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

Driven by technological advances, time series (or intensive longitudinal) data 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. A promising method to translate information on psychological processes unfolding over time into a statistical model is the hidden Markov model (HMM). In the HMM, time series are modeled with a process that switches between a number of hidden (i.e., latent) states, each associated with a different response distribution. This in contrast to commonly used Vector Autoregressive (VAR) based models, which assume the time series fluctuate around a single equilibrium point. By extending the HMM to the multilevel framework, we can obtain a description of subject-specific process dynamics and formally quantify heterogeneity across subjects. 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. To create the conditions for psychological researchers to be able to use the multilevel HMM in their research, we (1) provide an accessible introduction to the use of multilevel HMMs to model continuous outcome time series data typical of intensive longitudinal data; (2) evaluate model selection and estimation performance in situations that resemble typical psychological time series research designs using an extensive numerical evaluation study, varying the level of state separation and the number of states, modeled variables, subjects, and time series length; and (3) 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. Our numerical evaluation results show that researchers can expect the multilevel HMM to peform well when persons are expected to switch between multiple states. Finally, we discuss how multilevel HMMs can advance the study of psychological dynamics with time series, provide empirically based recommendations, and discuss directions for further methodological improvements.