Recovering Bistable Systems from Psychological Time Series

Conceptualizing mental disorders as complex dynamical systems has become a popular framework to study mental disorders. Especially bistable dynamical systems have received much attention, because their properties map well onto many characteristics of mental disorders. While these models were so far mostly used as stylized toy models, the recent surge in psychological time series data promises the ability to recover such models from data. In this paper we investigate how well popular (e.g., the Vector Autoregressive model) and more advanced (e.g., differential equation estimation) data analytic tools are suited to recover bistable dynamical systems from time series. Using a simulated high-frequency time series (measurement every six seconds) as an ideal case we show that while it is possible to recover global dynamics (e.g., position of fixed points, transition probabilities) it is difficult to recover the microdynamics (i.e., moment to moment interactions) of a bistable system. Repeating all analyses with a sampling frequency typical for Experience Sampling Method studies (measurement every 90 minutes) showed that the recovery of the global dynamics was still successful, but no microdynamics could be recovered. These results raise two fundamental issues involved in studying mental disorders from a complex systems perspective: first, it is generally unclear what to conclude from a statistical model about an underlying complex systems model; and second, if the sampling frequency is too low, it is impossible to recover microdynamics. In response to these results we propose a new modeling strategy based on substantively plausible dynamical systems models.