A Class of Bootstrap Based Residuals for Compositional Data

Regression models for compositional data are common in several areas of knowledge.As in other classes of regression models, it is desirable to perform diagnostic analysis in these models using residuals that are approximately standard normally distributed.However, for regression models for compositional data, there has not been any multivariate residual that meets this requirement.In this work, we introduce a class of asymptotically standard normally distributed residuals for compositional data based on bootstrap.Monte Carlo simulation studies indicate that the distributions of the residuals of this class are well approximated by the standard normal distribution in small samples.Two other simulation studies suggest that residuals of this class can detect a wrong linear predictor, while one of them performs well in identifying an incorrect response distribution.The usefulness of this residual is illustrated through an application on sleep stages.The class of residuals proposed here can also be used in other classes of multivariate regression models.