[RESOLVED] Global Fit -- Weighting wave alters fit wave even when parameters fixed

Welcome to the forum. Would it be possible to post a minimal example experiment file? Maybe someone can imagine what might be going on just from your description, but I think you might have more luck if we could test things directly. Also, I assume you are using the latest version of Igor 9?

To chime in after @chozo, I have to wonder if, in the process of doing your fits across batches of data curves, you have not somehow mis-named a source wave in at the next step in an iteration. By example, I would have to say that your second plot simply shows an attempt to fit the lower most data set twice, and the two curves are simply the natural outcome of uncertainties between experimental runs. IOW, your iteration at that point forgot to point the second fitting step to the upper wave. This is an administrative error in coding rather than a mathematical error in fitting.

Just FYI also, the future, please consider posting images where the data points and curves are not lost on the background.

Those pictures are taken straight from the Global Fit result graph. I used colors to try to make the various different data sets easily distinguishable. Usually it looks better than that :)

I would approach double exponentials with great caution. Surprisingly large differences in the time constants for two exponentials look very similar to a single exponential when added together. When you add quite a lot of noise, as in your example, then the fits will do very strange things while wandering around in a very flat-bottomed chi-square surface looking for a minimum.

If you can't figure this out, please send a copy of your Igor experiment file that I can use to actually run your fit myself. That would mean any external procedure file that might exist with definitions of fitting functions and such, and the data waves and an already set up Global Fit control panel.

If your fitting functions use global variables or waves, there are lots of ways to get very screwy results in Global Fit. The Global Fit code doesn't tolerate global objects well. Having said that, I recently made some changes that haven't come out in a release yet that improve on that behavior.

I just looked at those pictures in a larger format. I now see that they have a concave-up starting bit, then the exponential decay to a higher asymptote. Is that bit of a tail at the beginning part of instrument response, or is it part of the double exponential? If it is instrument response, and the exponential decay is expected to fit a double exponential, I will say that I see no support for two exponentials in that data.

> Those pictures are taken straight from the Global Fit result graph. I used colors to try to make the various different data sets easily distinguishable. Usually it looks better than that :)

I have difficulties seeing the dark colored data points on the dark background. So, if I might suggest from what I (a blissfully ignorant soul) know about color spaces, it is not that the different colors being used for the different traces are nearly indistinguishable, it is that the hue used for the colors for the data points may be too close to black (the background color) rather than white. And/or that the data points themselves are small at the resolution in the screen shot.

Just some thoughts.

Well, right. Usually you get bright colors on a dark background. In fact, I think some of the problem is from downsizing the images. If you click on one to view the image at more or less full size, they are better looking. Not great, but better.

Hi all, thanks for all the input!

Some clarifications:

• Yep, the images are barely edited from the default Global Fit package -- unfortunately they happen to be very similar colours in this case! I'll attach some better versions below.
• Version is 8.04 running through wine on ubuntu, sorry for not specifying! This has run surprisingly well for me, so far :)
• The early tail is in part the instrument response, and in part the expected behaviour of the biexponential. I'm definitely aware of the identifiability issues in fitting biexponentials, which is the reason for the Global Fit rather than an individualised fit. Unfortunately, the theory predicts the existence of biexponentials pretty unambiguously so it's difficult to avoid the issue totally.
• I have modified the version of Global Fit so that the fit tolerance can be changed, to aid in convergence -- but everything else should be the same!
• In terms of the second fit where they are the same -- in that (testing only) case, they *should* be the same. The issue is, that even when they have exactly the same parameters fixed for each curve (and therefore should coincide), this only actually happens when there is no weighting function included in the fit.

Qualitative drawing of the model in question -- species "a" reacts to "b" which then reacts to "c", starting at time t₀

Fitted waves become identical only when they have the same parameters AND no weighting present

For context, the full fit consisting of 15 different traces, 5 of each type

Just the "c" type traces, with the white one behaving oddly (yellow is cut off for display reasons, but is normal)

I'll see if I can put together a minimal experiment file that reproduces the issue (some of the files have a very large amount of data from which these plots are condensed)

Ok, this experiment file seems to reproduce the issue. Hopefully the comments aren't too sparse in the fitting function, sorry!

I've included two saved setups:

• fit_normal is the one that I'm actually trying to get to work -- the issue is in the 5th row (counting from 0)
• fit_linked I think best displays the issue: by forcing the 2nd and 5th to have every constant linked, the 2nd and 5th curves should be the same, but they're still different unless you also turn weighting off

Thank you for the example experiment file. I couldn't cut through the details to solve your issue, but as a first microstep I tried to cut out a bit of clutter from your fit function. General tips:

• you don't need to modify xw
• you don't need loops for simple wave assignments
• you may use free waves (although you will get surely a big speed improvement if you use static waves without killing them)
• avoid extreme values (very large exponent) as this may lead to floating-point errors
• you may precompute static values (terms which do not include x) before the actual wave assignment, so that they are not computed every step of a large assignment (also makes things more readable)

Hope this is still useful for you. I could imagine the fit bugging out because of some step in the ChiSq landscape due to replacing NaNs with fixed values.

I looked at your experiment file, in more detail than usual since I'm training a new employee. I think the problem is the linkage of the K4 coefficient between your row 2 and row 5 data sets; when I unlinked them, the fit appeared nearly perfect. As far as I can tell, that coefficient controls the Model 1 decay amplitude, so linking those between two data set with different amplitudes would cause exactly the sort of problem you show where the two fit curves converge on the same asymptote for the two data sets that clearly have different values.

I am attaching a copy of your experiment file with my work.

Thanks all again for taking a look at this!

chozo wrote:

Thank you for the example experiment file. I couldn't cut through the details to solve your issue, but as a first microstep I tried to cut out a bit of clutter from your fit function. General tips:

Thanks for this! I'm definitely on the amateur/"type until it works" side of coding so now that these models are getting large enough that efficiency is becoming more significant etc. it's nice to have some declutter/polish tips :)
 

johnweeks wrote:

I think the problem is the linkage of the K4 coefficient between your row 2 and row 5 data sets; when I unlinked them, the fit appeared nearly perfect.

Thanks for the in-depth look -- however I fear I'm communicating my issue poorly! The "fit_linked" model that was visible in the file is there to illustrate the issue. I've deliberately (and unphysically) linked all of the coefficients for row 2 and row 5, such that these fits should be identical, as they have the same parameters. In this minimal example I'm not really worried about the accuracy of the fit. The trouble is, that unless weighting is turned off, the curves that display for the row 2 and row 5 fits aren't identical, when they should be. I believe this is indicative of a problem in row 2 specifically in the true model (also in the uploaded file, under "fit_normal") -- I first noticed the issue due to one of the coefficients (r2 K6) having an unusual value.

Update: I've been able to resolve the issue, though I'm still not exactly sure why it was happening! The weighting waves contained some zeros in the error due to the Poisson weighting which was of course unphysical, which I've now corrected. One specific zero value in the row 2 weighting wave seemed to be causing the strange behaviour for reasons that are beyond me, perhaps something deep in the code was diverging that shouldn't have... thanks again all for going through this!