Why a course in compositional data analysis? Compositional data consist of vectors whose components are the proportion or percentages of some whole. Their peculiarity is that their sum is constrained to the be some constant, equal to 1 for proportions, 100 for percentages or possibly some other constant c for other situations such as parts per million (ppm) in trace element compositions. Unfortunately a cursory look at such vectors gives the appearance of vectors of real numbers with the consequence that over the last century all sorts of sophisticated statistical methods designed for unconstrained data have been applied to compositional data with inappropriate inferences. All this despite the fact that many workers have been, or should have been, aware that the sample space for compositional vectors is radically different from the real Euclidean space associated with unconstrained data. Several substantial warnings had been given, even as early as 1897 by Karl Pearson in his seminal paper on spurious correlations and then repeatedly in the 1960’s by geologist Felix Chayes. Unfortunately little heed was paid to such warnings and within the small circle who did pay attention the approach was essentially pathological, attempting to answer the question: what goes wrong when we apply multivariate statistical methodology designed for unconstrained data to our constrained data and how can the unconstrained methodology be adjusted to give meaningful inferences. A Concise Guide to Compositional Data Analysis

# Document worth reading: “A Concise Guide to Compositional Data Analysis”

**29**
*Monday*
Jun 2015

Posted Documents

in