When the outcome is compositional: A method for conducting compositional response linear mixed models for physical activity, sedentary behaviour and sleep research.
A practical framework for implementing a compositional multivariate-response linear mixed model is provided that can model the entire 24-hour movement-behaviour composition as the dependent variable within a multilevel framework, with results invariant to the chosen log-ratio basis.
Key Findings
Background
Time use data (sleep, sedentary behaviour, physical activity) is compositional in nature because all behaviours must sum to 24 hours/day, meaning any increase in one behaviour necessarily displaces time in another.
This compositional constraint means standard linear models are inappropriate for analyzing movement behaviour data as an outcome
Most mixed-model packages do not natively support a multivariate outcome such as movement-behaviour composition
Relatively few studies have investigated how movement-behaviour compositions change longitudinally due to this analytical challenge
Methods
The proposed compositional multivariate-response linear mixed model accounts for covariances across and within response variables at both the grouping level and the observation level.
The method accounts for covariances across and within response variables at the grouping level (individual, cluster, etc.)
The method also accounts for covariance between response variables at the observation level
Results are invariant to the chosen log-ratio basis used to construct the response variables, meaning mathematically equivalent models are produced regardless of basis choice
The framework is applicable to longitudinal cohort studies, intervention trials, and clustered cross-sectional designs (e.g., students within schools, patients within clinics)
Methods
The method enables modeling of the entire 24-hour movement-behaviour composition as the dependent variable within a multilevel framework.
The approach can handle experimental design elements such as intervention effects
The approach can handle differences due to participant socio-demographic characteristics such as sex and socio-economic status within clustered sampling designs
The framework addresses a gap where mixed-model packages that account for random effects do not natively support multivariate compositional outcomes
Results
In a worked example, the compositional multivariate-response linear mixed model was used to investigate how time is reallocated in children across the school year.
The worked example demonstrated practical application of the method in a longitudinal context
The example used a repeated-measures design with children as the unit of analysis
The school year served as the temporal frame for examining compositional changes in 24-hour movement behaviours
Conclusions
The proposed framework addresses a methodological gap in physical activity, sedentary behaviour, and sleep research by providing a practical implementation guide for compositional mixed models.
The method is described as applicable to 'many designs including longitudinal cohort studies, intervention trials, and clustered cross-sectional designs'
The paper provides a 'practical framework' intended to make the method accessible to researchers
The approach fills the need for analytical methods that respect the sum-to-constant constraint of time-use data while also accommodating clustered and repeated-measures study designs
What This Means
This research addresses a statistical problem in health research: how do you properly analyze data about how people spend their time across sleep, sitting, and physical activity? Because there are only 24 hours in a day, spending more time in one activity automatically means spending less in another — a property called 'compositional' data. Most standard statistical tools don't handle this constraint properly, and even fewer can handle studies where the same people are measured multiple times or where participants are grouped together (like students in the same school). This paper introduces a practical method — a compositional multivariate-response linear mixed model — that correctly accounts for all of these features at once.
The method works by transforming the time-use data using log-ratios (a standard technique for compositional data) and then fitting a mixed model that handles the interconnected nature of the behaviours, the clustering of participants, and repeated measurements over time. Importantly, the results are mathematically consistent regardless of which specific transformation approach is chosen, giving researchers flexibility. The authors demonstrate the approach using real data tracking how children's daily movement patterns change over the course of a school year.
This research matters because public health efforts often try to change how people allocate their time — for example, encouraging less sitting and more physical activity — and researchers need proper tools to measure whether such interventions work. By providing a step-by-step framework that handles the complexity of time-use data in real-world study designs, this paper gives researchers in physical activity, sleep, and sedentary behaviour fields a more rigorous and appropriate way to analyze their data and draw valid conclusions.
Miatke A, Stanford T, Olds T, Fraysse F, Maher C, Martin-Fernandez J, et al.. (2026). When the outcome is compositional: A method for conducting compositional response linear mixed models for physical activity, sedentary behaviour and sleep research.. PloS one. https://doi.org/10.1371/journal.pone.0340373