Abstract

Continuous-time dynamic models provide a principled and flexible framework for studying psychological processes that evolve over time while accommodating irregular measurement intervals and latent structure. This is achieved by linking non-linear stochastic differential equations, governing the process model, to a non-linear measurement / factor model. In the ctsem software this is estimated by means of a hybrid extended Kalman filter. Over the past decade, continuous-time models have been applied across domains ranging from affective dynamics and cognitive development to intervention monitoring and psychopathology. Some challenges to broader impact include scaling to larger, more realistic systems, challenges of specifying appropriate models, and ensuring confidence in interpretation.

Recent methodological advances directly target the scaling challenge. Re-working of core algorithms delivers substantial gains in speed and parallelization, while enhancing flexibility -- enabling estimation of higher dimensional models with nonlinear dependencies, hierarchical structure, multi-timescale dynamics and richer measurement components.

Model specification for complex models is demanding, I will discuss some existing approaches and highlight challenges, particularly in terms of iterative model building and testing approaches, and the diagnosis of model misspecification.

Confidence in interpretation depends on design and measurement assumptions. Continuous-time models do not by themselves guarantee causal validity, and many psychological systems operate across interacting time scales that are often observed in separate datasets or measurement regimes. Future work therefore emphasizes integrative modeling across datasets and time scales.