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.