Re: [ccp4bb] Rmergicide Through Programming

[Edward A. Berry]

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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