[Ifeffit] amplitude parameter S02 larger than 1

[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 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
>> 
>>