Re: [ccp4bb] Rmergicide Through Programming

[Frank von Delft]

It is quite easy to end up with low multiplicities in the low resolution 
shell, especially for low symmetry and fast-decaying crystals.

It is this scenario where Rmerge (lowres) is more misleading than Reas.
phx


On 08/07/2017 17:31, James Holton wrote:
What does Rmeas tell us that Rmerge doesn't?  Given that we know the 
multiplicity?

-James Holton
MAD Scientist

On 7/8/2017 9:15 AM, Frank von Delft wrote:

Anyway, back to reality:  does anybody still use R statistics to 
evaluate anything other than /strong/ data? Certainly I never look at 
it except for the low-resolution bin (or strongest reflections).  
Specifically, a "2%-dataset" in that bin is probably healthy, while a 
"9%-dataset" probably Has Issues.

In which case, back to Jacob's question:  what does Rmerge tell us 
that Rmeas doesn't.

phx




On 08/07/2017 17:02, James Holton wrote:
Sorry for the confusion.  I was going for brevity!  And failed.

I know that the multiplicity correction is applied on a per-hkl 
basis in the calculation of Rmeas.  However, the average 
multiplicity over the whole calculation is most likely not an 
integer. Some hkls may be observed twice while others only once, or 
perhaps 3-4 times in the same scaling run.

Allow me to do the error propagation properly.  Consider the scenario:

Your outer resolution bin has a true I/sigma = 1.00 and average 
multiplicity of 2.0. Let's say there are 100 hkl indices in this 
bin.  I choose the "true" intensities of each hkl from an 
exponential (aka Wilson) distribution.  Further assume the 
background is high, so the error in each observation after 
background subtraction may be taken from a Gaussian distribution. 
Let's further choose the per-hkl multiplicity from a Poisson 
distribution with expectation value 2.0, so 0 is possible, but the 
long-term average multiplicity is 2.0. For R calculation, when 
multiplicity of any given hkl is less than 2 it is skipped. What I 
end up with after 120,000 trials is a distribution of values for 
each R factor.  See attached graph.

What I hope is readily apparent is that the distribution of Rmerge 
values is taller and sharper than that of the Rmeas values.  The 
most likely Rmeas is 80% and that of Rmerge is 64.6%.  This is 
expected, of course.  But what I hope to impress upon you is that 
the most likely value is not generally the one that you will get! 
The distribution has a width.  Specifically, Rmeas could be as low 
as 40%, or as high as 209%, depending on the trial.  Half of the 
trial results falling between 71.4% and 90.3%, a range of 19 
percentage points.  Rmerge has a middle-half range from 57.6% to 
72.9% (15.3 percentage points).  This range of possible values of 
Rmerge or Rmeas from data with the same intrinsic quality is what I 
mean when I say "numerical instability".  Each and every trial had 
the same true I/sigma and multiplicity, and yet the R factors I get 
vary depending on the trial. Unfortunately for most of us with real 
data, you only ever get one trial, and you can't predict which Rmeas 
or Rmerge you'll get.

My point here is that R statistics in general are not comparable 
from experiment to experiment when you are looking at data with low 
average intensity and low multiplicity, and it appears that Rmeas is 
less stable than Rmerge.  Not by much, mind you, but still jumps 
around more.

Hope that is clearer?

Note that in no way am I suggesting that low-multiplicity is the 
right way to collect data.  Far from it.  Especially with modern 
detectors that have negligible read-out noise.  But when micro 
crystals only give off a handful of photons each before they die, 
low multiplicity might be all you have.

-James Holton
MAD Scientist



On 7/7/2017 2:33 PM, Edward A. Berry wrote:
I think the confusion here is that the "multiplicity correction" is 
applied
on each reflection, where it will be an integer 2 or greater (can't 
estimate
variance with only one measurement). You can only correct in an 
approximate
way using using the average multiplicity of the dataset, since it 
would depend
on the distribution of multiplicity over the reflections.

And the correction is for r-merge. You don't need to apply a 
correction
to R-meas.
R-meas is a redundancy-independent best estimate of the variance.
Whatever you would have used R-merge for (hopefully taking allowance
for the multiplicity) you can use R-meas and not worry about 
multiplicity.
Again, what information does R-merge provide that R-meas does not 
provide
in a more accurate way?

According to the denso manual, one way to artificially reduce
R-merge is to include reflections with only one measure (averaging
in a lot of zero's always helps bring an average down), and they say
there were actually some programs that did that. However I'm
quite sure none of the ones we rely on today do that.

