New method to compute Rcomplete enables maximum likelihood refinement for small datasets

The crystallographic reliability index R complete is based on a method proposed more than two decades ago. Because its calculation is computationally expensive its use did not spread into the crystallographic community in favor of the cross-validation method known as R free . The importance of R free has grown beyond a pure validation tool. However, its application requires a sufficiently large dataset. In this work we assess the reliability of R complete and we compare it with k -fold cross-validation, bootstrapping, and jackknifing. As opposed to proper cross-validation as realized with R free , R complete relies on a method of reducing bias from the structural model. We compare two different methods reducing model bias and question the widely spread notion that random parameter shifts are required for this purpose. We show that R complete has as little statistical bias as R free with the benefit of a much smaller variance. Because the calculation of R complete is based on the entire dataset instead of a small subset, it allows the estimation of maximum likelihood parameters even for small datasets. R complete enables maximum likelihood-based refinement to be extended to virtually all areas of crystallographic structure determination including high-pressure studies, neutron diffraction studies, and datasets from free electron lasers.