Outlier recognition in the crystal structure least-squares modelling by diagnostic techniques based on leverage analysis

Abstract

The identification of the actual outliers in a least-squares crystal-structure model refinement and their subsequent elimination from the data set is a non-trivial task that has to be carried out carefully when a high level of accuracy of the estimates is required. One of the most suitable tools for detecting the influence of each data entry on the regression is the identification of `leverage points'. On the other hand, the recognition of the actual statistical outliers is effectively possible by using some diagnostics as a function of the leverage, such as Cook's distance, DFFITS and FVARATIO. The evaluation of these estimators makes it possible to achieve a reliable identification of the outliers and the elimination of those that impair the least-squares fit. In this paper, a procedure for filtering data points based on this kind of analysis for crystallographic X-ray data is presented and discussed.