Overdispersed Generalized Linear Models

Abstract

Generalized linear models have become a standard class of models for data analysts. 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 (OGLM's) 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 is 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

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Document Details

Document Type
Technical Report
Publication Date
May 31, 1994
Accession Number
ADA283276

Entities

People

  • A. E. Gelfand
  • D. K. Dey
  • F. Peng

Organizations

  • Stanford University

Tags

Communities of Interest

  • Ground and Sea Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Bayesian Inference
  • Bayesian Networks
  • Classification
  • Data Analysis
  • Data Science
  • Information Science
  • Military Research
  • Models
  • Monte Carlo Method
  • New York
  • Probability
  • Random Variables
  • Sampling
  • Security
  • Statistics
  • United States

Fields of Study

  • Mathematics

Readers

  • Computational Modeling and Simulation
  • Materials Science and Engineering.
  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference