ctsem: Continuous Time Structural Equation Modelling
An easily accessible continuous (and discrete) time dynamic modelling package for panel and time series data, reliant upon the OpenMx. package (http://openmx.psyc.virginia.edu/) for computation. Most dynamic modelling approaches to longitudinal data rely on the assumption that time intervals between observations are consistent. When this assumption is adhered to, the data gathering process is necessarily limited to a specific schedule, and when broken, the resulting parameter estimates may be biased and reduced in power. Continuous time models are conceptually similar to vector autoregressive models (thus also the latent change models popularised in a structural equation modelling context), however by explicitly including the length of time between observations, continuous time models are freed from the assumption that measurement intervals are consistent. This allows: data to be gathered irregularly; the elimination of noise and bias due to varying measurement intervals; parsimonious structures for complex dynamics. The application of such a model in this SEM framework allows full-information maximum-likelihood estimates for both N = 1 and N > 1 cases, multiple measured indicators per latent process, and the flexibility to incorporate additional elements, including individual heterogeneity in the latent process and manifest intercepts, and time dependent and independent exogenous covariates. Furthermore, due to the SEM implementation we are able to estimate a random effects model where the impact of time dependent and time independent predictors can be assessed simultaneously, but without the classic problems of random effects models assuming no covariance between unit level effects and predictors.