On 07/07/2017 03:12 PM, Kay Diederichs wrote:
James,

I cannot follow you. "n approaches 1" can only mean n = 2 because 
n is integer. And for n=2 the sqrt(n/(n-1)) factor is 
well-defined. For n=1, neither contributions to Rmeas nor Rmerge 
nor to any other precision indicator can be calculated anyway, 
because there's nothing this measurement can be compared against.

just my 2 cents,

Kay

On Fri, 7 Jul 2017 10:57:17 -0700, James Holton 
<jmhol...@slac.stanford.edu> wrote:

I happen to be one of those people who think Rmerge is a very useful
statistic.  Not as a method of evaluating the resolution limit, 
which is
mathematically ridiculous, but for a host of other important things,
like evaluating the performance of data collection equipment, and
evaluating the isomorphism of different crystals, to name a few.

I like Rmerge because it is a simple statistic that has a simple 
formula
and has not undergone any "corrections".  Corrections increase
complexity, and complexity opens the door to manipulation by the
desperate and/or misguided.  For example, overzealous outlier 
rejection
is a common way to abuse R factors, and it is far too often swept 
under
the rug, sometimes without the user even knowing about it. This is
especially problematic when working in a regime where the 
statistic of
interest is unstable, and for R factors this is low intensity data.
Rejecting just the right "outliers" can make any R factor look a lot
better.  Why would Rmeas be any more unstable than Rmerge? Look 
at the
formula. There is an "n-1" in the denominator, where n is the
multiplicity.  So, what happens when n approaches 1 ? What 
happens when
n=1? This is not to say Rmerge is better than Rmeas. In fact, I 
believe
the latter is generally superior to the first, unless you are 
working
near n = 1. The sqrt(n/(n-1)) is trying to correct for bias in the R
statistic, but fighting one infinity with another infinity is a
dangerous game.

My point is that neither Rmerge nor Rmeas are easily interpreted 
without
knowing the multiplicity.  If you see Rmeas = 10% and the 
multiplicity
is 10, then you know what that means.  Same for Rmerge, since at 
n=10
both stats have nearly the same value.  But if you have Rmeas = 
45% and
multiplicity = 1.05, what does that mean?  Rmeas will be only 33% 
if the
multiplicity is rounded up to 1.1. This is what I mean by "numerical
instability", the value of the R statistic itself becomes 
sensitive to
small amounts of noise, and behaves more and more like a random 
number
generator. And if you have Rmeas = 33% and no indication of
multiplicity, it is hard to know what is going on.  I personally 
am a
lot more comfortable seeing qualitative agreement between Rmerge and
Rmeas, because that means the numerical instability of the 
multiplicity
correction didn't mess anything up.

Of course, when the intensity is weak R statistics in general are 
not
useful.  Both Rmeas and Rmerge have the sum of all intensities in 
the
denominator, so when the bin-wide sum approaches zero you have 
another
infinity to contend with.  This one starts to rear its ugly head 
once
I/sigma drops below about 3, and this is why our ancestors always
applied a sigma cutoff before computing an R factor. Our 
small-molecule
colleagues still do this!  They call it "R1".  And it is an 
excellent
indicator of the overall relative error.  The relative error in the
outermost bin is not meaningful, and strangely enough nobody ever
reported the outer-resolution Rmerge before 1995.

For weak signals, Correlation Coefficients are better, but for 
strong
signals CC pegs out at >95%, making it harder to see relative 
errors.
I/sigma is what we'd like to know, but the value of "sigma" is still
prone to manipulation by not just outlier rejection, but 
massaging the
so-called "error model".  Suffice it to say, crystallographic data
contain more than one type of error.  Some sources are important for
weak spots, others are important for strong spots, and still 
others are
only apparent in the mid-range.  Some sources of error are only
important at low multiplicity, and others only manifest at high
multiplicity. There is no single number that can be used to 
evaluate all
aspects of data quality.

So, I remain a champion of reporting Rmerge.  Not in the 
high-angle bin,
because that is essentially a random number, but overall Rmerge and
low-angle-bin Rmerge next to multiplicity, Rmeas, CC1/2 and other
statistics is the only way you can glean enough information about 
where
the errors are coming from in the data.  Rmeas is a useful addition
because it helps us correct for multiplicity without having to do 
math
in our head.  Users generally thank you for that. Rmerge, 
however, has
served us well for more than half a century, and I believe Uli Arndt
knew what he was doing.  I hope we all know enough about history to
realize that future generations seldom thank their ancestors for
"protecting" them from information.

