Compositional data analysis applied to a study of movement behaviours of recent retirees

Abstract

Studies of movement behaviours have numerous applications. A recent approach involves studying the time spent on different activity types using compositional data analysis. In compositional data analysis, several variables are constrained to an arbitrary sum and the primary interest is their proportions of the whole.

This thesis explores the mathematical foundations of the study of compositional data and their practical applications. First, mathematical operations are defined for compositions using Aitchison geometry. Methods are presented for transforming compositions into real-valued coordinates and back. Various statistical methods are also defined for compositions and compositional data.

Some of the techniques presented are demonstrated by applying them to a study of movement behaviours. REACT is a randomized controlled trial study focusing on whether commercial activity trackers affect movement behaviours among the recently retired. By using compositional data analysis, the proportions of time spent on different activity types can be studied. Based on the results, it would appear that those who used activity trackers spent a slightly higher portion of their day on physical activity than those who did not.