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A graphical aid for sensitivity analysis of estimated regression coefficients

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  • Diane I. Gibbons
  • Gary C. McDonald

Abstract

A problem often arising in applied linear regression modeling is determining the appropriate weight to attach to each observation. In the extreme, the problem extends to the deletion of observations from a data base. Since the choice of weights, fitting criteria, and estimation procedure depend on the specific objectives of the modeling, universally applicable guidelines are virtually nonexistent. However, the sensitivity of analytic conclusions to weights assigned to “suspect” observations can be conveniently assessed using a graphical display. This report develops such a display based on a modeling of outliers which leads naturally to estimators based on a weighted least‐squares criterion, and a data‐analytic method for determining how much downweighting to impose on a specific subset of observations. This technique is illustrated with several examples, including one relating air pollution to human mortality.

Suggested Citation

  • Diane I. Gibbons & Gary C. McDonald, 1988. "A graphical aid for sensitivity analysis of estimated regression coefficients," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(2), pages 269-283, April.
    • Handle: RePEc:wly:navres:v:35:y:1988:i:2:p:269-283
    DOI: 10.1002/1520-6750(198804)35:23.0.CO;2-#
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    References listed on IDEAS

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    1. Diane I. Gibbons & Gary C. McDonald & Richard F. Gunst, 1987. "The complementary use of regression diagnostics and robust estimators," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(1), pages 109-131, February.
    2. Gibbons, Diane I. & McDonald, Gary C., 1983. "Illustrating regression diagnostics with an air pollution and mortality model," Computational Statistics & Data Analysis, Elsevier, vol. 1(1), pages 201-220, March.
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