Introduction to OpenMx XSEM with Application to Dynamical Systems Analysis
OpenMx is a free, open source Extended Structural Equation Modeling (XSEM) package that allows specification and estimation of a wide variety of models from within the R statistical system. The first half of the workshop will introduce OpenMx and the specification of simple latent variable models within R as well as provide an overview of some of its more advanced features such as full information, definition variables, parallelizing, ordinal thresholds, multiple groups, and mixture distributions. The second half of the workshop will present dynamical systems analysis as a continuous-time generalization of time series models using systems of differential equations. We will begin by introducing first order (exponential decay) and second order (cyclic) linear differential equations and two methods for fitting these to time series data: state space forward prediction and time delay embedding. We will then move to coupled differential equations for estimating parameters of dyadic relationships. Finally, we will introduce models for individual differences in parameters of regulation and equilibria as well as time-varying versions of these equations. In preparation, the workshop attendee should have R loaded on her or his laptop and have some familiarity with the use of R. The R packages “OpenMx”, “psych”, and “deSolve” should be installed prior to attending. R scripts and data will be provided so that attendees can gain hands-on practice with OpenMx and data handling techniques for time-delay embedding and state space modeling.