Regression analysis with compositional data using orthogonal log-ratio coordinates

Abstract

Compositional data frequently arise when data refer to components which are proportions or fractions of a whole. Within the log-ratio approach, the analysis of compositional data can be conducted in terms of log-ratio transformations of components. These transformations make it possible to overcome the problem of the constant-sum constraint, making standard statistical methods applicable. In the present work, the log-ratio approach based on orthogonal log-ratio coordinates is adopted to show how it can lead to considerable improvements in the interpretation of the results of regression modeling with compositional data, both as explanatory or response variables. In order to demonstrate its practical usefulness, the methodology presented in this paper is applied to the analysis of air pollution produced by vehicles traveling through road intersections, with a specific focus on the effect of the type of traffic control (traffic signal vs. roundabout) on CO2 emissions.