Statistics and Computing

, Volume 6, Issue 3, pp 251–262

A general maximum likelihood analysis of overdispersion in generalized linear models

  • Murray Aitkin

DOI: 10.1007/BF00140869

Cite this article as:
Aitkin, M. Stat Comput (1996) 6: 251. doi:10.1007/BF00140869


This paper presents an EM algorithm for maximum likelihood estimation in generalized linear models with overdispersion. The algorithm is initially derived as a form of Gaussian quadrature assuming a normal mixing distribution, but with only slight variation it can be used for a completely unknown mixing distribution, giving a straightforward method for the fully non-parametric ML estimation of this distribution. This is of value because the ML estimates of the GLM parameters may be sensitive to the specification of a parametric form for the mixing distribution. A listing of a GLIM4 algorithm for fitting the overdispersed binomial logit model is given in an appendix.

A simple method is given for obtaining correct standard errors for parameter estimates when using the EM algorithm.

Several examples are discussed.


Overdispersion random effects GLM EM algorithm mixture model 

Copyright information

© Chapman & Hall 1996

Authors and Affiliations

  • Murray Aitkin
    • 1
  1. 1.Department of MathematicsUniversity of Western AustraliaNedlandsAustralia

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