The internal norm approach to influence diagnostics

Cook and Weisberg (1982) describe the external and internal norm approaches to assessing the influence of a subset of data on least squares regression estimates. External norms base influence measurement on the repeated sampling theory of the assumed model, while internal norm measures judge the influence of a size-k subset relative to all size-k subsets within the given data. Although intuitively appealing, intemal norms have been largely ignored in favor of external norms due to computational considerations. The purpose of this article is to present the internal norm approach as a viable alternative to external norm influence measurement. In addition to discussing conceptual and computational issues, empirical evidence is provided to show that the internal norm interpretation of influence is different from that of its external counterparts. Finally, comparisons are drawn between external calibration and internal scaling for evaluating influence measure values.