A general maximum likelihood analysis of overdispersion in generalized linear models
Statistics and ComputingPublished 1 September 1996
Murray Aitkin
Citations200
SJR quartileQ1
SJR score0.81
SNIP1.26
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TL;DR
An EM algorithm for maximum likelihood estimation in generalized linear models with overdispersion is presented, initially derived as a form of Gaussian quadrature assuming a normal mixing distribution, giving a straightforward method for the fully non-parametric ML estimation of this distribution.
Abstract
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.
Keywords
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