Classical and Robust Regression Analysis with Compositional Data

Abstract

Compositional data carry their relevant information in the relationships (logratios) between the compositional parts. It is shown how this source of information can be used in regression modeling, where the composition could either form the response, or the explanatory part, or even both. An essential step to set up a regression model is the way how the composition(s) enter the model. Here, balance coordinates will be constructed that support an interpretation of the regression coefficients and allow for testing hypotheses of subcompositional independence. Both classical least-squares regression and robust MM regression are treated, and they are compared within different regression models at a real data set from a geochemical mapping project.