Interpretation of Compositional Regression with Application to Time Budget Analysis

Abstract

Regression with compositional response or covariates, or even regression between parts of a composition, is frequently employed in social sciences. Among other possible applications, it may help to reveal interesting features in time allocation analysis. As individual activities represent relative contributions to the total amount of time, statistical processing of raw data (frequently represented directly as proportions or percentages) using standard methods may lead to biased results. Specific geometrical features of time budget variables are captured by the logratio methodology of compositional data, whose aim is to build (preferably orthonormal) coordinates to be applied with popular statistical methods. The aim of this paper is to present recent tools of regression analysis within the logratio methodology and apply them to reveal potential relationships among psychometric indicators in a real-world data set. In particular, orthogonal logratio coordinates have been introduced to enhance the interpretability of coefficients in regression models.