Correções de Bartlett baseadas em bootstrap no modelo de regressão Dirichlet com parametrização baseada no vetor de médias

Abstract

In parametric regression models, it is common to be interested in testing hypotheses about the values of their parameters. In this regard, the most commonly used test when testing more than one parameter is the Likelihood Ratio Test (LRT). This test can be used, for example, to infer the parameters of the Dirichlet multivariate regression model, which is widely applied in modeling compositional data, i.e., multivariate positive observations summing to one. A problem with this test is that the distribution of its statistic under H0 may not be well approximated by the chi-square distribution in small samples, making the test too liberal. Thus, we consider a model with a specific parameterization of the Dirichlet distribution, where the parameters are a function of the mean vector, and apply a Bartlett correction factor based on bootstrap to the LRT statistic. In this way, the corrected test is expected to have a test statistic whose distribution under H0 is closer to the chi-square distribution, regardless of the sample size. The main objective of this study is to compare the performance of the tests resulting from the bootstrap corrections to the usual LRT. Monte Carlo simulation studies showed that the tests with the applied corrections achieved null rejection rates close to nominal levels in small and moderate sample sizes, while also demonstrating good power. An application on sleep stages illustrates the usefulness of these corrected tests.