Modelo de Regressão Simplex Multivariado (Inferência, Diagnóstico, Aplicação).

Abstract

Beta and Simplex regression models have been widely used to analyze variables that represent rates, proportions or index, that is, variables measurable in the open interval (0.1). In some phenomena these variables are correlated, which requires obtaining a multivariate distribution, in particular the bivariate case, according to a certain approach. In this sense, the main objective of this work is to propose the Multivariate Simplex regression model (MRSM) via the copula function. Estimators for the parameters are found via the maximum likelihood (MV) method and, via a simulation study, their respective asymptotic behaviors are studied. A diagnostic analysis, such as: residual analysis and global influence (generalized Cook’s distance and likelihood departure), are developed with the aim of identifying possible atypical and/or influential points and the suitability of the model to the data. Finally, the results are applied to two sets of real data to exemplify the developed methodology.