Interpretation of Compositional Regression with Application to Time Budget Analysis

  • Ivo Muller Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacky University
  • Karel Hron Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacky University
  • Eva Fiserova Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacky University
  • Jan Smahaj Department of Psychology, Philosophical Faculty, Palacky University
  • Panajotis Cakirpaloglu Department of Psychology, Philosophical Faculty, Palacky University
  • Jana Vancakova Prostor Plus, Kolin

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.
Published
2018-02-02
Section
Articles