ctsem: Continuous Time Structural Equation Modelling

Hierarchical continuous 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), measurement models are typically multivariate normal factor models. Using the original ctsem formulation based on OpenMx, described in the JSS paper "Continuous Time Structural Equation Modeling with R Package ctsem", with updated version as CRAN vignette <https://cran.r-project.org/web/packages/ctsem/vignettes/ctsem.pdf> , linear mixed effects SDE's estimated via maximum likelihood and optimization are possible. Using the Stan based formulation, described in <https://www.researchgate.net/publication/310747987_Introduction_to_Hierarchical_Continuous_Time_Dynamic_Modelling_With_ctsem> , nonlinearity (state dependent parameters) and random effects on all parameters are possible, using either optimization (with optional importance sampling) or Stan's Hamiltonian Monte Carlo sampling. 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> . Stan based functions are not available on 32 bit Windows systems at present.

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