Outlier Identification Rules for Generalized Linear Models

  • Sonja Kuhnt
  • Jörg Pawlitschko
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


Observations which seem to deviate strongly from the main part of the data may occur in every statistical analysis. These observations, usually labelled as outliers, may cause completely misleading results when using standard methods and may also contain information about special events or dependencies. We discuss outliers in situations where a generalized linear model is assumed as null model for the regular data and introduce rules for their identification. For the special cases of a loglinear Poisson model and a logistic regression model some one-step identifiers based on robust and non-robust estimators are proposed and compared.


Generalize Linear Model Contingency Table Null Model Outlier Region Identification Rule 
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  1. BARNETT, V. and LEWIS, T. (1994): Outliers in Statistical Data. 3rd ed., Wiley, New York.Google Scholar
  2. BECKER, C. and GATHER, U. (1999): The Masking Breakdown Point of Multivariate Outlier Identification Rules. Journal of the American Statistical Association, 94, 947–955.MathSciNetCrossRefGoogle Scholar
  3. CHRISTMANN, A. (2001): Robust Estimation in Generalized Linear Models. In: J. Kunert and G. Trenkler (Eds.) Mathematical Statistics with Applications in Biometry: Festschrift in Honour of Siegfried Schach. Eul-Verlag, Lohmar, 215–230.Google Scholar
  4. DAVIES, P.L. and GATHER, U. (1993): The Identification of Outliers. Journal of the American Statistical Association, 88, 782–792.MathSciNetCrossRefGoogle Scholar
  5. HUBERT, M. (1997): The Breakdown Value of the L1 Estimator in Contingency Tables. Statistics and Probability Letters, 33, 419–425.MATHMathSciNetCrossRefGoogle Scholar
  6. GATHER, U., KUHNT, S., and PAWLITSCHKO, J. (2003): Concepts of Outlyingness for Various Data Structures. In: J.C. Misra (Ed.): Industrial Mathematics and Statistics. Narosa Publishing House, New Dehli, 545–585.Google Scholar
  7. KUHNT, S. (2000): Ausreißeridentifikation im Loglinearen Poissonmodell für Kontingenztafeln unter Einbeziehung robuster Schätzer. Dissertation, Department of Statistics, University of Dortmund, Germany.Google Scholar
  8. MOSTELLER, F. and PARUNAK, A. (1985): Identifying Extreme Cells in a Sizable Contingency Table: Probabilistic and Exploratory Approaches. In: D.C. Hoaglin, F. Mosteller, and J.W. Tukey (Eds.): Exploring Data Tables, Trends and Shapes. Wiley, New York, 189–224.Google Scholar
  9. MYERS, R.H., MONTGOMERY, D.C, and VINING, G.C. (2002): Generalized Linear Models. Wiley, New York.Google Scholar
  10. NELDER, J.A. and WEDDERBURN, R.W.M. (1972): Generalized Linear Models. Journal of the Royal Statistical Society A, 134, 370–384.Google Scholar
  11. SHANE, K.V. and SIMONOFF, J.S. (2001): A Robust Approach to Categorical Data Analysis. Journal of Computational and Graphical Statistics, 10, 135–157.MathSciNetCrossRefGoogle Scholar
  12. YICK, J.S. and LEE, A.H. (1998): Unmasking Outliers in Two-Way Contingency Tables. Computational Statistics & Data Analysis, 29, 69–79.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 2005

Authors and Affiliations

  • Sonja Kuhnt
    • 1
  • Jörg Pawlitschko
    • 1
  1. 1.Department of StatisticsUniversity of DortmundDortmundGermany

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