# Global Fitting X Range Full Width of Graph

Hello,

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
This is presently not supported by Global Fit, and it would be hard to implement given the number of cases I would have to consider.

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
Thank you. That was very useful.

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.
In the Global Analysis control panel, turn on the Constraints... checkbox. That will bring up a sub-panel where you can specify constraints. It can be complex, since it takes into account the linkages between data sets.

John Weeks
WaveMetrics, Inc.
support@wavemetrics.com

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.

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

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.

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.

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 :)