Compositional PLS biplot based on pivoting balances: an application to explore the association between 24-h movement behaviours and adiposity

Movement behaviour data are compositional in nature, therefore the logratio methodology has been demonstrated appropriate for their statistical analysis. Compositional data can be mapped into the ordinary real space through new sets of variables (orthonormal logratio coordinates) representing balances between the original compositional parts. Geometric rotation between orthonormal logratio coordinates systems can be used to extract relevant information from any of them. We exploit this idea to introduce the concept of pivoting balances, which facilitates the construction and use of interpretable balances according to the purpose of the data analysis. Moreover, graphical representation through ternary diagrams has been ordinarily used to explore time-use compositions consisting of, or being amalgamated into, three parts. Data dimension reduction techniques can however serve well for visualisation and facilitate understanding in the case of larger compositions. We here develop suitable pivoting balance coordinates that in combination with an adapted formulation of compositional partial least squares regression biplots enable meaningful visualisation of more complex time-use patterns and their relationships with an outcome variable. The use and features of the proposed method are illustrated in a study examining the association between movement behaviours and adiposity from a sample of Czech school-aged girls. The results suggest that an adequate strategy for obesity prevention in this group would be to focus on achieving a positive balance of vigorous physical activity in combination with sleep against the other daily behaviours.