Linear dynamical system theory is a broad theoretical framework that has been applied in various research areas such as engineering, econometrics and recently in psychology. It quantifies the relations between observed inputs and outputs that are connected through a set of latent state variables. State space models are used to investigate the dynamical properties of these latent quantities. These models are especially of interest in the study of emotion dynamics, with the system representing the evolving emotion components of an individual. However, for simultaneous modeling of individual and population differences, a hierarchical extension of the basic state space model is necessary. Therefore, we introduce a Bayesian hierarchical model with random effects for the system parameters. Further, we apply our model to data that were collected using the Oregon adolescent interaction task: 66 normal and 67 depressed adolescents engaged in a conflict interaction with their parents and second-to-second physiological and behavioral measures were obtained. System parameters in normal and depressed adolescents were compared, which led to interesting discussions in the light of findings in recent literature on the links between cardiovascular processes, emotion dynamics and depression. We illustrate that our approach is flexible and general: The model can be applied to any time series for multiple systems (where a system can represent any entity) and moreover, one is free to focus on whatever component of the versatile model.
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