Hi Brandon,
Matt and Bruce both gave good, thorough answers to your questions this
morning. Nevertheless, I'm going to chime in too, because there are
some aspects of this issue I'd like to put emphasis on.
On May 11, 2011, at 8:46 PM, Brandon Reese wrote:
I tried your suggestion with epsilon and the chi-square values came
out to be very similar values with the different windows. Does this
mean that reporting reduced chi-square values in a paper that
compared several data sets would not be necessary and/or appropriate?
Bruce said "no" emphatically, and I say "yes," but I think we've
understood the question differently. As Bruce says:
Of course, reduced chi-square can only be compared for fitting
models which compute epsilon the same way or use the same value for
epsilon.
That's the key point. I've gotten away from reporting values for
reduced chi-square (RCS). That's a personal choice, and is not in
accord with the International X-Ray Absorption Society's Error
Reporting Recommendation, available here:
http://ixs.iit.edu/subcommittee_reports/sc/
I think the difficulty in choosing epsilon is more likely to make a
reduced chi-square number confusing than enlightening. But I am moving
increasingly toward reporting changes in reduced chi-square between
fits on the same data, and applying Hamilton's test to determine if
improvements are statistically significant.
Would setting a value for epsilon allow comparisons across
different k-ranges, different (but similar) data sets, or a
combination of the two using the chi-square parameter?
Maybe not. After all, the epsilon should be different for different k-
ranges, as your signal to noise ratio probably changes as a function
of k. Using the same epsilon doesn't reflect that.
In playing around with different windows and dk values my fit
variables generally stayed within the error bars, but the size of
the error bars could change more than a factor 2. Does this mean
that it would make sense to find a window/dk that seems to "work"
for a given group of data and stay consistent when analyzing that
data group?
The fact that your variables stay within the error bars is good news.
The change in the size of the error bars may be related to a less-than-
ideal value for dk you may have used for the Kaiser-Bessel window.
But yes, find a window and dk combination that seems to work well and
then stay consistent for that analysis. Unless the data is
particularly problematic, I'd prefer making a reasoned choice before
beginning to fit and then sticking with it; a posteriori choices for
that kind of thing make me a little nervous.
* * *
At the risk of being redundant, four quick examples.
Example 1: You change the range of R values in the Fourier transform
over which you are fitting a data set.
For this example, RCS is a valuable statistic for letting you know
whether the fit supports the change in R-range.
Example 2: You change the range of k values over which you are fitting
your data.
For this example, comparing RCS is unlikely to be useful. You are
likely trying different k-ranges because you are suspicious about some
of the data at the extremes of your range. Including or excluding that
data likely implies epsilon should be changed, but by how much? Thus
the unreliability of comparing RCS in this case.
Example 3: You change constraints on a fit on the same data range.
For this example, comparing RCS is very useful.
Example 4: You compare fits on the same data range, with the same
model, on two different data sets which were collected during the same
synchrotron run under similar conditions.
For this example, proceed with caution. You may decide to trust
Ifeffit's method for estimating epsilon, or you may be able to come up
with your own (perhaps basing it on the size of the edge jumps).
Hopefully issues like glitches and high-frequency jitter are nearly
the same for both samples, which gives you a fighting chance of making
reasonable estimates of epsilon. Done with a little care, there may be
value in comparing RCS for this kind of case.
--Scott Calvin
Sarah Lawrence College
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