Modeling Psychological Time Series with Multilevel Hidden Markov Models: A Numerical Evaluation

Time series data are becoming a common type of data in psychological research, allowing researchers to study the dynamics of human functioning at an unprecedented level of granularity. The Hidden Markov Model (HMM) is a powerful model for capturing psychological processes. 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. By extending the HMM to the multilevel framework, we obtain better estimates of person-specific models under standard assumptions; and we get a model for heterogeneity across persons, which allow one to distinguish between population heterogeneity and sampling variation. Despite their potential, multilevel HMMs are currently not widely used to estimate psychological time series. A key reason is that the methodology has not been thoroughly evaluated in this context. In this paper, we address this issue. We evaluate model selection and estimation performance in an extensive simulation study, using scenarios typical for psychological time series research designs and varying the level of state separation and the number of states, modeled variables, persons, and time-series length. Our numerical evaluation results show that researchers can expect the multilevel HMM to perform well when persons are expected to switch between multiple states. Finally, we provide empirically based recommendations, and discuss directions for further methodological improvements.