Modelling Psychological Time Series with Multilevel Hidden Markov Models: A Numerical Evaluation and Tutorial

Time series are becoming a common type of data in psychological research, allowing us to study the dynamics of human functioning at an unprecedented level of granularity. Much of the current modelling work focuses on variations of vector autoregressive (VAR) models, in which variables are predicted by themselves and other variables at previous time points. An alternative to these models are Hidden Markov Models (HMMs), which model time series with a process that switches between a number of latent states, each associated with a different response distribution. Despite the fact that HMMs are often both theoretically interesting and can provide a better model fit for many time series, HMMs have rarely been used to model psychological time series. The reason for this has been the lack of software to fit HMMs in a multilevel setting, which is required both to make estimation feasible in a realistic applied setting, and to quantify and account for heterogeneity between subjects. In this paper, we address this issue by introducing multilevel HMMs and their estimation in a Bayesian setting; we evaluate with numerical experiments how well these models can be estimated in settings corresponding to empirical research using the R package mHMMbayes; and we provide a fully reproducible tutorial that guides the reader through all steps of model selection, model checking, and interpretation using an openly available dataset on emotion dynamics. Finally, we discuss the potential positive impact of adding multilevel HMMs to the time series modelling toolbox and discuss directions for further methodological improvements.