Continuous Time Structural Equation Modelling With R Package ctsem

Note: This paper introduces the frequentist, maximum likelihood based form of ctsem. For the Bayesian implementation, see Hierarchical Bayesian Continuous Time Dynamic Modelling and Introduction to Hierarchical Continuous Time Dynamic Modelling With ctsem. We introduce ctsem (Driver, Oud, and Voelkle 2017), an R package for continuous time structural equation modelling of panel (N > 1) and time series (N = 1) data using full information maximum likelihood. Most dynamic models (e.g., cross-lagged panel models) in the social and behavioural sciences are discrete time models. An assumption of discrete time models is that time intervals between measurements are equal, and that all subjects were assessed at the same intervals. Violations of this assumption are often ignored due to the difficulty of accounting for varying time intervals, therefore parameter estimates can be biased and the time course of effects becomes ambiguous. By using stochastic differential equations to estimate an underlying continuous process, continuous time models allow for any pattern of measurement occasions. By interfacing to OpenMx, ctsem combines the flexible specification of structural equation models with the enhanced data gathering opportunities and improved estimation of continuous time models. ctsem can estimate relationships over time for multiple latent processes, measured by multiple noisy indicators with varying time intervals between observations. Within and between effects are estimated simultaneously by modelling both observed covariates and unobserved heterogeneity. Exogenous shocks with different shapes, group differences, higher order diffusion effects and oscillating processes can all be simply modeled. We first introduce and define continuous time models, then show how to specify and estimate a range of continuous time models using ctsem.