Weighted Logratio Biplots, Correspondence Analysis and Spectral Maps

Starting with logratio biplots for compositional data, which are based on the principle of subcompositional coherence, and then adding weights, as in correspondence analysis, we rediscover Lewi's spectral map and many connections to analyses of two-way tables of non-negative data. Thanks to the weighting, the method also achieves the property of distributional equivalence

The single principle of compositional data analysis, continuing fallacies, confusions and misunderstandings and some suggested remedies

In any discipline, where uncertainty and variability are present, it is important to have principles which are accepted as inviolate and which should therefore drive statistical modelling, statistical analysis of data and any inferences from such an analysis. Despite the fact that two such principles have existed over the last two decades and from these a sensible, meaningful methodology has been developed for the statistical analysis of compositional data, the application of inappropriate and/or meaningless methods persists in many areas of application. This paper identifies at least ten common fallacies and confusions in compositional data analysis with illustrative examples and provides readers with necessary, and hopefully sufficient, arguments to persuade the culprits why and how they should amend their ways