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Sensitivity of parametric link functions in generalized linear models

J S Yick1, A H Lee

  • 1Faculty of Science, Northern Territory University, Darwin, Australia.

Journal of Biopharmaceutical Statistics
|September 19, 1998
PubMed
Summary
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Extreme observations can heavily influence generalized linear model link function selection. New diagnostics help identify these sensitive points in parametric link analysis, even with masking effects.

Area of Science:

  • Statistics
  • Statistical Modeling

Background:

  • Generalized linear models (GLMs) are widely used in statistical analysis.
  • Choosing an appropriate link function is crucial for GLM performance.
  • Parametric link families, while common, can be sensitive to extreme data points.

Purpose of the Study:

  • To develop diagnostic methods for assessing the influence of observations on parametric link function selection in GLMs.
  • To evaluate the effectiveness of these diagnostics in identifying influential data points.

Main Methods:

  • Derivation of new diagnostic statistics to measure observation influence on link parameter estimation.
  • Application of these diagnostics to two illustrative examples using GLMs.

Main Results:

Related Experiment Videos

  • The proposed diagnostics effectively assess the sensitivity of parametric link analysis to individual observations.
  • The diagnostics successfully identified jointly influential observations, even in the presence of masking, where multiple extreme points obscure individual influence.

Conclusions:

  • The developed diagnostics provide a valuable tool for validating parametric link function choices in GLMs.
  • These methods enhance the robustness of GLM analysis by detecting potentially distorting extreme observations.