# [Ifeffit] amplitude parameter S02 larger than 1

huyanyun at physics.utoronto.ca huyanyun at physics.utoronto.ca
Fri Mar 20 15:30:55 CDT 2015

```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 <scalvin at sarahlawrence.edu>:

> 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 at 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 <scalvin at sarahlawrence.edu>:
>>
>>> 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
>>>
>>>
>
>
> _______________________________________________
> Ifeffit mailing list
> Ifeffit at millenia.cars.aps.anl.gov
> http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit

```