Uncovering Latent Dynamics: Multilevel Hidden Markov Models for Intensive Longitudinal Data

Abstract

This dissertation advances the use of multilevel Hidden Markov Models (MHMMs) for analysing intensive longitudinal data (ILD) in social, behavioural, and neurophysiological research. Traditional statistical approaches often fail to account for the abrupt transitions and multimodal dynamics that characterize processes such as mood regulation, neural activity, or behaviour. By combining the Hidden Markov Model framework with multilevel structures, MHMMs capture discrete latent states while accounting for hierarchical data and individual variability, making them well suited for ILD. The dissertation has three central aims: (1) to evaluate the performance of MHMMs, (2) to further develop the methodological framework, and (3) to demonstrate their utility in applied research. To this end, the R package mHMMbayes was extended to handle categorical, continuous, and count data. Four empirical and simulation-based studies illustrate the flexibility and relevance of MHMMs across domains. The first study uses large-scale simulations to establish guidelines on sample size requirements, showing that multivariate data reduce the need for participants or observations. An empirical application on nonverbal communication demonstrates the model’s interpretive power. The second study applies MHMMs with Gaussian emissions to ecological momentary assessment data from patients with bipolar disorder, uncovering heterogeneous mood states and switching patterns that inform clinical understanding. Methodological extensions address missing and unevenly spaced data. The third study introduces an MHMM with Poisson emissions to model longitudinal count data, highlighting the importance of capturing heterogeneity in emission distributions and demonstrating applications in whale diving behaviour and macaque neural activity. The fourth study applies MHMMs to neural spiking data from macaques performing motor tasks, successfully identifying stable neural states despite trial-specific variability and electrode drift, outperforming single-level HMMs in accuracy and convergence. The dissertation concludes with methodological contributions, including practical guidelines for study design, software extensions, and strategies for handling missing data. It also identifies limitations such as variance overestimation and challenges in modelling heterogeneity in transition dynamics. Future directions include refining estimation techniques, addressing missing data mechanisms, and bridging continuous and discrete-time formulations. Overall, this work establishes the multilevel Hidden Markov Model as a suitable tool for analysing ILD, enabling researchers to uncover latent dynamics with abrupt transitions and offering new insights into psychological, behavioural, and neural processes.