-James Holton
MAD Scientist


On 7/5/2017 10:36 AM, Graeme Winter wrote:
Frank,

you are asking me to remove features that I like, so I would 
feel that the challenge is for you to prove that this is harmful 
however:

   - at the minimum, I find it a useful check sum that the stats 
are internally consistent (though I interpret it for lots of 
other reasons too)
   - it is faulty I agree, but (with caveats) still useful IMHO

Sorry for being terse, but I remain to be convinced that 
removing it increases the amount of information

CC’ing BB as requested

Best wishes Graeme


On 5 Jul 2017, at 17:17, Frank von Delft 
<frank.vonde...@sgc.ox.ac.uk> wrote:

You keep not answering the challenge.

It's really simple:  what information does Rmerge provide that 
Rmeas doesn't.

(If you answer, email to the BB.)


On 05/07/2017 16:04, graeme.win...@diamond.ac.uk wrote:
Dear Frank,

You are forcefully arguing essentially that others are wrong 
if we feel an existing statistic continues to be useful, and 
instead insist that it be outlawed so that we may not make use 
of it, just in case someone misinterprets it.

Very well

I do however express disquiet that we as software developers 
feel browbeaten to remove the output we find useful because 
“the community” feel that it is obsolete.

I feel that Jacob’s short story on this thread illustrates 
that educating the next generation of crystallographers to 
understand what all of the numbers mean is critical, and that 
a numerological approach of trying to optimise any one 
statistic is essentially doomed. Precisely the same argument 
could be made for people cutting the “resolution” at the wrong 
place in order to improve the average I/sig(I) of the data set.

Denying access to information is not a solution to 
misinterpretation, from where I am sat, however I acknowledge 
that other points of view exist.

Best wishes Graeme


On 5 Jul 2017, at 12:11, Frank von Delft 
<frank.vonde...@sgc.ox.ac.uk<mailto:frank.vonde...@sgc.ox.ac.uk>> 
wrote:


Graeme, Andrew

Jacob is not arguing against an R-based statistic;  he's 
pointing out that leaving out the multiplicity-weighting is 
prehistoric (Diederichs & Karplus published it 20 years ago!).

So indeed:   Rmerge, Rpim and I/sigI give different 
information.  As you say.

But no:   Rmerge and Rmeas and Rcryst do NOT give different 
information.  Except:

    * Rmerge is a (potentially) misleading version of Rmeas.

    * Rcryst and Rmerge and Rsym are terms that no longer have 
significance in the single cryo-dataset world.

phx.



On 05/07/2017 09:43, Andrew Leslie wrote:

I would like to support Graeme in his wish to retain Rmerge in 
Table 1, essentially for exactly the same reasons.

I also strongly support Francis Reyes comment about the 
usefulness of Rmerge at low resolution, and I would add to his 
list that it can also, in some circumstances, be more 
indicative of the wrong choice of symmetry (too high) than the 
statistics that come from POINTLESS (excellent though that 
program is!).

Andrew
On 5 Jul 2017, at 05:44, Graeme Winter 
<graeme.win...@gmail.com<mailto:graeme.win...@gmail.com>> wrote:

HI Jacob

Yes, I got this - and I appreciate the benefit of Rmeas for 
dealing with measuring agreement for small-multiplicity 
observations. Having this *as well* is very useful and I agree 
Rmeas / Rpim / CC-half should be the primary “quality” 
statistics.

However, you asked if there is any reason to *keep* rather 
than *eliminate* Rmerge, and I offered one :o)

I do not see what harm there is reporting Rmerge, even if it 
is just used in the inner shell or just used to capture a 
flavour of the data set overall. I also appreciate that Rmeas 
converges to the same value for large multiplicity i.e.:

Overall InnerShell  OuterShell
Low resolution limit                       39.02 39.02      1.39
High resolution limit                       1.35 6.04      1.35

Rmerge  (within I+/I-)                     0.080 0.057     2.871
Rmerge  (all I+ and I-)                    0.081 0.059     2.922
Rmeas (within I+/I-)                       0.081 0.058     2.940
Rmeas (all I+ & I-) 0.082 0.059     2.958
Rpim (within I+/I-)                        0.013 0.009     0.628
Rpim (all I+ & I-) 0.009 0.007     0.453
Rmerge in top intensity bin                0.050 -         -
Total number of observations             1265512 16212     53490
Total number unique                        17515 224      1280
Mean((I)/sd(I))                             29.7 104.3       1.5
Mn(I) half-set correlation CC(1/2)         1.000 1.000     0.778
Completeness                               100.0 99.7     100.0
Multiplicity                                72.3 72.4      41.8

