Modelagem composicional com regressão Dirichlet: correção de viés por bootstrap e teste para seleção de modelos não-encaixados

Abstract

This study aims to investigate the effectiveness of bias correction via the Bootstrap technique in Dirichlet regression models, and to adapt hypothesis tests for non-nested models, such as the J and MJ tests, to the Dirichlet regression context, in order to support the selection of competing models. Regression models are fundamental in statistical analysis, enabling the description and prediction of relationships between variables. In particular, the Dirichlet regression model is suitable for compositional data, which are characterised by components that represent proportional parts of a whole. Parameter estimation in this model using maximum likelihood may exhibit significant bias in small samples, compromising inferential quality. Thus, this work proposes to evaluate the performance of bias correction through the Bootstrap method, in both its parametric and non-parametric versions, by comparing it with the original estimators through Monte Carlo simulations. The results demonstrate that the resampling technique is effective in reducing bias, with a variable impact on the mean squared error. Regarding the model selection procedure, the Monte Carlo experiments demonstrated that the proposed adaptation of the MJ test, based on the choice of the maximum p-value among competing models, yielded null rejection rates close to the nominal significance levels and a high frequency of correctly selecting the true model.