Modeling Psychological Time Series with Multilevel Hidden Markov Models: A Tutorial

Time series (or intensive longitudinal) data are now used throughout psychological science, allowing researchers to study the dynamics of human functioning at an unprecedented level of granularity. Capturing these dynamics requires appropriate statistical models. A powerful class of models for such data are Hidden Markov Model (HMMs), which models systems that switch between a number of latent states, each associated with a different probability distribution. HMMs are able to capture behavior that is more complex than currently predominant linear models such as the Vector Autoregressive model: they can characterize multiple equilibrium states and also quantify how the system transitions between states. HMMs are also able to fit frequent empirical data patterns, such as highly skewed or multimodal distributions. Despite their power in modeling within-person dynamics, HMMs are currently not widely used. We see three reasons for this: 1) many researchers are not familiar with HMMs; 2) software to estimate multilevel HMMs has only recently become available; and 3) estimating, analyzing and reporting HMMs is more involved than for simple linear models and no easy-to-follow tutorials exist. Here, we address all of these issues. We first provide a gentle introduction to HMMs for researchers working with time series data in psychology. We then provide a fully reproducible tutorial that walks the reader through each of the steps of analyzing psychological time series data using the R-package mHMMbayes. Our goal is to removes barriers for researchers working with time series so that they can add (multilevel) HMMs to their methodological toolbox.