THE STANDARDIZED INFLUENCE MATRIX AND ITS APPLICATIONS

In this article we introduce the standardized influence matrix (SIM) o f parameter estimators as a conjugate of the sample covariance matrix of standardized influence functions (SIFs) evaluated at the data point s. We propose principal component analysis for the SIM and its complem ent (SIM analysis) as a diagnostic tool for regression or other statis tical inference, and provide theoretical insight to the local influenc e defined by Cook. We show that SIM analysis reveals the multivariate structure of outlying and/or influential points. Specifically, SIM ana lysis uncovers hidden structures of influence, such as clustering, tha t cannot be identified by the lengths of the standardized influences. Finally, examples in linear regression show that a diagnostic method u sing SIM is more effective if robust parameter estimates are used in c alculating the sample SIM.