  Researchers collecting intensive longitudinal data (ILD) are increasingly
looking to model psychological processes, such as emotional dynamics, that
organize and adapt across time in complex and meaningful ways. This is also the
case for researchers looking to characterize the impact of an intervention on
individual behavior. To be useful, statistical models must be capable of
characterizing these processes as complex, time-dependent phenomenon, otherwise
only a fraction of the system dynamics will be recovered. In this paper we
introduce a Square-Root Second-Order Extended Kalman Filtering approach for
estimating smoothly time-varying parameters. This approach is capable of
handling dynamic factor models where the relations between variables underlying
the processes of interest change in a manner that may be difficult to specify
in advance. We examine the performance of our approach in a Monte Carlo
simulation and show the proposed algorithm accurately recovers the unobserved
states in the case of a bivariate dynamic factor model with time-varying
dynamics and treatment effects. Furthermore, we illustrate the utility of our
approach in characterizing the time-varying effect of a meditation intervention
on day-to-day emotional experiences.
