In current applied research the most-used route to an analysis of composition is through log-ratios -- that is, contrasts among log-transformed measurements. Here we argue instead for a more direct approach, using a statistical model for the arithmetic mean on the original scale of measurement. Central to the approach is a general variance-covariance function, derived by assuming multiplicative measurement error. Quasi-likelihood analysis of logit models for composition is then a general alternative to the use of multivariate linear models for log-ratio transformed measurements, and it has important advantages. These include robustness to secondary aspects of model specification, stability when there are zero-valued or near-zero measurements in the data, and more direct interpretation. The usual efficiency property of quasi-likelihood estimation applies even when the error covariance matrix is unspecified. We also indicate how the derived variance-covariance function can be used, instead of the variance-covariance matrix of log-ratios, with more general multivariate methods for the analysis of composition. A specific feature is that the notion of `null correlation' -- for compositional measurements on their original scale -- emerges naturally.

翻译：在当前的实证研究中，最常用的组成分析方法是通过对数比率——即对对数变换后的测量值进行对比。本文主张采用更直接的方法，使用原始测量尺度上算术平均值的统计模型。该方法的核心理念是假设乘法测量误差，推导出一般的方差-协方差函数。由此，对组成的Logit模型进行拟似然分析，构成了对数比率变换后测量值多元线性模型应用的普遍替代方案，并具有显著优势。这些优势包括：对模型规范次要方面的稳健性、数据中存在零值或接近零值测量值时的稳定性，以及更直观的解释性。即使误差协方差矩阵未指定，拟似然估计通常具有的效率属性依然适用。我们还指出，所推导的方差-协方差函数可替代对数比率的方差-协方差矩阵，用于更通用的多元组成分析方法。其一个独特特征是，在原始尺度上组成测量的“零相关”概念会自然显现。