Clustering Vector Autoregressive Models: Capturing Qualitative Differences in Within-Person Dynamics

In psychology, studying multivariate dynamical processes within a person is gaining ground. An increasingly often used method is vector autoregressive (VAR) modeling, in which each variable is regressed on all variables (including itself) at the previous time points. This approach reveals the temporal dynamics of a system of related variables across time. A follow-up question is how to analyze data of multiple persons in order to grasp similarities and individual differences in within-person dynamics. We focus on the case where these differences are qualitative in nature, implying that subgroups of persons can be identified. We present a method that clusters persons according to their VAR regression weights, and simultaneously fits a shared VAR model to all persons within a cluster. The performance of the algorithm is evaluated in a simulation study. Moreover, the method is illustrated by applying it to multivariate time series data on depression-related symptoms of young women.