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Biometrika 1991 78(2):373-380; doi:10.1093/biomet/78.2.373
© 1991 by Biometrika Trust
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Influence diagnostics for linear measurement error models

JOYCE M. WELLMAN and RICHARD F. GUNST

Department of Statistical Science, Southern Methodist University Dallas, Texas 75275-0332, U.S.A.

Influence functions are used to show that extreme observations affect linear measurement error model estimators in directions orthogonal to and along the fitted plane, rather than vertically and horizontally as with least squares estimators. Influence diagnostics patterned after those for least squares and derived for generalized linear models by Pregibon (1981) are adapted to assess the influence of extreme observations on linear measurement error model estimators. Perturbation arguments and asymptotic theory are used to support the use of these diagnostics.

Key Words: Errors-in-variables • Influential observation • Outlier


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