Utilização da estatística gradiente nos modelos Hurdle

Abstract

In many practical problems, there is an interest in modeling data from counting, such as disease incidence. In many practical problems, there is an interest in modeling data from counting, such as incidence of diseases, number of transit, among others situations of interest. In most applications involving this type of data, the Poisson and Binomial Negative distributions are used for modeling. However, the structure of the counting data may exhibit excess zeros and superdispersion, which makes modeling using such distributions undue because they do not have the flexibility to accommodate such behavior. A class of models capable of accommodating both properties (zeros excess and superdispersion) is the class of the Hurdle Models (Cameron; Trivedi, 1998, Regression analysis of count data). In this class of models, because of their complexity, it is common to use hypothesis tests based on the generalized likelihood ratio (Wilks, 1938, Annals of Mathematical Statistics), Wald (Wald, 1943, Transactions of the American Mathematical Society) and Escore (Rao, 1948, Proceedings of the Cambridge Philosophical Society). However, a new statistic has been proposed, called Gradiente (Terrel, 2002, Computing Science and Statistics) as an alternative to classical tests and has received particular attention from the statistical community due to its good properties. The present work considers the performance of the Gradient statistic in comparison to the performance of the other statistics usual in the model textit Hurdle. For this, the class of textit Hurdle models are described, their properties, inferences aspects and the main asymptotic results of the tests are presented. A Monte Carlo simulation study based on the Poisson-Binomial and Hurdle Binomial Negative Binomial models is used to evaluate the performance of the tests in finite samples and at the end of the simulation, the results to a real set of data.