Double generalized nonlinear regression models

This chapter proposes an extension of the linear regression models in order to define the double generalized nonlinear regression models. After an introduction to the normal nonlinear regression models, the homoscedastic normal nonlinear regression models are defined, including the Gauss-Newton, Fisher scoring, and Bayesian algorithms used for their fit. After that, the joint mean and variance normal nonlinear regression models are defined, where the mean systematic component follows nonlinear regression structures and the systematic variance component follows a linear or nonlinear regression structure. For these models, defined under frequentist and Bayesian perspectives, maximum likelihood and Bayesian fitting methods are proposed and applied to analyze a European rabbit dataset. Then the class of double generalized nonlinear regression models is presented. These models are defined in the class of biparametric exponential family of distributions. In this class, the mean systematic component follows a nonlinear regression structure, and the systematic variance components follow nonlinear or linear regression structures. Finally, the overdispersed nonlinear regression models are defined, including relevant references.