is the standard deviation of the error and not just the standard deviation.

Thank you for your help and sorry for my not complete understanding of the topic.

January 22, 2019 at 07:59 am - Permalink

The W_sigma wave contains the standard deviation of the estimated underlying Gaussian distribution of the fit coefficients. It is related to the original data and the number of points in the original data only in that the summed residuals go into the computation of the chi-square surface approximation. Since it is the estimated distribution of the coefficients, it is the correct sigma to use in computing confidence intervals.

Be aware that this is all based on Gaussian statistics. That means everything assumes linear fits (that is, fits to functions that are linear in the coefficients). That would be line fits and polynomial fits, or a user-defined fit that is linear in the coefficients (something like a mixing function). It seems to me that a Global fit, because it doesn't use all the coefficients for all the data points, will be inherently nonlinear.

In a nonlinear fit, the chi-square surface is approximated by a quadratic surface around the solution point, and the statistics come from that approximation. It is often a good approximation, but can fail badly in some situations. On top of that, the Gaussian statistics are an estimate of the underlying distributions. So when you do Gaussian statistics on a nonlinear fit, you are using an approximation to an estimate...

Just something to think about :)

January 22, 2019 at 10:53 am - Permalink