Latent Differential Equation Modeling with Multivariate Multi-Occasion Indicators

Abstract

In the behavioral sciences, there is increasing interest in understanding and characterizing mechanisms of developmental and behavioral processes. Measurements of multiple indicators obtained on multiple occasions on a single individual may show some intraindividual change and intraindividual variability. Process-oriented theories may predict structural patterning in these ideographic measurements. Structural equations modeling techniques can be used to test such theories by fitting confirmatory models of the implied dynamical systems to repeated observations data. The current chapter explores one method for constructing and testing confirmatory latent variable structural models in which the latent constructs (a) evolve continuously over time and (b) have linear relationships between their derivatives. The method appears to generalize well and is expected to be able to be applied to systems well beyond the simple example presented here. The chapter will begin with a rationale for studying behavioral processes from a dynamical systems perspective, introduce latent differential equations confirmatory factor models, present the results of two simulations testing the viability of this model for estimating parameters of a simple linear system, and then discuss future substantive and methodological questions that this line of modeling may address.