Modelagem conjunta dos parâmetros de locação, escala, assimetria e curtose dos modelos skew-normal e skew-t utilizando o GAMLSS: aplicações na economia, medicina e zoologia

Abstract

Modeling real data via Linear Regression (LR) may be a difficult task when the response variable does not follow a normal distribution or may present non-linear or non-constant variability. Due to these problems, alternative models were proposed, among them we can cite the Generalized Linear Models (GLM), Generalized Additive Models (GAM) and the Generalized Additive Models for Location, Scale and Shape (GAMLSS). The GLM and GAM have the advantage over LR for requiring that the response variable follows any distribution of the exponential family. In GAMLSS, that requirement is no longer necessary, allowing continuous distributions that present asymmetry or even strong skewness, as well as discrete distributions. Additionally, the systematic part of GAMLSS allows not only the scale parameters, but also all the parameters of the response variable to be modeled through parametric or non-parametric (smoothing) functions and\or random effects terms. In this work, in order to assess the flexibility of the response variable in parametric GAMLSS, we will use the normal and t-Student distributions, as well as their asymmetrical versions, skew-normal and skew-t. The efficiency of GAMLSS will be demonstrated through real data analysis in different contexts, such as medicine, economy and zootechnics. The methodology applied in this work is implemented in the gamlss package of the R software.