Bayesian Multilevel Compositional Data Analysis: Introduction, Evaluation, and Application

Multilevel compositional data commonly occur in various fields, particularly in intensive, longitudinal studies using ecological momentary assessments. Examples include data repeatedly measured over time that are non-negative and sum to a constant value, such as sleep-wake movement behaviours in a 24-hour day. This article presents a novel methodology for analysing multilevel compositional data using a Bayesian inference approach. This method can be used to investigate how reallocation of time between sleep-wake movement behaviours may be associated with other phenomena (e.g., emotions, cognitions) at a daily level. We explain the theoretical details of the data and the models, and outline the steps necessary to implement this method. We introduce the R package multilevelcoda to facilitate the application of this method and illustrate using a real data example. An extensive parameter recovery simulation study verified the robust performance of the method. Across all simulation conditions investigated in the simulation study, the model had minimal convergence issues (convergence rate > 99%) and achieved excellent quality of parameter estimates and inference, with an average bias of 0.00 (range -0.09, 0.05) and coverage of 0.95 (range 0.93, 0.97). We conclude the article with recommendations on the use of the Bayesian compositional multilevel modelling approach, and hope to promote wider application of this method to answer robust questions using the increasingly available data from intensive, longitudinal studies.