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Biometrika 1993 80(1):99-106; doi:10.1093/biomet/80.1.99
© 1993 by Biometrika Trust
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Leverage, local influence and curvature in nonlinear regression

ROY T. ST. LAURENT and R. DENNIS COOK

Department of Biostatistics, School of Public Health, University of Michigan Ann Arbor, Michigan 48109, U.S.A.
Department of Applied Statistics, School of Statistics, University of Minnesota, St. Paul Minnesota 55108, U.S.A.

The connections between measures of leverage, statistical curvature, and the local influence of a mean-shift perturbation are explored in nonlinear regression models. The circumstances under which the Jacobian leverage reduces to a commonly-used linear approximation are found to be connected to the effective residual curvature of the nonlinear model. The local influence of a mean-shift perturbation in the model function is seen to be closely related to the Jacobian leverage.

Key Words: Diagnostics • Influential observation • Jacobian leverage • Mean-shift perturbation


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