Double Generalized Linear Models: Likelihood and Bayesian Methods

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.

Edilberto Cepeda-Cuervo has been a full professor of statistics at Universidad Nacional de Colombia (UNAL) in Bogotá, Colombia since 2004. He holds a Bachelor’s Degree in Physics and Mathematics from Universidad Libre de Colombia (1981); M.Sc. in Mathematics from Universidad de los Andes de Colombia (1983); and a Ph.D. in Mathematics from UFRJ (2001). He has been a full professor in the Statistics department of Universidad Nacional de Colombia since 2004.

He has authored or co-authored more than 60 scientific articles in the areas of generalized linear models, nonlinear regression, beta and gamma regression models, longitudinal data analysis, spatial statistics, overdispersion regression models and in interdisciplinary topics. These papers have been published in many statistical journals including Brazilian Journal of Probability and Statistics, Journal of Educational and Behavioral Statistics, Biometrical Journal, Journal of Applied Statistics and Computational Statistics.

Some research lines of interest are generalized linear models, double generalized linear models, overdispersion models, Bayesian statistics, longitudinal data analysis, and spatial econometrics.