Modelos aditivos generalizados para posição, escala e forma (Gamlss) na modelagem da área miocárdica sob risco de Necrose.

Abstract

The aim of this work is to study the Family of Generalized Additive Models for Position, Scale and Shape (GAMLSS) and apply it to a database, referring to patients who suffered from acute myocardial infarction (AMI), whose the response variable is limited to the continuous interval (0,1). In this way, it was necessary to study distributions that behave well with this type of variable, which stand out Beta and Generalized Beta Type 1. Beta regression models were obtained for comparison of the adjustments. The resulting GAMLSS models modeled two parameters, and the assumptions of normality, independency and homoscedasticity of the residues for both were reached. The generalized GAIC and R² values were superior to those of the beta regression models created, in addition to presenting better results in residue analysis. It is concluded that the GAMLSS models present themselves as a powerful tool in the adjustment of these models, since it assists the researcher in steps of the modeling that are often done in an intuitive way besides modeling not only the average, but also also the dispersion, asymmetry and kurtosis, opening possibilities to reach good adjustments without the need to exclude observations from the databases.