Graphing and communicating compositional data in high dimensions

Visualization of data becomes more challenging as the dimensionality of the data increases, impacting not only the display of the data itself but also the modeling results. This paper discusses common visualization techniques for compositional data. None of them seem to be well suited for changes in compositions that depend on either a metric covariate or a factor. The clr-deviation chart as a chart with a factor or covariate as abscissa and all centered log ratio-transformed component values superimposed on the ordinate axis is then introduced jointly with the clr-component chart. The clr-deviation chart takes advantage of the sum-equals-zero property of clr-transformed compositional data. It has some theoretical and practical advantages over alternatives and one major disadvantage – an arbitrarily scaled ordinate axis; its properties are discussed. The usefulness of the methods are illustrated using an example analyzing the changes of proportions of the different diseases treated by hospitalization over a period of 13 years in Germany