Item _refine_analyze.RG_free_work_ratio

Description

              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 A^t.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.

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