State Space Mixture Modeling: Finding People with Similar Patterns of Change

Increasingly, behavioral scientists encounter data where several individuals were measured on multiple variables over numerous occasions. Many current methods combine these data, assuming all individuals are randomly equivalent. An extreme alternative assumes no one is randomly equivalent. We propose state space mixture modeling as one possible compromise. State space mixture modeling assumes that unknown groups of people exist who share the same parameters of a state space model, and simultaneously estimates both the state space parameters and group membership. The goal is to find people that are undergoing similar change processes over time. The present work demonstrates state space mixture modeling on a simulated data set, and summarizes the results from a large simulation study. The illustration shows how the analysis is conducted, whereas the simulation provides evidence of its general validity and applicability. In the simulation study, sample size had the greatest influence on parameter estimation and the dimension of the change process had the greatest impact on correctly grouping people together, likely due to the distinctiveness of their patterns of change. State space mixture modeling offers one of the best-performing methods for simultaneously drawing conclusions about individual change processes while also analyzing multiple people.