Contributions to the analysis of dispersed count data

• Ano de defesa: 2019
• Autor(a) principal: Ribeiro Junior, Eduardo Elias
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Count data; Dados de contagens; Discrete probability models; Dispersão variável; Inferência baseada em verossimilhança; Likelihood-based inference; Modelos probabilísticos discretos; Overdispersion; Subdispersão; Superdipersão; Underdispersion; Varying dispersion
• Link de acesso: http://www.teses.usp.br/teses/disponiveis/11/11134/tde-14052019-152803/

In many agricultural and biological contexts, the response variable is a nonnegative integer value which we wish to explain or analyze in terms of a set of covariates. Unlike the Gaussian linear model, the response variable is discrete with a distribution that places probability mass at natural numbers only. The Poisson regression is the standard model for count data. However, assumptions of this model forces the equality between mean and variance, which may be implausible in many applications. Motivated by experimental data sets, this work intended to develop more realistic methods for the analysis of count data. We proposed a novel parametrization of the COM-Poisson distribution and explored the regression models based on it. We extended the model to allow the dispersion, as well as the mean, depending on covariates. A set of count statistical models, namely COM-Poisson, Gamma-count, discrete Weibull, generalized Poisson, double Poisson and Poisson-Tweedie, was reviewed and compared, considering the dispersion, zero-inflation, and heavy tail indexes, together with the results of data analyzes. The computational routines developed in this dissertation were organized in two R packages available on GitHub.