Overdispersed generalized linear models

✍ Scribed by Dipak K. Dey; Alan E. Gelfand; Fengchun Peng

• Book ID: 104340366
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 752 KB
• Volume: 64
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(96)00207-8

✦ Synopsis

Generalized linear models have become a standard class of models for data analyst:~. However, in some applications, heterogeneity in samples is too great to be explained by the simple variance function implicit in such models. Utilizing a two parameter exponential family which is overdispersed relative to a specified one-parameter exponential family enables the creation of classes of overdispersed generalized linear models (OGLMs) which are analytically attractive. We propose fitting such models within a Bayesian framework employing noninformative priors in order to let the data drive the inference. Hence, our analysis approximates likelihood-based inference but with possibly more reliable estimates of variability for small sample sizes. Bayesian calculations are carried out using a Metropolis-within-Gibbs sampling algorithm. An illustrative example using a data set involving damage incidents to cargo ships ~s presented. Details of the data analysis are provided including comparison with the standard generalized linear models analysis. Several diagnostic tools reveal the improved performance of the OGLM. :~ 1997 Elsevier Science B.V.