The observed ratio of RGfree to RGwork. The expected RG ratio
is the value that should be achievable at the end of a structure
refinement when only random uncorrelated errors exist in data
and model provided that the observations are properly weighted.
When compared with the observed RG ratio it may indicate that a
structure has not reached convergence or a model has been
over-refined with no corresponding improvement in the model.
In an unrestrained refinement the ratio of RGfree/RGwork with
only random uncorrelated errors at convergence depends only
on the number of reflections and the number of parameters as:
sqrt[(f + m) / (f - m) ]
where f = number of included structure amplitudes and
target distances, and
m = number of parameters being refined.
In the restrained case, RGfree is calculated from a random
selection of residuals including both structure amplitudes
and restraints. When restraints are included in refinement
the RG ratio requires a term for the contribution to the
minimized residual at convergence, Drest, due to those
restraints:
Drest = r - sum (w_i . (a_i)t . (H)-1 a_i
where
r is the number of geometrical, temperature factor and
other restraints
H is the (m,m) normal matrix given by At.W.A
W is the (n,n) symmetric weight matrix of the included
observations
A is the least-squares design matrix of derivatives of
order (n,m)
a_i is the ith row of A
Then the expected RGratio becomes
sqrt [ (f + (m - r + Drest))/ (f - (m - r + Drest)) ]
The expected RGfree/RGwork is not yet included in the mmCIF
dictionary.
Ref: "Rfree and the Rfree ratio. Part I: derivation of expected
values of cross-validation residuals used in macromolecular
least-squares refinement". Tickle, I. J., Laskowski, R. A.
& Moss, D.S. (1998). Acta Cryst. D, in the press.
