Modelo poisson zero-modificado com efeito aleatório para dados longitudinais

Abstract

In this work we present the Zero-Modified Poisson model with Normal random effect, and the Zero-Modified Poisson model with Generalized Log-Gamma random effect, which are extensions of the Zero-Modified Poisson model. Since the Generalized Log-Gamma effect generalizes the Normal effect, it can be used in atypical situations where the Normal effect is not the most appropriate (e.g. asymmetric data). The random effect induces correlation in the model and accommodates the intrinsic variability of each individual. Thus, these models allow us to deal with longitudinal counting data, regardless of its number of null observations (zero-inflated or zero-deflated data). We consider the classical and Bayesian approaches to estimate the parameters of the model and we developed a simulation study to evaluate the performance of the estimators. In order to illustrate the proposed procedure, we analysed a set of real data regarding the count of reports of deaths of children aged 1 to 4 years, in the cities of the State of Bahia, Brazil, during the years 2014, 2015 and 2016. The results showed that both models are effective for modeling a longitudinal data set without the preliminary knowledge about the existing inflation or zero deflation characteristic.