Hierarchical Bayesian Continuous Time Dynamic Modeling

Continuous time dynamic models are similar to popular discrete time models such as autoregressive cross-lagged models, but through use of stochastic differential equations can accurately account for differences in time intervals between measurements, and more parsimoniously specify complex dynamics. As such they offer powerful and flexible approaches to understand ongoing psychological processes and interventions, and allow for measurements to be taken a variable number of times, and at irregular intervals. However, limited developments have taken place regarding the use of continuous time models in a fully hierarchical context, in which all model parameters are allowed to vary over individuals. This has meant that questions regarding individual differences in parameters have had to rely on single-subject time series approaches, which require far more measurement occasions per individual. We present a hierarchical Bayesian approach to estimating continuous time dynamic models, allowing for individual variation in all model parameters. We also describe an extension to the ctsem package for R, which interfaces to the Stan software and allows simple specification and fitting of such models. To demonstrate the approach, we use a subsample from the German socioeconomic panel and relate overall life satisfaction and satisfaction with health. Translational Abstract Continuous time dynamic models allow us to examine how people change over time, and how changes in one aspect of a person, such as health, relate to changes in another aspect, such as satisfaction. The continuous time aspect accurately accounts for differences in time intervals between measurements, and as such allows for measurements to be taken a variable number of times, and at irregular intervals. However, limited developments have taken place regarding the use of continuous time models that allow for differences between people in terms of how their dynamic system functions. This has meant that for questions regarding individual differences, we have had to rely on models estimated independently for each individual, which require far more measurement occasions per individual. We present a hierarchical Bayesian approach to estimating continuous time dynamic models, which allows for individual variation in all aspects of the individuals' dynamic systems and measurement properties. We also describe an extension to the ctsem package for R, which interfaces to the Stan software and allows simple specification and fitting of such models. To demonstrate the approach, we use a portion of the German socio-economic panel and relate overall life satisfaction and satisfaction with health.