COMPSTAT 2008 pp 385-396 | Cite as

Modelling Background Noise in Finite Mixtures of Generalized Linear Regression Models

Abstract

In this paper we show how only a few outliers can completely break down EM-estimation of mixtures of regression models. A simple, yet very effective way of dealing with this problem, is to use a component where all regression parameters are fixed to zero to model the background noise. This noise component can be easily defined for different types of generalized linear models, has a familiar interpretation as the empty regression model, and is not very sensitive with respect to its own parameters.

Keywords

mixture models generalized linear models robust statistics 

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References

  1. BANFIELD, J.D. and RAFTERY, A.E. (1993): Model-based Gaussian and non-Gaussian clustering. Biometrics, 49(3), 803–821. MATHCrossRefMathSciNetGoogle Scholar
  2. CUESTA-ALBERTOS, J.A., GORDALIZA, A. and MATRAN, C. (1997): Trimmed k-means: An attempt to robustify quantizers. The Annals of Statistics, 25(2), 553–576. MATHCrossRefMathSciNetGoogle Scholar
  3. DEMPSTER, A., LAIRD, N. and RUBIN, D. (1977): Maximum likelihood from incomplete data via the EM-alogrithm. Journal of the Royal Statistical Society, B, 39, 1–1. MATHMathSciNetGoogle Scholar
  4. EVERITT, B.S. and HAND, D.J. (1981): Finite Mixture Distributions. London: Chapman and Hall. MATHGoogle Scholar
  5. GRÜN, B. and LEISCH, F. (2007): Fitting finite mixtures of generalized linear regressions in R. Computational Statistics & Data Analysis, 51(11), 5247–5252. CrossRefMathSciNetGoogle Scholar
  6. HENNIG, C. (2004): Breakdown points for maximum likelihood estimators of location-scale mixtures. The Annals of Statistics, 32(4), 1313–1340. MATHCrossRefMathSciNetGoogle Scholar
  7. HENNIG, C. and CORETTO, P. (2007): The noise component in model-based cluster analysis. In: Proceedings of GfKl-2007. Springer Verlag, Studies in Classification, Data Analysis, and Knowledge Organization. Google Scholar
  8. LEISCH, F. (2004): FlexMix: A general framework for finite mixture models and latent class regression in R. Journal of Statistical Software, 11(8), 1–18. Google Scholar
  9. MCLACHLAN, G. and PEEL, D. (2000): Finite Mixture Models. John Wiley and Sons Inc. Google Scholar
  10. R Development Core Team (2007): R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. Google Scholar
  11. TITTERINGTON, D., SMITH, A. and MAKOV, U. (1985): Statistical Analysis of Finite Mixture Distributions. Chichester: Wiley. MATHGoogle Scholar
  12. WEDEL, M. and DESARBO, W.S. (1995): A mixture likelihood approach for generalized linear models. Journal of Classification, 12, 21–21. MATHCrossRefGoogle Scholar
  13. WEDEL, M. and KAMAKURA, W.A. (2001): Market Segmentation - Conceptual and Methodological Foundations. Kluwer Academic Publishers, Boston, MA, USA, 2nd edition. Google Scholar

Copyright information

© Physica-Verlag Heidelberg 2008

Authors and Affiliations

  1. 1.Department of StatisticsLudwig-Maximilians-Universität MünchenMünchenGermany

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