论文标题
合成结果和预测因子的无转换线性回归
A Transformation-free Linear Regression for Compositional Outcomes and Predictors
论文作者
论文摘要
组成数据在许多领域都常见，无论是结果还是预测变量。当结果和预测变量的组成是有限的，并且由于使用复杂的对数比率变换，因此很难解释模型的模型清单。我们开发了一个无转换的线性回归模型，其中组成结果的预期值表示为从组成预测因子的单个马尔可夫过渡。我们的方法基于瞬间的广义方法，因此不需要完整的数据可能性规范，并且对不同的数据生成机制具有鲁棒性。我们的模型易于解释，在组成结果和协变量中允许0s和1s，并包含一些有趣的子案例。我们还为线性独立性开发了置换测试。最后，我们表明，尽管它很简单，但我们的模型还是准确地捕获了来自教育和医学研究的组成数据之间的关系。
Compositional data are common in many fields, both as outcomes and predictor variables. The inventory of models for the case when both the outcome and predictor variables are compositional is limited and the existing models are difficult to interpret, due to their use of complex log-ratio transformations. We develop a transformation-free linear regression model where the expected value of the compositional outcome is expressed as a single Markov transition from the compositional predictor. Our approach is based on generalized method of moments thereby not requiring complete specification of data likelihood and is robust to different data generating mechanism. Our model is simple to interpret, allows for 0s and 1s in both the compositional outcome and covariates, and subsumes several interesting subcases of interest. We also develop a permutation test for linear independence. Finally, we show that despite its simplicity, our model accurately captures the relationship between compositional data from education and medical research.
