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 nonparametric 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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 Title
 A general maximum likelihood analysis of overdispersion in generalized linear models
 Journal

Statistics and Computing
Volume 6, Issue 3 , pp 251262
 Cover Date
 19960901
 DOI
 10.1007/BF00140869
 Print ISSN
 09603174
 Online ISSN
 15731375
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Overdispersion
 random effects GLM
 EM algorithm
 mixture model
 Industry Sectors
 Authors

 Murray Aitkin ^{(1)}
 Author Affiliations

 1. Department of Mathematics, University of Western Australia, 6907, Nedlands, WA, Australia