The statistics of cross-validation residuals - Discussion

Restrained and unrestrained R_Gfree ratios

has been employed (Kleywegt & Brünger, 1996) to detect situations where addition of extra parameters to a refinement brings no significant improvement in the model. For example the extra parameters may concern the relaxation of non-crystallographic symmetry or the employment of individual atomic temperature factors. Relevant estimates of are summarised in Table 1 and help to make these discussions more quantitative. The Table gives the more important expressions derived earlier for a refinement at convergence with only random uncorrelated errors and weighting which correctly reflects the model and experimental errors.

The constrained and unrestrained statistics in the Table show what happens when constraints are imposed, assuming that the reduction in parameters does not introduce model error. It is seen that a reduction in the expected values of and the ratio takes place. A reduction also takes place when restraints are imposed, assuming again that the above conditions are not violated.

The statistics of cross-validation residuals - Discussion