When the outcome is compositional: A method for conducting compositional response linear mixed models for physical...

Area of Science:

• Movement behaviour science
• Biostatistics
• Public Health

Background:

• Time use is compositional, summing to 24 hours daily, meaning changes in one activity impact others.
• Public health initiatives often target time allocation for health benefits, but analyzing longitudinal changes in these compositions is challenging.
• Existing statistical models struggle with multivariate compositional outcomes in multilevel frameworks.

Purpose of the Study:

• To present a practical framework for compositional multivariate-response linear mixed models.
• To enable the analysis of the entire 24-hour movement-behaviour composition within a multilevel structure.
• To provide a method applicable to longitudinal, intervention, and clustered designs.

Main Methods:

• Implementation of a compositional multivariate-response linear mixed model.
• Accounting for covariances across and within response variables at grouping and observation levels.
• Ensuring results are invariant to the log-ratio basis used.

Main Results:

• The proposed framework effectively models 24-hour movement-behaviour compositions in a multilevel context.
• The method handles complex dependencies within and between individuals/clusters.
• A worked example demonstrates application to analyzing time reallocation in children during the school year.

Conclusions:

• This statistical approach offers a robust solution for analyzing compositional time-use data in various study designs.
• It facilitates a deeper understanding of how time is allocated and reallocated across different behaviours and populations.
• The framework is valuable for researchers investigating health-related time-use patterns, particularly in longitudinal and clustered studies.