Compound Poisson Regression Models

  • John Hinde
Conference paper

DOI: 10.1007/978-1-4612-5771-4_11

Part of the Lecture Notes in Statistics book series (LNS, volume 14)
Cite this paper as:
Hinde J. (1982) Compound Poisson Regression Models. In: Gilchrist R. (eds) GLIM 82: Proceedings of the International Conference on Generalised Linear Models. Lecture Notes in Statistics, vol 14. Springer, New York, NY

Summary

Count data are easily modelled in GLIM using the Poisson distribution. However, in modelling such data the counts are often aggregated over one or more factors, or important explanatory variables are unavailable and as a result the fit obtained is often poor. This paper examines a method of allowing for this unexplained variation by introducing an independent random variable into the linear model for the Poisson mean, giving a compound Poisson model for the observed data. By assuming a known form for the distribution of this random variable, in particular the normal distribution, and using a combination of numerical integration, the EM algorithm and iteratively reweighted least squares, maximum likelihood estimates can be obtained for the parameters. Macros for implementing this technique are presented and its use is illustrated with several examples.

Keywords

Count Data Poisson Distribution Over-Dispersion Compound Poisson Maximum Likelihood Numerical Integration Em Algorithm IRLS 

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Copyright information

© Springer-Verlag New York Inc. 1982

Authors and Affiliations

  • John Hinde
    • 1
  1. 1.Centre for Applied StatisticsUniversity of LancasterUK

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