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. An application to simulated data also suggests that one of the residuals of the proposed class is better to identify model misspecification than its competitors. Finally, the usefulness of the best residual of the proposed class 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.

翻译：成分数据的回归模型在多个知识领域均较为常见。与其他回归模型类似，人们期望在成分数据回归模型中使用近似服从标准正态分布的残差进行诊断分析。然而，目前针对成分数据的回归模型尚未出现满足这一要求的多元残差。本文基于自助法提出了一类渐近服从标准正态分布的成分数据残差。蒙特卡洛模拟研究表明，在小样本条件下，该类残差的分布可被标准正态分布良好近似。对模拟数据的应用分析还表明，所提残差类别中的一种残差在识别模型设定错误方面优于同类其他残差。最后，通过睡眠分期应用实例展示了该类最优残差的实用性。本文提出的残差类别还可推广至其他多元回归模型。