Re: [Ifeffit] amplitude parameter S02 larger than 1

Hi Yanyun, Good. So here's the procedure for a Hamilton test. We're comparing the fit with S02 guessed to the one with S02 set to 0.90, because that was your a priori best guess at S02. I take the ratio of the first R-factor to the second. You didn't actually say the R-factor for the fit with S02 guessed, but it's clearly around 0.0055 based on the other information you gave. The R-factor for the 0.90 fit is 0.021. So the ratio is 0.0055/0.021 = 0.26, which we'll call x. For the first fit the degrees of freedom is 31.2 - 24 = 8.2. Take half of that and call that a. So a is 4.1. The first fit guesses 1 parameter that the second one doesn't. Take half of 1 and call that b. So b is 0.5. Find a regularized lower incomplete beta function calculator, like this one: http://www.danielsoper.com/statcalc3/calc.aspx?id=37 Enter x, a, and b. The result is 0.001. This means that there is a 0.1% chance that the fits are actually consistent, and that the difference is just due to noise in the data. So in this case, we can't just explain away the high S02 as insignificant. Of course, you could pretty much eyeball that once you gave me the uncertainties; since your fit said 1.45 +/- 0.14, that's likely to be quite incompatible with S02 = 0.9. Still, it's nice to put that on a firmer statistical basis, and I've personally found the Hamilton test quite helpful for answering "do I need to worry about [X]?" type questions. But in your case, you do need to worry about it. This discussion has generated several suggestions; hopefully one of them is a good lead! --Scott Calvin Sarah Lawrence College

On Mar 20, 2015, at 4:30 PM, huyanyun@physics.utoronto.ca wrote:

Hi Scott,

In all situations, 31.2 independent data points and 24 variables were used. In the case of setting S02 to a value, 23 variables were used.

Let me know if there is any other info needed.

Best, Yanyun

Quoting Scott Calvin :

...

Hi Yanyun,

To actually do a Hamilton test, the one other thing I need to know the number of degrees of freedom in the fit...if you provide that, I'll walk you through how to actually do a Hamilton test--it's not that bad, with the aid of an online calculator, and I think it might be instructive for some of the other people reading this list who are trying to learn EXAFS.

--Scott Calvin Sarah Lawrence College

...

On Mar 20, 2015, at 3:46 PM, huyanyun@physics.utoronto.ca wrote:

Hi Scott,

Thank you so much for giving me your thought again. It is very helpful to know how you and other XAFS experts deal with unusual situations.

The floating S02 is fitted to be 1.45+/-0.14, this just means the fit doesn't like the idea of an S02 in a typical range. Instead of setting S02 to 0.9, I have to figure out why it happens and what it might indicate.

I guess a Hamilton test is done by adjusting one parameter (i.e., S02) while keeping other conditions and model the same. Is that right? So I record this test as following:

1) Floating S02: S02 fits to 1.45+/-0.14, R=0.0055, reduced chi^2=17.86, Percentage=0.53+/-0.04 2) Set S02=0.7, R=0.044, reduced chi^2=120.6, percentage=0.81+/-0.2 3) set S02=0.8, R=0.030, reduced chi^2=86.10, percentage=0.77+/-0.07 3) set S02=0.9, R=0.021, reduced chi^2=60.16, percentage=0.72+/-0.06 4) set S02=1.0, R=0.017, reduced chi^2=49.5, percentage=0.67+/-0.05 5) set S02=1.1, R=0.012, reduced chi^2=35.1, percentage=0.62+/-0.03 6) set S02=1.2, R=0.009, reduced chi^2=24.9, percentage=0.59+/-0.02 7) set S02=1.3, R=0.007, reduced chi^2=18.9, percentage=0.57+/-0.02 8) set S02=1.4, R=0.0057, reduced chi^2=16.1, percentage=0.55+/-0.02 9) Floating S02 to be 1.45+/-0.14 10) set S02=1.6, R=0.006, reduced chi^2=17.8, percentage=0.53+/- 0.02 11) set S02=2.0, R=0.044, reduced chi^2=120.7, percentage=0.37+/-0.06.

