Continuous Time Structural Equation Modelling
Description
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.