MATLAB Example to Illustrate John Aitchison’s Log-Ratio Transformation

Anyone who has ever dealt with the statistical analysis of compositional data must have stumbled across John Aitchison’s (1926-2016) log-ratio transformation. The Scottish statistician spent much of his career on the statistics of such data, wrote the famous book “The Statistical Analysis of Compositional Data” (Aitchison, 1986, 2003) and multiple papers on the same topic, with associated MATLAB 5 software package CODA available from the author at the time of publication, updated versions now available for download at CoDAWeb. Aitchison’s log-ratio transformation overcomes the close-sum problem of closed data, i.e. data expressed as proportions and adding up to a fixed total such as 100 percent. The close-sum problem causes spurious negative correlations between pairs of variables that are avoided by logarithmizing ratios of the variables. Here is a simple MATLAB example illustrating the effect of Aitchison’s log-ratio transformation on compositional data. Continue reading “MATLAB Example to Illustrate John Aitchison’s Log-Ratio Transformation”