Overdispersed Nonlinear Regression Models

Abstract

In this paper we propose nonlinear regression models in the biparametric family of distributions. In this class of models we propose two new classes of overdispersed nonlinear regression models: the first, defined from the overdispersion family of distributionsproposed by Dey, Gelfand, and Peng (1994), and the second from a class of compound distributions. For these models, we develop a Bayesian method in which samples of the posterior distributions are obtained by applying an iterated Metropolis-Hastings algorithmobtained by assuming two groups of parameters, defined by the mean and dispersion regression structures. In the first subclass of models, to improve the performance of the iterated Metropolis-Hastings algorithm, we develop worked variables from the applicationof Fisher scoring algorithm, to build the kernel transition function. A Bayesian method to fit compound regression models is also proposed. Finally, we present an application to neonatal mortality dataset to illustrate the use of the proposed models and the perfor-mance of the Bayesian method to fit the proposed models.