Latent Differential Equation Modeling with Multivariate Multi-Occasion Indicators

A number of models for estimating the coefficients of dynamical systems have been proposed. One is the exact discrete model, another is the latent differences model or proportional change model, and a third is a continuous time manifest variable differential structural model. These models differ from standard growth curve modeling in that they intend to illuminate processes generating individual trajectories over time rather than just estimate an aggregate best trajectory. The current work proposes a novel approach to the modeling of multivariate change by first creating a lagged covariance matrix. Then rather than using factor loadings to estimate average growth characteristics as in other growth curve modeling related methods, confirmatory factor loadings are fixed across the time dimension and freed across the variables dimension, in such a way as to force the factor scores to estimate instantaneous derivatives. Then, the factor covariances are structured as a regression that allows the estimation of parameters of differential equation models of dynamical systems theories proposed to account for the data. Results of a simulation will be presented illustrating strengths and weaknesses of the latent differential equation model. Funding for this work was provided in part by NIH Grant R29 AG14983. Correspondence may be addressed to Steven M. Boker, Department of Psychology, The University of Notre Dame, Notre Dame Indiana 46556, USA; email sent to [email protected]; or browsers pointed to http://www.nd.edu/ ̃ sboker. LATENT DIFFERENTIAL EQUATION MODELING 2