The use of working variables in the bayesian modeling of mean and dispersion parameters in generalized nonlinear models with random effects

Abstract

This article is aimed at reviewing a novel Bayesian approach to handle inference and estimation in the class of generalized nonlinear models. These models include some of the main techniques of statistical methodology, namely generalized linear models and parametric nonlinear regression. In addition, this proposal extends to methods for the systematic treatment of variation that is not explicitly predictedwithin themodel, through the inclusion of random effects, and takes into account the modeling of dispersion parameters in the class of two-parameter exponential family. The methodology is based on the implementation of a two-stage algorithm that induces a hybrid approach based on numerical methods for approximating the likelihood to a normal density using a Taylor linearization around the values of current parameters in an MCMC routine.