Beta regression with a small cluster at a boundary - Nóbrega, Daniel Araújo (2021)
Analyses of data that have response variables contained in the (0,1) interval have received a lot of attention in the past two decades, most notably through the use of the beta regression model. However, there are situtations where there are boundary observations in the data, i.e. observations equal to zero or to one, in which other methodologies must be considered. In this work, the focus is on data that have a small custer of observations at one of the boundaries and the methods used either provide ways to still fit a beta regression model, via maximum likelihood or via a robust estimation method, for these scenarios by adapting the data to fit onto the (0,1) interval or using a model that can naturally cope with the presence boundary observations; here, the inflated beta regression model and a quasi-likelihood model were used for this purpose. The methods were applied to two different datasets that had distinct characteristics; diagnostic analyses were conducted to assess the quality of the fits and then simulation scenarios were carried out to evaluate the performance of each of the methods in situations that may arise in practice. Finally, some conclusions were made about which methods work best in each of the situations explored.