A composition is a vector of proportions describing the contribution of each of k components to the whole. We introduce an algebra for compositions that provides a natural definition for additive statistical models. The algebra eases interpretation of treatment effects, treatment interactions, and covariates. Our developments extend the logistic normal modeling framework of Aitchison (1982, 198...

The application of compositional data analysis through log ratio transformations corresponds to a multinomial logit model for the shares themselves. This model is characterized by the property of Independence of Irrelevant Alternatives (IIA). IIA states that the odds ratio –in this case the ratio of shares – is invariant to the addition or deletion of outcomes to the problem. It is exactly this...

The so-calledAir Quality Index (AQI), expresses the quality of atmospheric air. The overall AQI is determined from the AQIs of some reference air pollutants, which are calculated by a transform of the respective concentrations. Concentrations of air pollutants are compositional data; they are expressed as part of mass of each pollutant in a total air volume or mass. Therefore, air pollution con...

Compositional data arises in a wide variety of research areas when some form standardization and composition is necessary. Estimating covariance matrices fundamental importance for high-dimensional compositional analysis. However, existing methods require the restrictive Gaussian or sub-Gaussian assumption, which may not hold practice. We propose robust adjusted thresholding procedure based on ...

The common approach to compositional data analysis is transform the by means of logratios. Logratios between pairs parts (pairwise logratios) are easiest interpret in many research problems. When number large, some form logratio selection a must, for instance an unsupervised learning method based on stepwise pairwise logratios that explain largest percentage variance dataset. In this article we...