Double Generalized Linear Models

This book provides an introduction to double generalized linear models (DGLMs), under frequentist and Bayesian frameworks. These models include the class of generalized linear models and compose a unified class of models, where appropriate functions of the mean and dispersion parameters follow linear regression structures that are linear combinations of the explanatory variables. The heteroscedastic normal linear regression models, gamma regression models (where both mean and shape have regression structures) and beta regression models (where both mean and dispersion have regression structures) are examples of this family of regression models. A central topic in the framework of DGLMs is count overdispersion regression models, specifically those associated with the Poisson and binomial distributions. An extension of double generalized linear models is the family of double generalized nonlinear models.

Features:

• Covers generalized linear models and double generalized linear models, under frequentist and Bayesian approaches.

• Presents normal heteroscedastic linear regression models as an introduction to double generalized linear models.

• Defines double generalized linear regression models under frequentist and Bayesian perspectives, including as examples the beta and the gamma regression models.

• Presents models with overdispersion along with frequentist and Bayesian estimation methods.

The book is primarily aimed at researchers and graduate students of statistics and mathematics.