Modelos de regressão beta com medidas repetidas via teoria de equações de estimação generalizadas

Abstract

In the most diverse areas of knowledge, such as Actuarial Science, Biology, Economics, Engineering, Medicine, among others, it is common to observe studies with repeated measurements, that is, each sample plot is observed at least twice. Moreover, it should be understood that the presence of repeated measurements imply the existence of dependence between the measurements of the sample intraunits. Regarding the modeling, adjustment and evaluation of the quality of the model for data with repeated measurements, this study highlights the use of Generalized Estimation Equations (GEE’S) proposed by Liang and Zeger (1986) from the perspective of estimation functions (Godambe, 1991). The choice was due to the advantage that this proposal allows the flexibility of the probabilistic model adopted for the response variable. Thus, it is not even necessary to have the knowledge about the associated joint distribution, but only the marginal distributions, in which it was initially assumed to be members of the exponential linear family, thus allowing a high flexibility of modeling. Based on the above, this study, based on the proposal of Venezuela (2008), presents the extent of the use of EEGs in the presence of repeated measures when the marginal distribution is Beta, thus generalizing the Beta de Ferarri and Cribari-Neto regression model (2004).