Anomalous completeness                     100.0 100.0     100.0
Anomalous multiplicity                      37.2 42.7      21.0
DelAnom correlation between half-sets      0.497 0.766    -0.026
Mid-Slope of Anom Normal Probability       1.039 -         -

(this is a good case for Rpim & CC-half as resolution limit 
criteria)

If the statistics you want to use are there & some others 
also, what is the pressure to remove them? Surely we want to 
educate on how best to interpret the entire table above to get 
a fuller picture of the overall quality of the data? My 
0th-order request would be to publish the three shells as 
above ;o)

Cheers Graeme



On 4 Jul 2017, at 22:09, Keller, Jacob 
<kell...@janelia.hhmi.org<mailto:kell...@janelia.hhmi.org>> 
wrote:

I suggested replacing Rmerge/sym/cryst with Rmeas, not Rpim. 
Rmeas is simply (Rmerge * sqrt(n/n-1)) where n is the number 
of measurements of that reflection. It's merely a way of 
correcting for the multiplicity-related artifact of Rmerge, 
which is becoming even more of a problem with data sets of 
increasing variability in multiplicity. Consider the case of 
comparing a data set with a multiplicity of 2 versus one of 
100: equivalent data quality would yield Rmerges diverging by 
a factor of ~1.4. But this has all been covered before in 
several papers. It can be and is reported in resolution bins, 
so can used exactly as you say. So, why not "disappear" Rmerge 
from the software?

The only reason I could come up with for keeping it is 
historical reasons or comparisons to previous datasets, but 
anyway those comparisons would be confounded by variabities in 
multiplicity and a hundred other things, so come on, 
developers, just comment it out!

JPK




-----Original Message-----
From: 
graeme.win...@diamond.ac.uk<mailto:graeme.win...@diamond.ac.uk> 
[mailto:graeme.win...@diamond.ac.uk]
Sent: Tuesday, July 04, 2017 4:37 PM
To: Keller, Jacob 
<kell...@janelia.hhmi.org<mailto:kell...@janelia.hhmi.org>>
Cc: ccp4bb@jiscmail.ac.uk<mailto:ccp4bb@jiscmail.ac.uk>
Subject: Re: [ccp4bb] Rmergicide Through Programming

HI Jacob

Unbiased estimate of the true unmerged I/sig(I) of your data 
(I find this particularly useful at low resolution) i.e. if 
your inner shell Rmerge is 10% your data agree very poorly; if 
2% says your data agree very well provided you have sensible 
multiplicity… obviously depends on sensible interpretation. 
Rpim hides this (though tells you more about the quality of 
average measurement)

Essentially, for I/sig(I) you can (by and large) adjust your 
sig(I) values however you like if you were so inclined. You 
can only adjust Rmerge by excluding measurements.

I would therefore defend that - amongst the other stats you 
enumerate below - it still has a place

Cheers Graeme

On 4 Jul 2017, at 14:10, Keller, Jacob 
<kell...@janelia.hhmi.org<mailto:kell...@janelia.hhmi.org>> 
wrote:

Rmerge does contain information which complements the others.

What information? I was trying to think of a counterargument 
to what I proposed, but could not think of a reason in the 
world to keep reporting it.

JPK


On 4 Jul 2017, at 12:00, Keller, Jacob 
<kell...@janelia.hhmi.org<mailto:kell...@janelia.hhmi.org><mailto:kell...@janelia.hhmi.org>> 
wrote:

Dear Crystallographers,

Having been repeatedly chagrinned about the continued use and 
reporting of Rmerge rather than Rmeas or similar, I thought of 
a potential way to promote the change: what if merging 
programs would completely omit Rmerge/cryst/sym? Is there some 
reason to continue to report these stats, or are they just 
grandfathered into the software? I doubt that any journal or 
crystallographer would insist on reporting Rmerge per se. So, 
I wonder what developers would think about commenting out a 
few lines of their code, seeing what happens? Maybe a comment 
to the effect of "Rmerge is now deprecated; use Rmeas" would 
be useful as well. Would something catastrophic happen?

All the best,

Jacob Keller

*******************************************
Jacob Pearson Keller, PhD
Research Scientist
HHMI Janelia Research Campus / Looger lab
Phone: (571)209-4000 x3159
Email: 
kell...@janelia.hhmi.org<mailto:kell...@janelia.hhmi.org><mailto:kell...@janelia.hhmi.org>
*******************************************


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