A general maximum likelihood analysis of overdispersion in generalized linear models
- Murray Aitkin
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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.
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- A general maximum likelihood analysis of overdispersion in generalized linear models
Statistics and Computing
Volume 6, Issue 3 , pp 251-262
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- Kluwer Academic Publishers
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- random effects GLM
- EM algorithm
- mixture model
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- Murray Aitkin (1)
- Author Affiliations
- 1. Department of Mathematics, University of Western Australia, 6907, Nedlands, WA, Australia