On the directed likelihood statistic in simplex regressions

We address the issue of performing testing inference in small-sized samples in the class of simplex regression models, which is tailored to continuous response variables that assume values in the standard unit interval, such as rates and proportions. We consider the directed likelihood test statistic and derive a simple adjustment factor to this statistic to improve its performance in small samples. We compare the finite sample performances of the (usual and adjusted) directed likelihood test statistics using Monte Carlo simulation experiments. The numerical results favor the adjusted directed likelihood test we propose. We also provide an empirical application for illustrative purposes.