Therefore, I will say S02 falling in the range 1.2~1.6 gives statistically improved fit, but S02=0.9 is not terrible as well. I agree with you that I could always be confident to say the percentage is 0.64+/-0.15, but I do want to shrink down the uncertainty and think about other possibilities that could cause a large S02.

I did double-check the data-reduction and normalization process. I don't think I can improve anything in this step. By the way, I have a series of similar samples and their fittings all shows floating S02 larger than one based on the same two-sites model.

Best, Yanyun

Quoting Scott Calvin :

...

Hi Yanyun,

Lots of comments coming in now, so I’m editing this as I write it!

One possibility for why you're getting a high best-fit S02 is that the fit doesn't care all that much about what the value of S02; i.e. there is broad range of S02's compatible with describing the fit as "good." That should be reflected in the uncertainty that Artemis reports. If S02 is 1.50 +/- 0.48, for example, that means the fit isn't all that "sure" what S02 should be. That would mean we could just shrug our shoulders and move on, except that it correlates with a parameter you are interested in (in this case, site occupancy). So in such a case, I think you can cautiously fall back on what might be called a "Bayesian prior"; i.e., the belief that the S02 should be "around" 0.9, and set the S02 to 0.9. (Or perhaps restrain S02 to 0.9; then you're really doing something a bit more like the notion of a Bayesian prior.)

On the other hand, if the S02 is, say, 1.50 +/- 0.07, then the fit really doesn’t like the idea of an S02 in the typical range. An S02 that high, with that small an uncertainty, suggests to me that something is wrong—although it could be as simple as a normalization issue during data reduction. In that case, I’d be more skeptical of just setting S02 to 0.90 and going with that result; the fit is trying to tell you something, and it’s important to track down what that something is.

Of course, once in a while, a fit will find a local minimum, while there’s another good local minimum around a more realistic value. That would be reflected by a fit that gave similarly good quantitative measures of fit quality (e.g. R-factors) when S02 is fit (and yields 1.50 +/- 0.07) as when its forced to 0.90. That’s somewhat unusual, however, particularly with a global parameter like S02.

A good way to defend setting S02 to 0.90 is to use the Hamilton test to see if floating S02 yields a statistically significant improvement over forcing it to 0.90. If not, using your prior best estimate for S02 is reasonable.

If you did that, though, I’d think that it would be good to mention what happened in any eventual publication of presentation; it might provide an important clue to someone who follows up with this or a similar system. It would also be good to increase your reported uncertainty for site occupancy (and indicate in the text what you’ve done). I now see that your site occupancies are 0.53 +/- 0.04 for the floated S02, and 0.72 +/-0.06 for the S02 = 0.90. That’s not so bad, really. It means that you’re pretty confident that the site occupancy is 0.64 +/- 0.15, which isn’t an absurdly large uncertainty as these things go.

To be concrete, if all the Hamilton test does not show statistically significant improvement by floating S02, then I might write something like this in any eventual paper: “The site occupancy was highly correlated with S02 in our fits, making it difficult to determine the site occupancy with high precision. If S02 is constrained to 0.90, a plausible value for element [X] [ref], then the site occupancy is 0.53 +/- 0.04. If constrained to 1.0, the site occupancy is [whatever it comes out to be] To reflect the increased uncertainty associated with the unknown value for S02, we are adopting a value of 0.53 +/- [enough uncertainty to cover the results found for S02 = 1.0].

Of course, if you do that, I’d also suggest tracking down as many other possibilities for why your fit is showing high values of S02 as you can; e.g., double-check your normalization during data reduction.

If, on the other hand, the Hamilton test does show the floated S02 is yielding a statistically significant improvement, I think you have a bigger issue. Looking at, e.g., whether you may have constrained coordination numbers incorrectly becomes more critical.

—Scott Calvin Sarah Lawrence College

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