Title: Weighting of logratios in compositional regression
Authors: Karel Hron - Palacky University (Czech Republic) [presenting]
Nikola Stefelova - Palacky University Olomouc (Czech Republic)
Javier Palarea-Albaladejo - Biomathematics and Statistics Scotland (United Kingdom)
Abstract: Compositional data are multivariate positive observations which are characterized by the scale invariance property: any positive multiple does not change the essential information contained in ratios between components. As such, compositional data represent observations carrying relative information, commonly expressed in units like proportions, percentages, mg/kg, mg/l and so on; thus including also those which do not necessarily impose a constant sum constraint of components. The logratio analysis approach to compositional data builds on a Euclidean space structure for scale invariant observations, so-called the Aitchison geometry, and expresses compositions in real coordinates, preferably with respect to an orthonormal basis. One particular choice are pivot coordinates, by which the first coordinate aggregates all logratios with respect to a component of interest. Because some logratios may be affected by data quality problems, or may represent a completely different process than the others, it is desirable in practice to be able to reduce their contribution to the first pivot coordinate. Therefore, in a context of regression analysis with compositional explanatory variables, weights are sensibly defined according to correlations between a (real) response and the logratios. Theoretical aspects will be accompanied by demonstrations with both simulated and real-world metabolomic data.