© 2004 by Biometrika Trust
A diagnostic procedure based on local influence
1 Department of Psychiatry, Columbia University and New York State Psychiatric Institute, 1051 Riverside Drive, Unit 74, New York, New York 10032, U.S.A. hz2114{at}columbia.edu, 2 Department of Epidemiology and Public Health, Yale University School of Medicine, New Haven, Connecticut 06520-8034, U.S.A. heping.zhang{at}yale.edu
Cook's (1986) normal curvature measure is useful for sensitivity analysis of model assumptions in statistical models. However, there is no rigorous approach based on the normal curvature for addressing two fundamental issues: to assess the extent of discrepancy between an assumed model and the underlying model from which the data are generated, and to identify suspicious data points for which the discrepancy is most evident. Our purpose is to establish a theoretically sound procedure for resolving these issues for case-weight perturbation under the framework of independent distributions. We show that the local influence measure, Cook's distance and likelihood distance are asymptotically equivalent. A diagnostic procedure, based on local influence, is proposed for evaluating model misspecification and for detecting influential points simultaneously. We analyse two real datasets.
Key Words: Case weight; Cook's distance; Likelihood displacement; Local influence measure; Model misspecification; Normal curvature
Received April 2003. Revised November 2003.
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