Hierarchical continuous time modeling

Abstract We describe the basic usage of the hierarchical formulation of the ctsem software for continuous-time dynamic modeling in R, the scope of which been expanded to include nonlinear models and optimization with optional importance sampling, meaning that the approach described herein largely supersedes the initial mixed effects approach based upon OpenMx, as estimation options now include maximum likelihood, maximum a posteriori, and fully Bayesian. We describe the continuous time dynamic model governing within-subject dynamics, and the hierarchical model governing the distribution of subject-level parameters, then walk through installing the ctsem software, setting up a data structure, specifying and fitting the model, followed by summary and plotting functions. Some details on additional complexity are then provided, including an example model with a more complex dynamic structure, a discussion of the various options for incorporating stationarity assumptions into the model, and a walk-through of the various transformations involved in the model.