Bartlett Adjustments for Overdispersed Generalized Linear Models

Abstract

Heteroscedastic regression models have recently gained popularity in industrial applications for analyzing unreplicated experiments, experiments for robust design, and the analysis of process data. Many authors have also considered dispersion modeling to obtain correct standard errors and confidence intervals for mean parameters in regression analysis. The popularity of overdispersed generalized linear models is growing steadily to explore and model many kinds of data, especially counts and proportions. In this article, Bartlett corrections for overdispersed generalized linear models are derived. Our formulae cover many important and commonly used models, thus generalizing results by Botter and Cordeiro (1998) for double generalized linear models and by Cordeiro (1983) for generalized linear models. By simulation, the practical use of such corrections is illustrated.

Keywords:

• Asymptotic distribution
• Bartlett correction
• Chi-squared distribution
• Double generalized linear model
• Likelihood ratio test
• Maximum likelihood estimate
• Overdispersed generalized linear model

Mathematics Subject Classification:

• 62F03
• 62F05

Acknowledgment

The financial support of CNPQ/Brazil to first author and CAPES/Brazil to others authors are gratefully acknowledged.