Bootstrap-based corrections in the Dirichlet regression model with mean vector parametrization

The Dirichlet regression model is a tool for modeling compositional data, particularly when using an alternative parameterization in which the mean components are explicitly represented. In this context, hypothesis testing is typically conducted using the likelihood ratio test (LRT). However, the asymptotic chi-squared distribution assumed for the LRT statistic may lead to size distortions when the sample size is small. To address this limitation, this work evaluates two bootstrap-based corrections to the LRT within the Dirichlet regression model using mean vector parametrization. Monte Carlo simulation studies are performed under five different scenarios, varying both parameter values and covariate distributions. Results show that both corrected tests exhibit null rejection rates close to the nominal levels and similar power, while the LRT is liberal in small samples. A real-data application involving sleep stage proportions further illustrates the usefulness of the considered corrections.