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Local influence to detect influential data structures for generalized linear mixed models
M J Ouwens1, F E Tan, M P Berger
1Department of Methodology and Statistics, Maastricht University, The Netherlands. mario.ouwens@stat.unimaas.nl
Biometrics
|January 5, 2002
Summary
This study extends local influence measures for generalized linear models with random effects, proposing a two-step diagnostic approach to identify influential subjects and observations.
Area of Science:
- Statistics
- Biostatistics
- Statistical Modeling
Background:
- Local influence measures are crucial for identifying outliers in statistical models.
- Existing methods primarily focus on normally distributed responses.
- Generalized linear models with random effects are widely used in various scientific fields.
Purpose of the Study:
- To generalize local influence measures for generalized linear models with random effects.
- To propose a novel observation-oriented influence measure.
- To introduce a two-step diagnostic procedure for detecting influential subjects and observations.
Main Methods:
- Generalization of local influence measures.
- Development of an observation-oriented influence measure.
- Formulation of a two-step diagnostic strategy: subject influence followed by observation influence.
Main Results:
- The subject-oriented influence measure is demonstrated to be a specific instance of the proposed observation-oriented measure.
- The proposed two-step diagnostic procedure effectively identifies influential subjects and observations.
- The study highlights the importance of detecting both influential subjects and observations.
Conclusions:
- The proposed methodology provides a robust framework for influence diagnostics in generalized linear models with random effects.
- The two-step approach enhances the reliability of statistical analyses by identifying critical data points.
- Practical application in crossover trials underscores the clinical relevance of these diagnostic tools.
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