Between- and Within-subject Variability in Actigraphy Data: A Case Study on Sleep Patterns in Schizophrenia

Abstract

Variability in longitudinal health outcomes provides critical insight into disease dynamics, yet most statistical analyses continue to prioritize mean trajectories. This limitation is particularly consequential in psychiatric and mobile health (mHealth) research, where intensive repeated measurements increasingly reveal pronounced heterogeneity and temporal instability that cannot be captured by average responses alone. Standard mixed-effects models typically impose homoscedastic variance assumptions and relegate variability to a nuisance component, despite mounting evidence that both variability information, at both between- and within-subject level, carry independent clinical significance. Here, we describe an improved mixed-effects location-scale model for longitudinal outcomes that simultaneously characterizes mean structure, between-subject heterogeneity, and within-subject fluctuations. The proposed framework explicitly links variance components to both time-invariant and time-varying covariates, extending classical mixed-effects models to accommodate heteroscedastic and dynamically evolving variability. By jointly modeling location and scale parameters, the method enables direct inference on variability (or stability) of the data alongside mean trends. We evaluated the approach using an actigraphy-based mHealth case study of sleep patterns in schizophrenia. Our results demonstrate that explicitly modeling variability uncovers clinically relevant structure obscured by mean-based analyses, underscoring the importance of variability-aware modeling for modern longitudinal and mHealth research.