Dados de área na família GAMLSS em estudos epidemiológicos

Abstract

The progress in the field of statistical analysis has been increasingly significant in recent years. In particular, regression models comprise a set of statistical tools that have received major contributions in a short period of time. These models are one of the most used tools in the scientific world to describe several phenomena in the most varied areas of knowledge. Since the beginning, the normal linear model has been used in many scientific researches for data modeling. However, due to the limitations found in this model, the Generalized Linear Models were introduced, which encompass more probabilistic distributions for the response variable. Subsequently, Generalized Additive Models were proposed, which made the relationship between variables more flexible. Then the GAMLSS models were introduced, which can be seen as a generalization of the other models mentioned above. This new class of models allows not only a greater number of probabilistic distributions for modeling the response variable, but also greater flexibility for the relationship between the variables, as well as the modeling of other distribution parameters, in addition to the location. Recently, an adaptation was made in the GAMLSS models to incorporate the effect of a spatial dependence structure when the assumption of independence of the observations of the response variable is not met and there is correlation in space. In this study, we aimed to study the GAMLSS models in the context of spatial analysis and apply them to real data. For this, data on the occurrence of bovine tuberculosis in the state of Minas Gerais and dengue in the state of Paraíba were used. Satisfactory adjustments were obtained for both databases, even when they presented structural problems such as strong asymmetry and kurtosis and a problem of overdispersion. For dengue data, a spatial component was introduced in the model through an intrinsic autoregressive model, since the data showed significant spatial autocorrelation.