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Hierarchical continuous (and discrete) time state space modelling, for linear
and nonlinear systems measured by  continuous variables, with limited support for
binary data. The subject specific dynamic system is modelled as a stochastic
differential equation (SDE) or difference equation, measurement models are typically multivariate normal factor models.
Linear mixed effects SDE's estimated via maximum likelihood and optimization are the default.
Nonlinearities,  (state dependent parameters) and random effects on all parameters
are possible, using either max likelihood / max a posteriori optimization
(with optional importance sampling) or Stan's Hamiltonian Monte Carlo sampling.
See  <https://github.com/cdriveraus/ctsem/raw/master/vignettes/hierarchicalmanual.pdf>
for details. See <https://osf.io/preprints/psyarxiv/4q9ex_v2> for a detailed tutorial.
Priors may be used. For the conceptual overview of the hierarchical Bayesian
linear SDE approach,
see <https://www.researchgate.net/publication/324093594_Hierarchical_Bayesian_Continuous_Time_Dynamic_Modeling>.
Exogenous inputs may also be included, for an overview of such possibilities see <https://www.researchgate.net/publication/328221807_Understanding_the_Time_Course_of_Interventions_with_Continuous_Time_Dynamic_Models> .
<https://cdriver.netlify.app/> contains some tutorial blog posts.

Charles Driver

ctsem

Continuous Time Structural Equation Modelling

Manuel Voelkle

Han Oud

Trustees of Columbia University 

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