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.
Highlights
Regression analysis becomes challenging when compositional data as observations carrying relative information (Aitchison 1986; Pawlowsky-Glahn, Egozcue, and Tolosana-Delgado 2015) occur in the role of response or explanatory variables
In the statistical analysis we focused on those relations that are primarily not gender related
Specific habits of time allocation reveal a lot about an individual, a community, a society, or a culture
Summary
Regression analysis becomes challenging when compositional data as observations carrying relative information (Aitchison 1986; Pawlowsky-Glahn, Egozcue, and Tolosana-Delgado 2015) occur in the role of response or explanatory variables. This might frequently seem to be a purely numerical problem, compositional data in any form inducing a constant sum constraint (proportions, percentages) rather represent a conceptual feature. Compositional data may not necessarily be expressed with a constant sum of components (parts). Apart from the compositional context, due to its psychological, social, and economic
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