When the outcome is compositional - a method for conducting compositional response linear mixed models for physical activity, sedentary behaviour and sleep research

Time use is compositional in nature because time spent in sleep, sedentary behaviour and physical activity will always sum to 24 h/day meaning any increase in one behaviour will necessarily displace time spent in another behaviour(s). Given the link between time use and health, and its modifiable nature, public health campaigns often aim to change the way people allocate their time. However, relatively few studies have investigated how movement-behaviour composition changes longitudinally (with repeated measures) due to experimental design elements or participant characteristics. This may be because most mixed-model packages that account for the random effects of repeated measures do not natively allow for a multivariate outcome such as movement-behaviour composition. In the current paper we provide a practical framework of how to implement a multivariate response linear mixed model to investigate how movement-behaviour compositions change with repeated measures. In an example we show how time is reallocated in children across the school year.